User's Manual

Appendices
September 2008

Prepared for
Office of Air Quality Planning and
Standards
U.S. Environmental Protection Agency
Research Triangle Park, NC
Neal Fann, Project Manager

Prepared by
Abt Associates Inc.
 Table of Contents
Appendix A: Training Courses 9
A.1 ................................................................................................................................... 11
United States
A.1.1 Section 1...........................................................................................................................................................
Data Files Needed for Training 11
A.1.2 Section 2...........................................................................................................................................................
Mapping Introduction 11
.........................................................................................................................................................
Raw Monitor Data 12
Example PM2.5 .........................................................................................................................................
monitor data for 2000 12
Example O3 monitor .........................................................................................................................................
data for 2000 19
Model Data......................................................................................................................................................... 21
Example Air Quality .........................................................................................................................................
Grid File: Baseline PM2.5 22
......................................................................................................................................................... 24
Health Incidence
Example Configuration .........................................................................................................................................
Results File: Control PM2.5 24
Valuation .........................................................................................................................................................
Map 27
Example Valuation .........................................................................................................................................
Results File: Control PM2.5 27
Audit Trail......................................................................................................................................................... 35
Example Health .........................................................................................................................................
Incidence: Control PM2.5 35
Report ......................................................................................................................................................... 37
Example Pooled.........................................................................................................................................
Incidence: Control PM2.5 RIA 37
Additional.........................................................................................................................................................
Mapping Activities 40
A.1.3 Section 3...........................................................................................................................................................
One-Step Analysis 40
.........................................................................................................................................................
Example PM2.5 Control 2020 15/35 National 40
.........................................................................................................................................................
Example PM2.5 Control 2020 14/35 State 53
A.1.4 Section 4...........................................................................................................................................................
Creating Grids 55
Air Quality.........................................................................................................................................................
Model Grids 55
Example: PM2.5.........................................................................................................................................
Control 2020 15/35 Adjusted 55
Example: Control .........................................................................................................................................
PM2.5 RIA 2020 14/35 adjusted 56
......................................................................................................................................................... 56
Monitor Grids
Example: Baseline .........................................................................................................................................
PM2.5 2004 57
......................................................................................................................................................... 60
Monitor Rollback
Example: Control .........................................................................................................................................
PM2.5 2004 Percentage Rollback 60
Example: Control .........................................................................................................................................
PM2.5 2004 Multiple Rollback Techniques 65
A.1.5 Section 5...........................................................................................................................................................
Health Incidence 69
Example: .........................................................................................................................................................
PM2.5 Control 2020 14/35 70
Example: .........................................................................................................................................................
PM2.5 Control 2020 14/35 Adjusted 87
A.1.6 Section 6...........................................................................................................................................................
Aggregation, Pooling, and Valuation 91
Example: .........................................................................................................................................................
PM2.5 Control 2020 14/35 92
Example: .........................................................................................................................................................
PM2.5 Control 2020 14/35 Adjusted 123
Example: .........................................................................................................................................................
Modifying One-Step Analysis Parameters 126
..........................................................................................................................................................
A.1.7 Section 7. Adding New Datasets & Independent Study 128
Example:.........................................................................................................................................................
Adding Datasets for Detroit 129
.........................................................................................................................................................
Independent Study: Detroit Benefits Analysis 145
A.1.8 Answers ..........................................................................................................................................................
to Training Exercises 152

A.2 CityOne ................................................................................................................................... 160

..........................................................................................................................................................
A.2.1 Step 1. Data Files Needed for Training 161
..........................................................................................................................................................
A.2.2 Step 2. Create Air Quality Grids for the Baseline and Control Scenarios 161
..........................................................................................................................................................
A.2.3 Step 3. Specify Configuration Settings 167
..........................................................................................................................................................
A.2.4 Step 4. Select Health Impact Functions 170

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A.2.5 Step 5. Specify Aggregation, Pooling and Valuation

.......................................................................................................................................................... 172
A.2.6 Step 6. Generate Reports
.......................................................................................................................................................... 180
A.2.7 Step 7. View Your Reports
.......................................................................................................................................................... 183
A.2.8 Step 8. Map Your Results
.......................................................................................................................................................... 184

Appendix B: Monitor Rollback Algorithms 191

B.1 Percentage...................................................................................................................................
Rollback 191
B.2 ...................................................................................................................................
Incremental Rollback 192
B.3 Rollback to...................................................................................................................................
a Standard 192
..........................................................................................................................................................
B.3.1 Interday Rollback - Generating Target Metric Values 193
Interday .........................................................................................................................................................
Rollback - Percentage 194
Interday .........................................................................................................................................................
Rollback - Incremental 195
Interday .........................................................................................................................................................
Rollback - Peak Shaving 196
..........................................................................................................................................................
B.3.2 Intraday Rollback - Adjusting Hourly Observations 197
Intraday .........................................................................................................................................................
Rollback - Percentage 198
Example: All Hourly Observations Exceed the Intraday Background
(Single Iteration) ......................................................................................................................................... 199
Example: Some Hourly Observations are Below the Intraday
Background (Multiple .........................................................................................................................................
Iterations Required) 199
..........................................................................................................................................................
B.3.3 Intraday Rollback - Incremental 202
..........................................................................................................................................................
B.3.4 Interday and Intraday Rollback - Quadratic 204
.........................................................................................................................................................
Quadratic Rollback - Interday 205
.........................................................................................................................................................
Quadratic Rollback - Intraday 206

Appendix C: Air Pollution Exposure Estimation Algorithms 207

C.1 ................................................................................................................................... 208
Direct Modeling
C.2 ................................................................................................................................... 208
Closest Monitor
..........................................................................................................................................................
C.2.1 Closest Monitor – Temporal Scaling 209
..........................................................................................................................................................
C.2.2 Closest Monitor – Spatial Scaling 210
..........................................................................................................................................................
C.2.3 Closest Monitor – Temporal and Spatial Scaling 211

C.3 ...................................................................................................................................
Voronoi Neighbor Averaging (VNA) 212
..........................................................................................................................................................
C.3.1 VNA | Temporal Scaling 216
..........................................................................................................................................................
C.3.2 Voronoi Neighbor Averaging (VNA) – Spatial Scaling 220
..........................................................................................................................................................
C.3.3 Voronoi Neighbor Averaging (VNA) – Temporal & Spatial Scaling 221

C.4 ................................................................................................................................... 222

Fixed Radius
C.5 ...................................................................................................................................
Temporal and Spatial Scaling Adjustment Factors 222
..........................................................................................................................................................
C.5.1 Calculation of Scaling Factors 222
.........................................................................................................................................................
Example: PM2.5 Scaling Factors in U.S. Setup 223
.........................................................................................................................................................
Example: Ozone Scaling in U.S. Setup 224
C.6 ................................................................................................................................... 226
Binned Metrics

Appendix D: Deriving Health Impact Functions 227

D.1 Overview ................................................................................................................................... 227
D.2 ...................................................................................................................................
Review Relative Risk and Odds Ratio 228

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 D.3 Linear Model
................................................................................................................................... 229
D.4 Log-linear ...................................................................................................................................
Model 230
D.5 Logistic Model
................................................................................................................................... 232
D.6 Cox proportional Hazards Model
................................................................................................................................... 239

Appendix E: Health Incidence & Prevalence Data in U.S. Setup 241

E.1 Mortality ................................................................................................................................... 241
E.1.1 Mortality ..........................................................................................................................................................
Rates 1996-1998 241
E.1.2 Mortality ..........................................................................................................................................................
Rate Projections 2000-2050 242

E.2 ................................................................................................................................... 243

Hospitalizations
E.3 Emergency...................................................................................................................................
Room Visits for Asthma 245
E.4 ...................................................................................................................................
Nonfatal Heart Attacks 246
E.5 ...................................................................................................................................
School Loss Days 247
E.6 ...................................................................................................................................
Other Acute and Chronic Effects 248
.......................................................................................................................................................... 249
E.6.1 Acute Bronchitis
..........................................................................................................................................................
E.6.2 Chronic Bronchitis Incidence Rate 249
..........................................................................................................................................................
E.6.3 Chronic Bronchitis Prevalence Rate 250
..........................................................................................................................................................
E.6.4 Lower Respiratory Symptoms 250
..........................................................................................................................................................
E.6.5 Minor Restricted Activity Days (MRAD) 250
..........................................................................................................................................................
E.6.6 Work Loss Days 250

E.7 ...................................................................................................................................
Asthma-Related Health Effects 250
..........................................................................................................................................................
E.7.1 Shortness of Breath 251
E.7.2 Wheeze .......................................................................................................................................................... 251
E.7.3 Cough .......................................................................................................................................................... 251
..........................................................................................................................................................
E.7.4 Upper Respiratory Symptoms 252
..........................................................................................................................................................
E.7.5 Asthma Population Estimates 252

Appendix F: Particulate Matter Health Impact Functions in U.S.

Setup 253
F.1 Long-term...................................................................................................................................
Mortality 253
.......................................................................................................................................................... 254
F.1.1 Expert Functions
.........................................................................................................................................................
Parametric Distributions 255
.........................................................................................................................................................
Non-Parametric Distributions 259
.........................................................................................................................................................
Using Expert Functions in BenMAP 260
.........................................................................................................................................................
Distributional Details by Expert 261
Expert A ......................................................................................................................................... 261
Expert B ......................................................................................................................................... 262
Expert C ......................................................................................................................................... 264
Expert D ......................................................................................................................................... 265
Expert E ......................................................................................................................................... 266
Expert F ......................................................................................................................................... 267
Expert G ......................................................................................................................................... 269
Expert H ......................................................................................................................................... 270
Expert I ......................................................................................................................................... 271

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Expert J ......................................................................................................................................... 272

Expert K ......................................................................................................................................... 273
Expert L ......................................................................................................................................... 274
F.1.2 Laden et ..........................................................................................................................................................
al (2006) 276
F.1.3 Pope et al (2002)
.......................................................................................................................................................... 276
F.1.4 Woodruff..........................................................................................................................................................
et al (1997) 277
F.1.5 Woodruff..........................................................................................................................................................
et al (2006) 278

F.2 ...................................................................................................................................
Chronic / Severe Illness 278
F.2.1 Abbey et ..........................................................................................................................................................
al (1995b) 279
F.2.2 Peters et..........................................................................................................................................................
al (2001) 279

F.3 ................................................................................................................................... 280

Hospitalizations
F.3.1 Ito (2003).......................................................................................................................................................... 282
..........................................................................................................................................................
F.3.2 Moolgavkar (2000a), Chronic Lung 283
..........................................................................................................................................................
F.3.3 Moolgavkar (2000b), Cardiovascular 284
..........................................................................................................................................................
F.3.4 Moolgavkar (2003) 285
F.3.5 Sheppard..........................................................................................................................................................
(2003) 285

F.4 Emergency...................................................................................................................................
Room Visits 286
F.4.1 Norris et ..........................................................................................................................................................
al (1999) 286

F.5 ................................................................................................................................... 287

Minor Effects
..........................................................................................................................................................
F.5.1 Dockery et al (1996) 287
.......................................................................................................................................................... 288
F.5.2 Ostro (1987)
..........................................................................................................................................................
F.5.3 Ostro and Rothschild (1989) 289
F.5.4 Schwartz..........................................................................................................................................................
and Neas (2000) 291

F.6 ...................................................................................................................................
Asthma-Related Effects 291
..........................................................................................................................................................
F.6.1 Ostro et al (2001) 292
..........................................................................................................................................................
F.6.2 Pope et al (1991) 293
..........................................................................................................................................................
F.6.3 Vedal et al (1998) 294

F.7 Calculating...................................................................................................................................
Threshold-Adjusted Functions 295

Appendix G: Ozone Health Impact Functions in U.S. Setup 300

G.1 Short-term...................................................................................................................................
Mortality 300
G.1.1 Bell et al ..........................................................................................................................................................
(2004) 301
G.1.2 Bell et al ..........................................................................................................................................................
(2005) 302
G.1.3 Huang et..........................................................................................................................................................
al (2005) 302
..........................................................................................................................................................
G.1.4 Levy et al, 2005 303
..........................................................................................................................................................
G.1.5 Ito and Thurston (1996) 304
.......................................................................................................................................................... 304
G.1.6 Ito et al (2005)
..........................................................................................................................................................
G.1.7 Moolgavkar et al (1995) 305
G.1.8 Samet et..........................................................................................................................................................
al (1997) 305
G.1.9 Schwartz..........................................................................................................................................................
(2005) 306

G.2 ................................................................................................................................... 306

Hospital Admissions
G.2.1 Burnett et
..........................................................................................................................................................
al (2001) 307
..........................................................................................................................................................
G.2.2 Moolgavkar et al (1997) 308
G.2.3 Schwartz..........................................................................................................................................................
(1994a) 308
G.2.4 Schwartz..........................................................................................................................................................
(1994b) 309

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 G.2.5 Schwartz..........................................................................................................................................................
(1995) 309

G.3 Emergency...................................................................................................................................
Room Visits 311
G.3.1 Jaffe et al..........................................................................................................................................................
(2003) 311
G.3.2 Peel et al..........................................................................................................................................................
(2005) 311
.......................................................................................................................................................... 312
G.3.3 Stieb (1996)
G.3.4 Wilson et..........................................................................................................................................................
al (2005) 313

G.4 ................................................................................................................................... 314

Minor Effects
..........................................................................................................................................................
G.4.1 Chen et al (2000) 314
..........................................................................................................................................................
G.4.2 Crocker and Horst (1981) 316
G.4.3 Gilliland ..........................................................................................................................................................
et al (2001) 316
..........................................................................................................................................................
G.4.4 Ostro and Rothschild (1989) 318

G.5 Converting...................................................................................................................................
Functions to 8-Hour Daily Maximum Metric 319

Appendix H: Health Valuation Functions in U.S. Setup 323

H.1 Mortality ................................................................................................................................... 323
..........................................................................................................................................................
H.1.1 Value of a Statistical Life Based on 26 Studies 324
..........................................................................................................................................................
H.1.2 Value of a Statistical Life Based on Selected Studies 324

H.2 ................................................................................................................................... 325

Chronic Illness
.......................................................................................................................................................... 325
H.2.1 Chronic Bronchitis
.........................................................................................................................................................
Unit Value Based on Two Studies of WTP 325
.........................................................................................................................................................
Alternative Cost of Illness Estimates 327
..........................................................................................................................................................
H.2.2 Chronic Bronchitis Reversals 328
.......................................................................................................................................................... 328
H.2.3 Chronic Asthma
H.2.4 Non-Fatal..........................................................................................................................................................
Myocardial Infarctions (Heart Attacks) 329

H.3 ...................................................................................................................................
Hospital Admissions & Emergency Room Visits 331
H.3.1 Hospital ..........................................................................................................................................................
Admissions 331
..........................................................................................................................................................
H.3.2 Emergency Room Visits for Asthma 334

H.4 ...................................................................................................................................
Acute Symptoms and Illness Not Requiring Hospitalization 334
..........................................................................................................................................................
H.4.1 Acute Bronchitis in Children 336
..........................................................................................................................................................
H.4.2 Upper Respiratory Symptoms (URS) in Children 337
..........................................................................................................................................................
H.4.3 Lower Respiratory Symptoms (LRS) in Children 338
H.4.4 Any of 19..........................................................................................................................................................
Respiratory Symptoms 339
..........................................................................................................................................................
H.4.5 Work Loss Days (WLDs) 340
..........................................................................................................................................................
H.4.6 Minor Restricted Activity Days (MRADs) 340
.......................................................................................................................................................... 341
H.4.7 Asthma Exacerbation
..........................................................................................................................................................
H.4.8 School Loss Days 341

Appendix I: Population & Other Data in U.S. Setup 343

I.1 Population...................................................................................................................................
Data in U.S. Setup 343
..........................................................................................................................................................
I.1.1 How BenMAP Forecasts Population 344
..........................................................................................................................................................
I.1.2 Data Needed for Forecasting 346
.........................................................................................................................................................
Block-Level Census 2000 346
.........................................................................................................................................................
County-Level Forecasts 350
I.1.3 PopGrid .......................................................................................................................................................... 351

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How to Use PopGrid

......................................................................................................................................................... 351
PopGrid.........................................................................................................................................................
Output 356
I.2 Monitor Data in U.S. Setup
................................................................................................................................... 358
I.2.1 Data Processing
.......................................................................................................................................................... 360
I.2.2 Output Files
.......................................................................................................................................................... 361

Appendix J: Uncertainty & Pooling 362

J.1 Uncertainty................................................................................................................................... 362
..........................................................................................................................................................
J.1.1 Characterization of Uncertainty Surrounding Incidence Changes 362
..........................................................................................................................................................
J.1.2 Characterization of Uncertainty Surrounding Dollar Benefits 363
..........................................................................................................................................................
J.1.3 Characterization of Uncertainty Surrounding QALY Estimates 364

J.2 Pooling ................................................................................................................................... 364

J.2.1 Weights ..........................................................................................................................................................
Used for Pooling 365
.........................................................................................................................................................
Subjective Weights 365
.........................................................................................................................................................
Automatically Generated Weights 366
.........................................................................................................................................................
Fixed-Effect Weights 366
Random-.........................................................................................................................................................
/ Fixed-Effect Weights 367
J.2.2 Mechanics..........................................................................................................................................................
of Pooling in BenMAP 370
J.2.3 Summing..........................................................................................................................................................
Distributions 371
..........................................................................................................................................................
J.2.4 Subtracting Distributions 372

Appendix K: Command Line BenMAP 374

K.1 Overview ................................................................................................................................... 374
K.2 Variables ................................................................................................................................... 374
K.3 Commands................................................................................................................................... 375
..........................................................................................................................................................
K.3.1 Set Active Setup 375
.......................................................................................................................................................... 375
K.3.2 Create AQG
......................................................................................................................................................... 376
Model Direct
......................................................................................................................................................... 377
Monitor Direct
.........................................................................................................................................................
Monitor Model Relative 379
......................................................................................................................................................... 379
Monitor Rollback
K.3.3 Run CFG.......................................................................................................................................................... 380
K.3.4 Run APV.......................................................................................................................................................... 381
K.3.5 Generate..........................................................................................................................................................
Report 382
......................................................................................................................................................... 382
Audit Trail
......................................................................................................................................................... 382
CFGR Report
......................................................................................................................................................... 383
APVR Report
K.4 Example 1 ................................................................................................................................... 383
K.5 Example 2 ................................................................................................................................... 385

Appendix L: Function Editor 387

L.1 ...................................................................................................................................
User Defined Variables 387
L.2 The Script ...................................................................................................................................
Language 388

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 L.3 Operands ................................................................................................................................... 389
L.4 Operations................................................................................................................................... 389
L.5 Arithmetic ...................................................................................................................................
Functions 390
L.6 Aggregate ...................................................................................................................................
Functions 391

References 392

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 Appendix A: Training Courses

Appendix A: Training Courses

BenMAP is intended primarily as a tool for estimating the health impacts, and associated
economic values, associated with changes in ambient air pollution. It accomplishes this by
running health impact functions, which relate a change in the concentration of a pollutant
to a change in the incidence of a health endpoint. Inputs to health impact functions
typically include:
(a) the change in ambient air pollution level,
(b) a health effect estimate,
(c) the background incidence rate of the health endpoint, and
(d) the exposed population.
For example, in the case of a premature mortality health impact function, we might have
the following:
Mortality Change = Air Pollution Change × Mortality Effect Estimate

× Mortality Incidence × Exposed Population

where each term on the right is defined as follows:

 Air Pollution Change. The air quality change is calculated as the difference between the starting
air pollution level, also called the baseline, and the air pollution level after some change, such as
that caused by a regulation. In the case of particulate matter, this is typically estimated in
micrograms per cubic meter (µg/m3).
 Mortality Effect Estimate. The mortality effect estimate is an estimate of the percentage change
in mortality due to a one unit change in ambient air pollution. Epidemiological studies provide a
good source for effect estimates.
 Mortality Incidence. The mortality incidence rate is an estimate of the average number of people
that die in a given population over a given period of time. For example, the mortality incidence
rate might be the probability that a person will die in a given year. Mortality incidence rates and
other health data are typically collected by each country’s government. In addition, the World
Health Organization is a good source for data.
 Exposed Population. The exposed population is the number of people affected by the air
pollution reduction. The government census office is a good source for this information. In
addition, private companies may collect this information and offer it for sale.
BenMAP also calculates the economic value of health impacts. For example, after the
calculation of the mortality change, you can value the premature deaths avoided by
multiplying the change in mortality by an estimate of the value of a statistical life:
Value Mortality = Mortality Change × Value of Statistical Life

where the rightmost term is defined as follows:

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 Appendix A: Training Courses

 Value of Statistical Life. The value of a statistical life is the economic value placed on
eliminating the risk of one premature death.

Figure 1-1 provides the overall schematic of BenMAP, and the various major steps
involved in using it. This figure also highlights that BenMAP does not have air quality
modeling capabilities, and instead relies on modeling and monitoring inputs.

Figure 1-1. Overall schematic of BenMAP.

BenMAP also serves as a Geographic Information System (GIS), allowing users to create,
utilize, and visualize maps of air pollution, population, incidence rates, incidence rate
changes, economic valuations, and other types of data. BenMAP can thus be used for a
variety of purposes, including:
 Generating population/community level ambient pollution exposure maps;
 Comparing benefits associated with regulatory programs;
 Estimating health impacts and costs of existing air pollution concentrations;
 Estimating health benefits of alternative ambient air quality standards; and
 Performing sensitivity analyses of health or valuation functions, or of other inputs.

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 Appendix A: Training Courses

A wide range of people can use BenMAP, including scientists, policy analysts, and
decision makers. Advanced users can explore a broad array of options, such as using the
map querying features and exploring the impacts of different health impact and valuation
functions.

A.1 United States

This training is intended for a beginning user of BenMAP that wants to use the U.S. setup
that comes with BenMAP. The training manual is organized into seven sections.
 Section 1. Data Files Needed. This provides a list of the files that you will need for this training
and where you can get them.
 Section 2. Mapping. This module is designed to help you become comfortable using BenMAP
by analyzing the various types of data that we will use throughout this course.
 Section 3. One-step Analyses. You will create health incidence and valuation results. This
one-step analysis uses pre-defined health incidence and economic valuation configurations,
which you can combine with your own baseline and control air quality grids.
 Section 4. Creating Grids. In this section, you will create air quality grids (aqg) from both air
quality (AQ) model data and from monitor data. The overall goal will be to produce baseline
and control air quality grids for later estimations of health incidence and valuation.
 Section 5. Health Incidence Estimation. In this section, you will modify an existing health
incidence configuration and use it to create new health incidence results. You will create two
separate sets of health incidence results based on the same configuration and two similar, but
distinct, control strategies.
 Section 6. Aggregation, Valuation, and Pooling. In this section, you will create an aggregation,
pooling, and valuation (APV) configuration and use it to produce new valuation results. You
will create two separate sets of valuation results based on the same configuration and two
similar, but distinct, control strategies.
 Section 7. Adding New Datasets and an Independent Case Study. In this section, you will add
new datasets to BenMAP and run a local-scale benefit analysis in Detroit, Michigan.
We have broken down each of the above sections into various modules, and each module
provides a context section, a module goal, and one or more example BenMAP
applications. In addition, there is a section with answers to embedded exercise questions for
Sections 2 through 7.

A.1.1 Section 1. Data Files Needed for Training

A range of data files are needed for this training and can be accessed at the BenMAP
website: http://www.epa.gov/air/benmap/.

A.1.2 Section 2. Mapping Introduction

This module is designed to help you become comfortable using BenMAP by analyzing the
various types of data that you will use throughout this course. In this lesson, you will focus
on using BenMAP's GIS tool to view maps of air quality data (file names ending in .aqg),

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health incidence results (ending in .cfgr), and economic valuation results (ending in .apvr).

A.1.2.1 Raw Monitor Data

Several years of recent monitor data for Ozone, PM10 and PM2.5 have been pre-loaded
into the BenMAP database. These data are derived from the extensive network of
monitoring sites throughout the U.S. For the PM (particulate matter) data, most of the
monitor data is recorded on a daily basis. The ozone measurements are recorded on an
hourly basis. When displaying the data for a pollutant, you can display different averaging
techniques, typically referred to as air quality metrics.

A.1.2.1.1 Example PM2.5 monitor data for 2000

Goal: To start learning about BenMAP and the GIS tool, and to explore PM2.5 monitor
data for the year 2000. You will be working with monitor values preloaded into BenMAP’s
underlying database
(a) Open BenMAP by clicking on the desktop icon or by choosing “Launch BenMAP 3” from the
Window's Start menu. This will bring up the main BenMAP window (Figure 2-1).

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Figure 2-1. Main BenMAP window.

(b) From the Tools menu, choose “GIS/Mapping” (Figure 2-2).

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Figure 2-2. Opening the GIS tool.

This will open the BenMAP GIS window (an example is shown later in Figure 2-4). At the
top of the GIS window, you will see a series of buttons, described below. Note that in this
terminology a layer is a map, and “active layer” means the topmost map in the GIS
window. You can have multiple maps layered on top of each other in the GIS tool.

Open a File

Save active layer

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Zoom to full extent

Zoom in, Zoom out

Select a region to zoom into

Drag map

Display info - Displays information for all variables in active layer of that cell

Build queries to limit data displayed (e.g. values > 80 ppb)

Calculate layer statistics of the active layer

(c)Click on the Open a File button and choose “Monitors”. In the Select Monitors window
(Figure 2-3), set the pollutant to “PM2.5”, and under the library tab set the dataset to
“EPA Standard Monitors” and year to “2000”.
Although you will not use the Advanced button in this module, we could use it to further
limit the monitors that we would display based on location, state, or other monitor criteria.

Figure 2-3. Select Monitors window.

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 Appendix A: Training Courses

(d) Click the OK button. This will bring up the monitor locations on the BenMAP GIS
window (Figure 2-4).

Figure 2-4. PM2.5 monitors locations.

(e) Double-click on the “PM2.5, 2000” layer. This will open the Display Options window
(Figure 2-5).

Set the variable to “QuarterlyMean”, which represents the average of the four quarterly
means (i.e., the annual average).
Set start and end sizes to “100”; this is the size of the monitor points.
Do not change the other seven fields in the window. The min and max values define your
range. You can edit this to narrow in on a specific range. The start and end color allow
you to pick the colors of the monitor points in your range. The default size and default
color are for areas that are outside your range. The decimal digits are the number of
decimal digits displayed.

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Figure 2-5. Display Options window.

Background: The main PM metrics are D24HourMean (the daily value) and
QuarterlyMean (the mean of all days within an individual yearly quarter). The
GIS tool does not display the monitor values for particular day or quarter; rather,
the GIS tool will show seasonal averages of these variables. For PM, the default
"season" is typically the full year. This will likely cause some confusion. When
we display D24HourMean, we are actually displaying the average of the 365 days
of data, and when we display QuarterlyMean we are showing the average of the 4
quarterly means. In short, both these variables should be thought of as more akin
to an annual average. Note: the definition of metrics and seasons can be changed
(discussed in Lab 7).

(f) After clicking OK, you will get a map of the annually averaged PM2.5 values at all the
monitor locations. To gain a better sense of the monitor locations, use the
"-- Reference Layer --" drop down menu in the top right corner of the BenMAP GIS
window to select the "County" overlay (Figure 2-6). The reference layer overlays a
specific grid type (e.g. county, state, CMAQ) on top of your data layer. It provides
geographic context to your data layer.

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Figure 2-6. PM2.5 monitor locations overlaid with county boundaries.

(g)Now overlay a State reference layer. Experiment with zooming in and out of the map
(using the toolbar). Try out some of the other buttons, including Display info and
Create layer statistics. Note: the values are in micrograms per cubic meter (µg/m3).

(h)Exercise (2.1): What are the D24HourMean, QuarterlyMean, and lat/lon of the monitor
at the northern tip of Maine? Hint: Use the Display info and Zoom buttons.
Answer:

(i) Use the Build queries button to bring up the Build Query window (Figure 2-7). Use the
fields list and mathematical operator buttons or simply type in that window to create a
query that limits the monitors to those with QuarterlyMean less than 10 micrograms per
cubic meter (µg/m3). Click OK or Execute.

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Figure 2-7. Build Query window.

Tip: You construct a query in the query text field (indicated by red arrow above).
You can type in the field name (or double-click it, e.g. "QuarterlyMean"), the values,
and the operators (e.g. ">" or "=") in the query text field. To remove the query (i.e. see
all your monitors), delete the query text field and click OK (or Execute). Execute is
the same as OK except that it keeps the Build Query window open.

(j) Exercise (2.2): What states have monitors with QuarterlyMean values >20 µg/m3?

Answer:

(k)Remove the query so that you can see all the monitors. Do not close the BenMAP GIS
window, because it will be used again in the next example.
A.1.2.1.2 Example O3 monitor data for 2000

The goal of this task is to learn about layers in the GIS tool and to explore the O3 monitor
data for 2000.
(a) Using the same GIS window, open a second dataset by clicking on Open a File and selecting
"Monitors". This time, set the pollutant to “Ozone“. As before, set the year to “2000”. Click
OK.
(b) Uncheck “PM2.5” in the Layers panel by clicking in the checkbox. The PM2.5 monitors
should disappear.
(c) Double-click on the “Ozone, 2000” layer to open up the Display Options window for that layer
(Figure 2-8). For the variable, select “D8HourMax”, which is the average of the 8 hr maximum

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window for each day in the ozone season.

Change the "Start Size" and "End Size" to “100” and colors from dark blue (Start Color) to
light blue (End Color). In other words, we are differentiating the ozone monitors from the
PM2.5 monitors by having them range from dark to light blue. Click OK. Note: these
values are the concentrations of ozone in parts per billion (ppb).

Figure 2-8. Display Options window values described in step (c) above.

Background: There are a series of ozone metrics: D1HourMax (the maximum 1 hour
value in a day), D24HourMean (daily mean), D5HourMean (daily mean of hours 10am -
2pm), D8HourMax (the greatest mean for any 8 hour window in a day), and
D8HourMean (daily mean of hours 9am - 4pm). Again, the GIS tool does not display
the monitor values for any particular day. It calculates and displays a seasonal average
for each of the above metrics. The default ozone season is from May 1st through
September 30th. For example, the D1HourMax is calculated by adding up the maximum
value for that monitor for each day in the season and then dividing by the number of days
in the ozone season. Note: the definition of metrics and seasons can be changed
(discussed in Lab 7).

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(d)Recheck “PM2.5, 2000” in the Layers panel. You should now see both the O3 and PM2.5 data.

In the Layers panel, switch the order of the layers by right-clicking on the "PM2.5, 2000"
layer and select "Move up" in the pop-up window. The active layer is always the topmost
layer in the Layers panel. Note: Only the active layer is used in getting information or
performing queries.
(e)Exercise (2.3): What are the maximum and minimum QuarterlyMean values for the PM2.5
monitors? Hint: use the Layer Statistics button and PM2.5 should be the active layer.

Answer:

(f) Exercise (2.4): What are the maximum and minimum D8HourMax values for the ozone
monitors? Which states have a D8HourMax greater than 60 parts per billion (ppb)?
Hint: ozone should be the active layer. When performing the query, you might want to
uncheck PM2.5 so that it is easier to see the ozone monitors.

Answer:

(g)After you are done, click Close at the bottom right of the GIS window. This completes
the “Raw Monitor Data” module for this lab.
A.1.2.2 Model Data
You will use CMAQ (an AQ model that simulates the chemistry and movement of various
pollutants) outputs from the PM2.5 Regulatory Impact Analysis (RIA) for this training
module. Unlike the monitor data visualized in the previous module, the model data has
values that are on a regular grid and cover the whole area of the map. The RIA model data
is a forecast of the air quality (AQ) for the year 2020. We will focus on a baseline scenario
(think of this as "business-as-usual") and two control scenarios (in these cases additional
regulations have been applied to emission source, resulting in generally lower pollution
levels).
We recommend that you are detailed and consistent in naming your BenMAP files. In this
lab, the file name includes references to the annual PM2.5 NAAQS (National Ambient Air
Quality Standards) and a daily PM2.5 NAAQS. For example, the file
“Baseline_PM25_RIA_2020_cmaq_grid_15_Annual_65_Daily.aqg” refers to the baseline
model run on the CMAQ grid type in which most annual PM2.5 values are below 15
µg/m3 and most daily values are below 65 µg/m3. For the rest of the modules, we will use
the shorthand “Baseline PM2.5 RIA 2020 15/65” to refer to the baseline scenario with 15
µg/m3 annual NAAQS and 65 µg/m3 daily NAAQS. An equivalent shorthand will be used

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for the control scenarios.

A.1.2.2.1 Example Air Quality Grid File: Baseline PM2.5

The goal of this example is to look at model data using the BenMAP GIS tool and to learn
about the differences between political-type grids and CMAQ-type grids.
(a)From the main BenMAP window, open a new GIS window by choosing “GIS/Mapping” in the
Tools menu.
(b)Click on the Open a File button, then choose “Air Quality Grid (*.aqg)“. Under the “Air
Quality Grids” folder in the Open an Air Quality Grid window, navigate to the folder
“PM25_RIA”, select the file named
“Baseline_PM25_RIA_2020_cmaq_grid_15_Annual_65_Daily.aqg”, and click Open.
(c)In the GIS window that appears, double-click on the
“Baseline_PM25_RIA_2020_cmaq_grid_15_Annual_65_Daily.aqg” layer to open the Display
Options window.
In that window, set the variable to “QuarterlyMean”. This will cause the annual average data to be
displayed.
Also uncheck the grid outline; this is usually preferred, because the window often looks messy
with both the data and the grid outlines displayed. Click OK in the Display Options window.
Finally, use the drop-down menu near the upper right corner of the GIS window to overlay a
"State" reference layer (Figure 2-9).

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Figure 2-9. PM2.5 model output overlaid with state boundaries.

(d)Exercise (2.5): Use the Zoom in button to zoom into a state border region until you can
see the model grid cells. Do the grid cells align with the state boundaries? In other
words, do the model grid cells perfectly fit within the political boundaries?

Answer:

(e)Exercise (2.6): What states are out of attainment in this baseline model scenario? States
that are out of attainment are those that have at least one QuarterlyMean grid cell value
above 15 µg/m3.

Answer:

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(f) Try overlaying the "CMAQ 36km Nation Overlap” overlay reference layer. Zoom into a
small region. Note how the model values line-up with the reference layer.

(g)When you are done exploring, close the GIS window by clicking Close. This completes
the “Model Data” module.
A.1.2.3 Health Incidence
To produce health incidence results, the first step is to calculate the change in pollution
concentrations that would be produced by the application of a given set of emissions
controls. The concentration change in a pollutant (say, PM2.5) is the difference (the
“delta”) between the modeling results from a control scenario and the modeling results
from the baseline scenario. These deltas and a gridded population dataset are then used in
concentration-response (C-R) functions to calculate the change in health incidence that
would result from this change in pollution. These C-R functions are based on
epidemiological studies and can be selected by the user (see Lab 5). Typically, these health
incidence results show the number of avoided health incidence (e.g. the decrease in
asthma, bronchitis, mortality, etc) due to a decrease in pollution.
In the rest of this module, we refer to the health incidence results via the shorthand
versions of their control scenario names (as explained in Section 2.2.1). Also recall that the
abbreviation “cfgr” refers to health incidence results. Note: we don't actually go through
the procedure of creating these health incidence results in this lab (see Labs 3 and 5);
rather, we are just looking at the pre-computed results.

A.1.2.3.1 Example Configuration Results File: Control PM2.5

The goal of this exercise is to use the GIS tool to explore the reductions in health incidence
that would be due to the reductions in PM2.5 caused by the RIA control scenario. In
particular, we will look at reductions in mortality, acute respiratory symptoms, chronic
bronchitis, and emergency room (ER) visits.
(a)From the main BenMAP window, open a new GIS window.
(b)Click on the Open a File button, then select “Configuration Results (*.cfgr)”. Under the
"Configuration Results" folder, select the file named
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily.cfgr”. Click Open.
(c)This will bring up an additional window Edit GIS Field Names. In the last column of
this window, change the names of the fields to more meaningful names, by highlighting
the contents of each of the four cells and typing in “Mortality”, “ChronBronc”, “ER”,
and “AcutResp” (Figure 2-10). Note: the GIS field names cannot exceed 10 characters
in length.
Before clicking OK, do the next exercise.

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Figure 2-10. Edit GIS Field Names window.

(d)Exercise (2.7): Look at the various columns in the Edit GIS Field Names window
(information and variables used in the C-R functions, e.g. "Pollutant" and "Author").
For what age range are we calculating the change in mortality? When finished with this
exercise, click OK.

Answer:

(e)In the BenMAP GIS window, display mortality data, uncheck the CMAQ grid outline,
and overlay a state reference layer. Note: these values are number of deaths prevented
by the control scenario.
(f) Exercise (2.8): Under this control strategy, which states had more than 25 avoided
deaths?

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Answer:

(g)Display acute respiratory symptoms, "AcutResp".

(h)Exercise (2.9): How do the number of acute respiratory incidences avoided compare to
the number of premature deaths avoided? Hint: use the Display info or Calculate layer
statistics buttons.

Answer:

(i) Display and explore the GIS fields DELTAX and POPX. Here, "X" refers to a number.

Background: For each health incidence result, there is a corresponding population

and delta variable. For example, DELTA0 and POP0 are the PM2.5 delta and the
population that mortality was calculated from. The number comes from the initial
result names. For example, Result0 (mortality) matches DELTA0 and POP0;
Result1 (ChronBronc) matches DELTA1 and POP1; etc. Note, the population of
interest is determined by the C-R function and is not necessarily equivalent
between the various health incidence results (e.g. different age ranges, gender, or
ethnic groups).

(j) Exercise (2.10): Compare the delta and mortality values. Look at the spatial pattern of
these two variables. Why do the delta and the mortality values not exactly correlate?

Answer:

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(k)Close the GIS window. This completes the “Health Incidence” module.

A.1.2.4 Valuation Map

For the purposes of this course, “valuation results” are the economic benefits of avoiding
the previously calculated changes in health incidence. These are the monetized benefits of
the avoided premature mortalities and morbidities (i.e., non-fatal health effects), which are
the two measures we discuss in this module. These valuation results are calculated by
taking the estimates of health incidence avoided and applying valuation functions to
express those incidences in dollar terms. For example, the economic value of premature
mortality avoided has a monetary value that is expressed as a distribution. If you calculate
a mean value of that distribution, you can then multiply that mean value by the number of
mortalities avoided (due to your control strategy), resulting in an estimate of the economic
benefit of avoiding those premature mortalities.
The valuation results (and the underlying health incidence) are typically aggregated from
the CMAQ or county grid to State or National totals. The results (health incidence and
valuation) are often pooled. Pooling are methods for combining similar health incidence
or valuation results. For example, if you have two different studies (valuation functions)
for calculating the monetized benefit of avoided ER visits, you would "pool" together these
two results to create a single valuation for ER (see Lab 6).
As in the “Health Incidence” module just completed, here we refer to the valuation results
via the shorthand versions of their control scenario names. (Recall that the abbreviation
“apvr” refers to economic valuation results.)

A.1.2.4.1 Example Valuation Results File: Control PM2.5

The goal of this exercise is to use the GIS tool to explore the economic benefits of the
above reductions in health incidence due to this control scenario. In particular, we will
look at the cost savings due to reductions in mortality and in morbidity. We will also
compare the economic benefits to the pooled and aggregated health incidence results.
(a)Open a new GIS window, click on the Open a File button, select “APV Configuration
Results (*.apvr)”, then select “Pooled Valuation Results” (Figure 2-11).

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Figure 2-11. Selecting the “Pooled Valuation Results” file.

Tip: There are a lot of options for what type of data to map with apvr files. Typically we use
"Pooled Incidence Results" (aggregated and pooled health incidence) or "Pooled Valuation
Results" (aggregated and pooled valuations).

(b)In the Open an APV Configuration Results File window, under the folder
"Configuration Results", select the file named
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_state.apvr”. Click Open.
(c)In the Edit GIS Field Names window that appears, edit the GIS field names. Use the
same four field names as in the previous module (“Mortality”, “ChronBronc”, “ER”,
and “AcutResp”).
(d)After clicking OK, a Valuation Sums Layer window (Figure 2-12) will appear. This
window is the starting point for adding together various valuation results to get total
values for mortality and morbidity. We will view these summed results in the GIS
window.

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Figure 2-12. Valuation Sums Layer window.

(1)To create a morbidity layer, click on the Add Sum button. An Add Valuation Sum
window will appear (Figure 2-13).
In the Include in Total column at the right, check all the health incidences that will be
summed together to make morbidity (chronic bronchitis, ER visits, and acute
respiratory symptoms).
At the bottom left corner of this window, type “Morbidity” into the Valuation Sum
Identifier field. Leave the Summation Type field as “Dependent“.

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Figure 2-13. An Add Valuation Sum window showing the settings

for creating the morbidity layer.

(2)Click OK, which will return us to the Valuation Sums Layer window. In the GIS
Field Name column, highlight the cell and type in “Morbidity” (Figure 2-14).

Do not click OK in the Valuation Sums Layer window. Continue on to

step (3).

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Figure 2-14. Valuation Sums Layer window after the

morbidity sum identifier and GIS field name have been added.

(3)Next, add mortality to the Valuation Sums Layer window by clicking on the Add
Sum button again, then checking “Mortality” in the Add Valuation Sum window,
typing “Mortality” into the Valuation Sum Identifier field, and clicking OK.

Return to the Valuation Sums Layer window and enter “Mortality” into
the GIS Field Name cell in the mortality row that has been added to that
window. Finally, click OK to close the window.

(e)In the Layers area of the GIS window, you will see that two layers have been added:
“Pooled Valuation Results Sums” and
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_state.apvr”.

Double click on the "Pooled Valuation Results Sums" layer and set the display
variable to "Mortality" (Figure 2-15).

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Figure 2-15. Economic benefit due to the reduction in deaths.

(f) Display the morbidity valuation data. Use the Display info button to explore some of
the morbidity and mortality valuation values for specific states. Note: these benefits are
in dollars.

(g)In the same GIS window, we will now overlay a pooled and aggregated health incidence
layer for the same control scenario. We can use this layer to see the total number of
prevented health incidences in each State.

(1)Use the Open a File button, select “APV Configuration Results (*.apvr)”, then
choose “Pooled Incidence Results” (Figure 2-16).

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Figure 2-16. Selecting the “Pooled Incidence Results” file.

(2)Under the “Configuration Results” folder, open the same file:

“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_state.apvr”.
(3)In the Edit GIS Field Names window, edit the field names as before, then close
that window.
Double click the top layer,
"Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_state.apvr (Pooled
Incidence Results)" and set the variable to "Mortality".
(4)We should now have the pooled and aggregated mortality incidence (number of
deaths avoided per state) overlaying the pooled and aggregated mortality valuation
(economic benefits per state) (Figure 2-17).

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Figure 2-17. State mortality totals overlaying state economic benefit totals.

(h)Exercise (2.11): Compare the number of incidences for mortality and acute respiratory
symptoms (one of the components of morbidity). What are the values for Washington
State? Now compare the economic valuations for mortality and morbidity in the same
state. What values did you get? What does contrasting the incidence numbers with the
valuation numbers tell us about the valuation function for mortality versus the one for
morbidity? Hint: you may need to switch the active layer by right clicking on the layer
of interest in the Layers panel.

Answer:

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(i) Close the GIS window. This completes the “Valuation Map” module.
A.1.2.5 Audit Trail
The audit trail is a tool for looking at the headers of files created through BenMAP. In
other words, it allows you to explore the metadata (the settings, inputs, and/or configura­
tions) for a BenMAP file. An audit trail is a useful feature to check your work and see
which options you selected in your analysis. You can use the audit trail to look at all of
BenMAP's output files, including air quality grids, configuration files, and results files.

A.1.2.5.1 Example Health Incidence: Control PM2.5

The goal of this exercise is to use the audit trail tool to explore the metadata of files created
in BenMAP.
(a)In the main BenMAP window, click on the Report graphic that is at the bottom of the
right-hand panel (under “Custom Analysis”). In the Select Report Type window that
appears, select “Audit Trail Reports” (Figure 2-18). Click OK.

Figure 2-18. Select Report Type window.

(b)In the Open window, under the “Configuration Results” folder, open the file
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily.cfgr”.
(c)An Audit Trail Report window will open that contains a tree structure giving the audit
trail information (Figure 2-19). You can expand any section of the tree by clicking on
the plus sign next to the heading, or collapse a section by clicking on the minus sign.

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Figure 2-19. Audit Trail Report window.

(d)Exercise (2.12): What population year was used in this study? What is the name of the
grid type?

Answer:

(e)Exercise (2.13): What is the age range for the emergency room (ER) CR function, and
who was the author of the study?

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Answer:

(f) Export the audit trail. Click the Export button. In the Save as window, save the file
under the "Reports" folder as
"Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily". This is a ".txt" file that
can be easily opened in Microsoft Word or Notepad.
Answer:

(g)Close the Audit Trail Report window by clicking OK. This completes the “Audit Trail”
module.

A.1.2.6 Report
Reports are a good way to summarize your BenMAP results in a table (columns and rows)
and export them to be used in Excel or some other data analysis tool.

A.1.2.6.1 Example Pooled Incidence: Control PM2.5 RIA

The goal of this exercise is to create reports from BenMAP results. In particular, to look at
the pooled and aggregated health incidence results from the 2020 RIA control scenario.
(a)In the main BenMAP window, click on the Report graphic under “Custom Analysis”.
In the Select Report Type window, select the “Incidence and Valuation Results” item.
In the Open window, under the “Configuration Results” folder, open the file
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_state.apvr”.
(b) In the Choose a Result Type window that appears (Figure 2-20), select “Pooled
Incidence Results”. Click OK.

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Figure 2-20. Choose a Result Type window.

(c)In the Configuration Results Report window that appears (Figure 2-21), click on the
checkbox for “Endpoint Group” in the “Pooled C-R Function Fields” area, and uncheck
the checkboxes for "Variance" and "Latin Hypercube" in the “Result Fields” area. In
other words, we are selecting which of the many available columns to display in the
results table.
Under the "Display Options", the "Elements in Preview" field determines the number of
rows included in this preview window (in our example, 25). When you save the report,
you will get all the rows.

Background: In the report window, there are two columns in the report that are grid
fields ("Column" and "Row"). They are unique identifiers of each minimum spatial
unit. For a CMAQ grid, these are merely the column and row number for each cell in
the grid. For political grids, their meaning depends on your grid definition. In our
example, the column is the state code and the row is the FIPS code.

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Figure 2-21. Configuration Results Report window.

(d)Save the report to a file. To do this, you can either drop down the File menu at the upper
left-hand corner of the window and choose “Save” or simply hit Ctrl-S on the keyboard.

In the Save As window, save the file under the "Reports" folder as
“Control_PM25_RIA_2020_15_annual_35_daily_incidence_state.csv“, a
comma-separated-value file.

(e)Open the .csv file in Excel to review outputs. The full path to this folder is:
"C:\Program Files\Abt Associates Inc\BenMAP 2.4 US Version\Reports"

(f) Close the Configuration Results Report window by clicking Done. This completes the
“Report” module.

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This completes the "Mapping Introduction" lab. In the next lab, “One-Step Analysis” we
will run the one-step analysis, creating both health incidence results (cfgr) and valuation
results (apvr).

A.1.2.7 Additional Mapping Activities

1. Overlay the PM2.5 monitor data over the baseline model data. Look at the similarity
and differences in the pattern of monitor versus modeled data. Make sure that the
monitors' layer is topmost.
2. Overlay the baseline model data over the control 2020 RIA 14/35 data. Compare the
regions in the two layers that are out of attainment. Also, compare the regions that show
PM2.5 concentrations greater than 10 µg/m3.

A.1.3 Section 3. One-Step Analysis

In this section, you will create health incidence and valuation results. This one-step
analysis uses pre-defined health incidence and economic valuation configurations, which
you can combine with your own baseline and control air quality grids. We will run two
separate one-step analyses for two similar, but distinct control strategies.
The One-Step Analysis encapsulates all three stages of BenMAP: (1) Calculate the change
in pollution concentrations that would be produced by the application of a given set of
emissions controls. The concentration change in a pollutant (say, PM2.5) is the difference
(the “delta”) between the modeling results from an emissions control scenario and the
modeling results from the baseline scenario. (2) These deltas, background incidence rates,
and a gridded population dataset are then used in concentration-response (C-R) functions
to calculate the change in health incidence that would result from this change in pollution.
Typically, these health incidence results show the decrease in health incidence (e.g. the
decrease in asthma, bronchitis, mortality, etc) due to a decrease in pollution. (3) These
health incidence results are then used to calculate economic benefits due to changes in the
population's mortality and morbidity. For example, what is the economic valuation of the
avoided premature mortality due to the emissions control? The valuation results (and the
underlying health incidence) are typically then aggregated to county, state, or national
totals. Note: in One-Step Analysis, the health incidence and valuation functions are
standard EPA configurations.

A.1.3.1 Example PM2.5 Control 2020 15/35 National

The goal of this exercise is to re-create the control RIA 2020 15 annual, 35 daily µg/m3 health
incidence and valuation study that we saw in the “Mapping Introduction” lab. We will
produce similar health incidence results (.cfgr file) and valuation results (.apvr file).

Procedures:

(a) In the main BenMAP window, open one-step analysis. Simply click on the
left-hand panel graphic under the label "One-Step Analysis". This will open the

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One Step Analysis window.

Figure 3-1. One-Step Analysis window.

(b) Set the "Run Name". This is the name that will be used for our cfgr and apvr files.
A recommended practice is to be specific and base it on the control. In the "Run
Name" field, type:
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_county”.
Note: we have added "county" to differentiate these results from our previous Control
RIA 2020 15/35 results that had been aggregated to State totals.
(c) Set the output directory. Use the Select button to select the “Configuration
Results” directory

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(d) In the panel "1. Air Quality Grids", set the baseline and control aqg. In many cases,
the control AQG will have lower pollution values than our baseline. This
reduction in modeled ambient PM2.5 is the result of our policy scenario that
reduced emissions from industrial or other sources. Click the Open button next to
the "Baseline File" field.
An Open window will appear. Navigate to the “PM25_RIA” folder under the “Air
Quality Grids” folder, select
“Baseline_PM25_RIA_2020_cmaq_grid_15_Annual_65_Daily.aqg”, and click Open.
Repeat these steps for the "Control File", this time selecting

“Control_PM25_RIA_2020_cmaq_grid_15_Annual_35_Daily.aqg”.
(e) Map the change in pollution (the deltas) between the baseline and the control.
Click on the Map Deltas button. A BenMAP GIS window will appear with 3
layers: "Delta" (the change in PM2.5), "Control Grid" (the control modeled
values), and "Baseline Grid" (the baseline modeled values) (Figure 3-2):

Figure 3-2. GIS window for mapping deltas between the baseline and the control.

(1) Double click the “Delta” layer in the BenMAP GIS window. In the Display

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Option window, set the variable to “QuarterlyMean” and turn off the grid
outlines. Click OK.
In the BenMAP GIS window, uncheck the "Control Grid" and "Baseline Grid" layers
and overlay a state reference layer.

Background: The "Delta" is a map of the change in AQ between your baseline and control
scenarios (i.e. baseline - control). Typically it is a good practice to check the delta. You
can use this map to see if the changes in air quality are in the right direction (typically that
you are getting positive values, i.e. reductions) and magnitude and that the changes are
occurring in the appropriate places. You can also use this window to look at the
underlying control or baseline scenarios: "Control Grid" and "Baseline Grid" in the Layers
panel.

Figure 3-3. The resulting deltas between the baseline and the control.

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(1) Exercise (3.1): In which states are the difference between the
baseline and the control greater than 0.2 µg/m3? Hint: use the Build
queries button.

Answer:

(2) Exercise (3.2): Off the coast of California and on the Northeastern
edge of the CMAQ grid, there are significant reductions in
concentrations. Will these areas change our health incidence and
valuation values? Explain your answer.

Answer:

(f) Click Close in the BenMAP GIS window. This will return you to the One Step
Analysis window.

(g) Aggregation. Aggregation refers to the summing of health incidence results and
valuation results to get more meaningful totals. In our case, the baseline and
control modeled AQ data are at the fine scale of CMAQ grid cells. We want to
aggregate them up to the county level.

(1) Exercise (3.3): Look at the aggregation levels for Incidence and
Valuation. What grids are available? If we set the Incidence grid to
state, what grids are now available for Valuation?

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Answer:

(2) Set the aggregation levels to “County” under “2. Incidence” and “3.
Valuation”.

(h) Run one-step analysis. Click the Go button on the bottom of the One Step Analysis
window. A Progress window will appear. The run will have completed when the
One Step Results window appears (Figure 3-4). Do not close the One Step Results
window when it appears.

Running a one-step analysis will take a few minutes. If we were running a larger
domain, the grid cells had finer resolution, or our configuration included more
functions, the one-step analysis would take much longer. The majority of the
computation time is taken up in calculating the valuation results (apvr).

Analysis: The rest of the exercises in Section 3.2 focus on analyzing the results of our
BenMAP One-step Analysis run. Specifically, we will look at the newly created health
incidence results (cfgr) and valuation results (apvr) files.

(a) One Step Results are a series of customized reports and plots that were designed
for EPA’s apvr setup. Because we are using a simplified configuration, these
reports provide limited results.

Click the Audit Trail Report button in the One Step Results window.

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Figure 34. One Step Results window providing custom reports and plots.

Tip: By using the Load Apvr button (bottom of the One Step Analysis window), you
can select any results file (apvr). Note, the full capabilities of the One Step Results
currently only work for a full EPA RIA configuration.

(b) Exercise (3.4): In the audit trail report and under "Configuration Results", open
"CR Function 0"? What is the function's endpoint? Who is the author of the
underlying study? Under "Advanced", what is the aggregation name for incidence
and valuation results?

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Answer:

(c) In the Audit Trail Report window, click OK to close the window. Click Close in
the One Step Results window. This will return you to the main BenMAP window.

(d) Open a new BenMAP GIS window, click on the Open a File button, then select
“Configuration Results (*.cfgr)”. Under the "Configuration Results" folder, select
the newly created file:
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_county.cfgr”.

(e) In the Edit GIS Field Names window, change the field names to: “Mortality”,
“ChronBronc”, “ER”, and “AcutResp”. Click OK.

In the BenMAP GIS window, double click the layer

"Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_county.cfgr” and
display the "AcutResp" variable.

(f) Exercise (3.5): Which grid is used in the health incidence results? Why is this
different than the aggregation level in the One-step analysis window? Note: you
can use either the audit trail or the GIS tool for this exercise.

Answer:

(g) Exercise (3.6): Which states have a reduction of more than 4000 acute respiratory
incidences? Hint: use the Build queries button.

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Answer:

(h) Overlay the new .apvr (valuation results). Use the Open a File button, select
“APV Configuration Results (*.apvr)”, then choose “Pooled Incidence Results”
(Figure 35).

Open the file

“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_county.apvr”. Edit
the GIS field names to more meaningful names.

Figure 3-5. Opening pooled incidence results.

(i) Exercise (3.7): What grid is used in the pooled incidence results?

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Answer:

(j) Exercise (3.8): Select mortality for your pooled (and aggregated) incidence
results. What is the state (col) and FIPS (row) codes for the county with the
highest number of avoided mortalities? What is the value?

Answer:

(k) Exercise (3.9): What are the maximum value and sum for avoided mortalities in
the pooled incidence results? Make the incidence results
("Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_county.cfgr ") the
active layer. What are the maximum value and sum for avoided mortalities in the
incidence results? Hint: Use the Calculate layer statistics button.

Answer:

(l) Overlay the pooled valuation results. As a reminder:

· Open a File, select “APV Configuration Results (*.apvr)”, then select

“Pooled Valuation Results”. Open
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_county.apvr”.

· Edit the GIS field names. Use the same four field names (“Mortality”,
“ChronBronc”, “ER”, and “AcutResp”).

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· In the Valuation Sums Layer window, click Add Sum to create a Mortality
and a Morbidity Sum (Figure 3-6). Click OK when you have added the two
sums. We will view these summed results in the GIS window.

Figure 3-6. Creating valuation sums for the pooled valuation results.

· In the BenMAP GIS window, double click the “Pooled Valuation Result
Sum” layer and display the "Morbidity" variable.

(m) Exercise (3.10): What is the state (col) and FIPS (row) codes for the county with
the greatest benefit (valuation of avoided morbidity and mortality)? What are the
morbidity and mortality benefits for this county? What is the sum of the mortality
and morbidity benefits across the whole country? Note: you could also do this
through Reports.

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Answer:

(n) Save the pooled valuation results to a shapefile. Click on the Save Active Layer
icon . The Save the active layer to file window will appear.

Under the "Reports" folder, save the shapefile as

"PM25_RIA_2020_15_annual_35_daily_county_pooled_valuation". Click Save.
This shapefile can be used as an input for another GIS software program. Click
Close in the GIS window returning you to the main BenMAP window.

(o) From the main BenMAP window, run a standard pooled valuation report on our
apvr. As a reminder:

Close the One-Step Analysis window. From the main BenMAP window, click the
Report graphic (bottom of the right-hand panel). Select a report type of “Incidence
and Valuation Results”.

After we have opened the newly created county apvr, select the “Pooled Valuation
Results” in the Choose a Results Type window.

In the report window, check the “Endpoint Group” in the “Pooled Valuation
Method Fields”, uncheck the “Latin Hypercube” from the “Result Fields”, and
reduce the digits after decimal point to 0 (Figure 3-7).

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Figure 3-7. Report of pooled valuation results.

(p) Exercise (3.11): For col 1 and row 9, which endpoint (i.e. ER visits, Mortality,
etc) has the greatest standard deviation? Which endpoint has the greatest
coefficient of variation, a.k.a. relative standard deviation (standard
deviation/mean)?
Answer:

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(q) Close the APV Configuration Results Report window by clicking Done.
A.1.3.2 Example PM2.5 Control 2020 14/35 State
The goal of this exercise is to create a control RIA 2020 14 annual, 35 daily µg/m3 health
incidence and valuation study. Unlike our previous example, we will aggregate to the state
level. Our intuition is that this will have greater benefits than the control 2020 RIA 15/35
µg/m3 analysis because we have a lower annual NAAQS.

Procedures: We have abbreviated the instructions because they are very similar to the steps
you just completed in Section 3.2.
(a)Open the One Step Analysis window.
(a)Set the run name to:
“Control_PM25_RIA_2020_cmaq_grid_14_annual_35_daily_state”.
(b)Set the output directory to "Configuration Results"
(c)Set the baseline and control to:
“Baseline_PM25_RIA_2020_cmaq_grid_15_Annual_65_Daily.aqg” and
“Control_PM25_RIA_2020_cmaq_grid_14_Annual_35_Daily.aqg”, respectively.
(d)Go through the process of mapping the deltas. See section 3.2(e) for explicit
instructions.
(e)Exercise (3.12): How do the deltas for this analysis compare to our previous analysis.
For example, you could use the same query (QuarterlyMean > 0.2) to compare the
deltas.

Answer:

(f) Set the health incidence and valuation aggregation to the “State” grid and click Go.

Note: the One-step Results will not work for State aggregation. The current
One-step Reports are designed only for National or Report region aggregation
levels. They also assume that we are using the full EPA configuration. Instead, we
will use normal reports and mapping to analyze this run.

Analysis: The rest of the exercises in Section 3.3 focus on analyzing the results of our

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BenMAP One-step Analysis run. Specifically, we will look at the newly created health
incidence c results (cfgr) and valuation results (apvr) files.

(a)Exercise (3.13): Map the pooled incidence results for

“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_state.apvr” and
“Control_PM25_RIA_2020_cmaq_grid_14_annual_35_daily_state.apvr”. Note: for
detailed instructions see Section 3.2(d) in the analysis section. How do the mortality
values for IL compare between the 2 control scenarios? How does the mortality values
for CA compare? What are the overall differences between the 2 control strategies?

Answer:

(b)Exercise (3.14): Overlay the pooled valuation results for

“Control_PM25_RIA_2020_cmaq_grid_14_annual_35_daily_state”. Remember to
create “Mortality” and “Morbidity” variables in the Valuation Sums Layer window.
What are the mortality and morbidity values for CA? For IL? How does the sum of
mortality and morbidity benefits across the 48 states compare to our results from
“Control_PM25_RIA_2020_cmaq_grid_15_annual_35_daily_county” (see Exercise
3.10)? Note: for detailed instructions see Section 3.2(l) in the analysis section. You
could also use reports to answer this question.

Answer:

(c)After finishing the exercise, close the BenMAP GIS window.

(d)This completes the "One-Step Analysis" lab. In the next lab, “Creating Grids” we will
create new air quality grids (aqg results) from both monitor and model data.

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A.1.4 Section 4. Creating Grids

In this section, you will create air quality grids (aqg) from both air quality (AQ) model data
and from monitor data. The overall goal will be to produce baseline and control air quality
grids for later estimations of health incidence and valuation.

A.1.4.1 Air Quality Model Grids

Think of AQ models as weather models for air pollution. They produce model results over
the whole map on a regular grid. Examples of AQ models are CMAQ and CAMx. These
models are post-processed to generate a csv file or a database table and their values are
usually averaged to daily or yearly statistics. These post-processed datasets can now be
imported into BenMAP.

A.1.4.1.1 Example: PM2.5 Control 2020 15/35 Adjusted

The goal of this exercise is to create a control AQ grid for PM2.5. The CMAQ model data
input is similar to the 15 annual, 35 daily µg/m3 control scenario that we saw in the
“Mapping Introduction” and “One-Step Analysis” sections, except that it has been
post-processed (adjusted) to remove the extreme high values.
Procedures:
(a)Open Air Quality Grid Creation. Click on the graphic on the right-hand panel of
BenMAP’s main window
(b)Choose “Model Direct” in the Air Quality Grid Creation Method window (Figure 41).

Figure 4-1. Air Quality Grid Creation Method window.

(c)In the Model Direct Settings window, set the grid type to “CMAQ 36km Nation
Overlap” and the pollutant to "PM2.5". Leaving the tab as “Generic Model Databases”,
click Browse. Navigate to the "PM25_RIA" folder under the "Air Quality Grids"
folder. In the Open window, change the "Files of type" field to "Text files" and select

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the model data:

"Control_PM25_RIA_2020_cmaq_grid_15_Annual_35_Daily_adjusted".

(d)Click OK to create a new model derived aqg. Save the output under the “PM25_RIA”
folder as: “Control_PM25_RIA_2020_cmaq_grid_15_Annual_35_Daily_adjusted”.
Note: this may take a few minutes to run.
A.1.4.1.2 Example: Control PM2.5 RIA 2020 14/35 adjusted

The goal of this exercise is to create a control AQ grid for PM2.5, similar to the 14 annual,
35 daily µg/m3 control that we saw in the Mapping Introduction and One-step Analysis
sections. Again, this model data has been post-processed to remove the extreme high
values.
Procedures:
(a)Repeat the above steps, now using the 14 annual 35 daily adjusted model data
Analysis:
(a)Exercise (4.1): Open up either of the newly created adjusted model data using the GIS
tool. Using the Query button, select regions that have a PM2.5 QuarterlyMean greater
than 10 µg/m3. Now change the query to QuarterlyMean greater than 15 µg/m3(i.e. out
of attainment). How do these results compare to the non-adjusted aqg’s that we
analyzed in the “Mapping Introduction” section (see Exercise 2.6)?

Answer:

(b)Close the GIS window. This completes the “AQ Model Grids” module.
A.1.4.2 Monitor Grids
When we convert monitor data into an AQG, we need to interpolate from the monitor
locations to all the grid locations. There are two overarching interpolation techniques:
Closest Monitor (also known as nearest neighbor) and Voronoi Neighborhood Averaging
(VNA). Closest Monitor means that the grid cell will have the same value as the nearest
monitor. VNA uses distance to weight the average of monitors in calculating the grid cell’s
value. There are multiple advanced options to change the distance weighting functions and
to apply maximum distance thresholds to these calculations. Additional details are
provided in the User’s Manual.

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A.1.4.2.1 Example: Baseline PM2.5 2004

The goal of this exercise is to generate an AQ grid from PM2.5 monitoring data from
2004. In addition, we will compare closest monitor and VNA interpolation techniques.
Procedures:
(a)Click the Create Air Quality Grid button.
(b)Select “Monitor Direct” and click the Go! button (Figure 4-2).

Figure 4-2. Selecting Monitor Direct.

(c)In the Monitor Direct Settings window (Figure 4-3), select “CMAQ 36km Nation
Overlap” as the grid type.
Select “PM2.5” as the pollutant ,and “Closest Monitor” in the “Interpolation Method” list.
Make sure that the “Library” tab is selected, and select “EPA Standard Monitors” as the
monitor dataset and set the monitor library year to “2004”.

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Figure 4-3. Monitor Direct Settings window.

(d)Click the Map button. This will bring up the BenMAP GIS window (Figure 4-4).

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Figure 4-4. Map of monitors and closest monitor.

(e)Double click the “Air quality grid” in the Layers list on the left side of the window.
Select “QuarterlyMean” in the Variable list, and uncheck the “Grid Outline” box.
(f) In the GIS window, overlay the state reference layer
(g)Zoom into the California-Nevada border area and look at the pattern of the AQG.
(h)Click Close on the GIS window. This will return you to the Monitor Direct Settings
window.
(i) Exercise (4.2): Change the interpolation technique to VNA. Remap the data and look at
the California-Nevada border. How does the VNA AQG compare to the Closest monitor
AQG? Note: this will likely take significantly longer to calculate.

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Answer:

(j) Return to the Monitor Direct Settings window (by closing the GIS window), and click
Go!

Tip: If you click Cancel at this point, you will not have created an aqg. Only by
clicking Go! do you actually create a new aqg file. The Map button gives you a
preview of the interpolated aqg, it does not actually produce the file.

(k)In the Save as window, create a new folder, “PM25_Monitor” under the "Air Quality
Grids" folder. Save the aqg as: “Baseline_PM25_2004_VNA_CMAQ_grid”.

(l) This completes the “Monitor Grid” module.

A.1.4.3 Monitor Rollback
Monitor rollback is a method for creating control scenarios. The rollback technique has
three main steps: (1) the pollutant and the monitoring data are chosen, (2) the chosen
monitoring data is reduced through one or more of the three rollback approaches, and (3)
the rolled back monitors are then interpolated to the chosen grid type. The three rollback
approaches are: percentage, incremental, and rollback to a standard. Note: in constructing
the rollback, we differentiate between the rolled back grid and the control grid. The
rollback grid is the grid type under which we want to perform the rollback. This typically is
a political grid (e.g. State or county). In contrast, the monitor data will be interpolated to
our control grid type.

A.1.4.3.1 Example: Control PM2.5 2004 Percentage Rollback

The goal of this exercise is to create a control by performing a 10% rollback of monitors in
the West coast and in Pennsylvania (remember, these regions had the largest deltas in the
One-step analysis section). With this rollback approach, each daily value above the
background level is rolled back by 10 percent. We will produce a county grid aqg.
Procedures:
(a)Click the Create Air Quality Grid button. This will bring up the Air Quality Grid
Creation Method window.
(b)Select “Monitor Rollback” and click the Go! button (Figure 4-5).

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Figure 4-5. Selecting Monitor Rollback.

(c)This will bring up the Monitor Rollback Settings: (1) Select Monitors window (Figure
4-6). Select “PM2.5” from the pollutant list.
Make sure that the “Library” tab is selected, and select “EPA Standard Monitors” from the
monitor dataset list. Set the monitor library year to “2004”. Select “State” from the
rollback grid type list.

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Figure 4-6. Monitor Rollback Settings: (1) Select Monitors window.

(d)Click Next, which will bring up the Monitor Rollback Settings: (2) Select Rollback
Regions & Settings window.

(e)In that window, click Add Region. A Select Region Rollback Type window will appear
(Figure 4-7). Throughout this region, we will apply one rollback technique. In this case,
we will be using a percentage rollback.
Select “Percentage Rollback” and click OK. You will be returned to the Monitor Rollback
Settings: (2) Select Rollback Regions & Settings window.

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Figure 4-7. Select Region Rollback Type window.

(f) In region 1, set the rollback to 10% and the background to 3 µg/m3. In other words, all
monitor values that are greater than 3 will have a 10% reduction in value.

(g)Apply the controls to the West coast states and PA (four states in total). Use your
mouse to click on the map to select a state. For example, we have selected California in
Figure 4-8.

Figure 4-8. Monitor Rollback Settings (2) Select Rollback Regions and Settings window.
Selecting a region for a 10% monitor rollback.

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(h)Click Next

(i) In the Monitor Rollback Settings (3) Additional Grid Settings window (Figure 4-9), we
want to use VNA interpolation and county grid type (i.e., the control grid). Uncheck
“Make Baseline Grid (in addition to Control Grid)” because we did this in a previous
step.

Figure 4-9. Monitor Rollback Settings (3) Additional Grid Settings

window. Setting county grid type.

(j) Click Go! and save the aqg under “PM25_Monitor”:

“Control_PM25_2004_VNA_county_10pct_rollback_3_background”

Analysis:
(a) Exercise (4.3): Create an audit trail report on our new monitor rollback aqg. Under
"Advanced", what is the neighbor scaling type? Under "Monitor Rollback", what are the four
states (names and codes) that have been rolled back? What is the rollback method and value?

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Answer:

(b)Exercise (4.4): Map our new monitor rollback aqg. What states have a QuarterlyMean greater
than 15 µg/m3?

Answer:

A.1.4.3.2 Example: Control PM2.5 2004 Multiple Rollback Techniques

The goal of this exercise is to combine multiple rollback techniques into one control
scenario. We will rollback the West coast incrementally. On the East coast, we will
rollback to a standard using peak shaving. In other words, on the West coast, we will
decrease all monitors by a fixed amount, while on the East coast we will define a standard
and only reduce those monitors that exceed that standard, for only those hours over the
standard. The aqg will have a CMAQ grid type.
Procedures:
(a)Go through the same steps as above to setup a monitor rollback for PM2.5 for 2004.
Again select “State” as the rollback grid type.
(b)Add the first region, then select “Incremental Rollback” in the Select Region Rollback
Type window (Figure 4-10) and click OK.

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Figure 4-10. Selecting incremental rollback.

(c)Set the rollback to 4 µg/m3 and the background to 3. Select all the West coast states.

(d)Add a second region. In the Select Region Rollback Type window, set the type to
“Rollback to a Standard”. Here we have many more options in defining what our
standard is and how we want to reduce the monitors so that they match that standard. In
our case, we will set a standard that no monitor should have a daily mean value greater
than 35 µg/m3.

(1)Set daily metric to “D24HourMean”. Leave the seasonal metric blank and the
annual statistic type blank.

(2)Set the standard to 35 and leave the ordinality as 1.

Background: Ordinality refers to the number of monitor values in the season

that can exceed your standard. For example, if we had set the ordinality to 4,
than a monitor can have as many as three daily averages >35 µg/m3 without
violating the standard (i.e. it would not be rolled back). If it has more than 3
daily averages in an exceedance of the standard, then the rollback technique
will be applied to that monitor.

(3)Set the rollback method to “Peak Shaving”, and the background to 3 µg/m3.

(4)Select all the East coast states. Figure 4-11 shows the selection of the first state,
Maine. Note: You may need to use the zoom button to get some of the smaller
states.

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Figure 4-11. Monitor Rollback Settings (2) Select Rollback Regions and Settings window.
Adding a second rollback region, rollback to standard.

(e)Click Next to go to the Monitor Rollback Settings: (3) Additional Grid Settings
window. This time, set the grid type to “CMAQ 36km Nation Overlap” and the
interpolation to “VNA”.

Uncheck “Make Baseline Grid (in addition to Control Grid)” because we did this
in a previous step (Figure 4-12).

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Figure 4-12. Monitor Rollback Settings (3) Additional Grid Settings window.
Setting CMAQ grid type.

(f) Click Go!. Save the results under “PM25_Monitor” as:

“Control_PM25_2004_VNA_CMAQ_4_incremental_35_daily_3_background”

Analysis:

(a)Exercise (4.5): Create an audit trail report on our new monitor rollback aqg. Under
"Monitor Rollback", describe the two rollback regions, focusing on their techniques?

Answer:

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(b)Exercise (4.6): Map the deltas between the Baseline PM2.5 VNA 2004 and this multiple
rollback control that we just created. How do the East Coast and West Coast deltas
differ? How do you explain the pattern on the eastern boundary of CA, WA, and OR?
Hint: Use the One-step analysis window to map the deltas. You don't need to perform a
full One-step analysis. Instead, in the "1. Air Quality Grids" panel, select your newly
created "Baseline_PM25_2004_VNA_CMAQ_grid.aqg" as the "Baseline File" and your
newly created control as the "Control File". Click Map Deltas.

Answer:

(c)Close any open BenMAP windows. This completes the “Monitor Rollback” module.

(d)This completes the "Creating Grids" lab. In the next lab, “Health Incidence” we will
take our aqg results and calculate the corresponding health incidence results due to the
change in air quality.
A.1.5 Section 5. Health Incidence
In this section, you will modify an existing health incidence configuration and use it to
create new health incidence results. You will create two separate sets of health incidence
results based on the same configuration and two similar, but distinct, control strategies.
Creating health incidence results has three main stages:
(1)Select baseline and control air quality grids (AQG) and other general settings.
These general settings include population dataset and analysis year, air quality
threshold, and statistical parameters. The delta between the baseline and control
AQGs is combined with the population data as a major input to the health impact
functions.
(2)Select specific health impact functions and modify default parameters. Some of
these parameters include demographics (e.g., gender, race, or age ranges) and
incidence and prevalence rates.
(3)Save all the settings from the first two stages as a configuration (cfg), which can
be re-used later with other baseline/control pairs if desired. Finally, run the health
incidence configuration, which will create a new health incidence results file
(cfgr).
Health impact functions relate the change in number of observed, adverse health effects in

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a given population to a given change in concentration for a given pollutant. These

functions are usually based upon epidemiological studies with specific sub-populations,
and have a baseline estimate of the health effect. Having estimated changes in air quality
levels from monitored or modeled data in previous labs, in this section, we will learn how
to use these changes in concentrations and health impact functions to estimate changes in
health incidence.
In this lab, we start from an existing configuration to help you develop a new
configuration. After working through this lab, however, you should also be able to create a
new configuration from scratch.
Note: For many of the health endpoints (e.g., mortality), there are many different health
impact functions that you could choose to include in your configuration. This lab has you
select specific functions and teaches you how to differentiate these functions and modify
the input parameters. This lab does not teach you how to determine which functions are the
best ones for a particular study. To determine the best choices for a particular analysis, we
recommend that you read the appendices accompanying BenMAP that describe the specific
epidemiological studies that correspond to the specific health impact functions and/or that
you discuss your choices with an epidemiologist. If you want to use EPA’s standard set of
functions, you can use the configurations that are pre-loaded for the one-step analysis when
you download BenMAP.

A.1.5.1 Example: PM2.5 Control 2020 14/35

The goal of this exercise is to create a new configuration by modifying the health incidence
configuration that was used in the One-step analysis (Section 3) and create health
incidence results for the control scenario RIA 2020 14 annual, 35 daily µg/m3. We will
add the following health impact functions to the previous configuration: mortality for
infants, hospital admissions due to respiratory problems, and acute myocardial infarctions
(AMIs), also known as heart attacks.
Procedures:
(a)In the main BenMAP window, begin a health incidence estimation by clicking on the
graphic titled "Incidence Estimation" located in the right-hand panel, under the “Step 2”
heading. This will open the Configuration Creation Method window (Figure 5-1).

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Figure 5-1. Health incidence Configuration Creation Method window.

(b)In this window, select "Open Existing Configuration". This means that we are starting
from some already selected health impact functions (i.e., we are not "starting from
scratch"). Click Go!. An Open window will appear. In the "Configurations" folder.
Select the "PM25_RIA_2020_course.cfg" file and click Open.

(c)The Configuration Settings window (Figure 5-2) is used to set the baseline and control
AQG files, and also to set some general parameters that will be used by all the health
impact functions. In this window, we will change only the baseline and control AQG
files. The rest of the settings (Latin Hypercube Points, Population DataSet and Year,
Point Mode, and Threshold) will be left unchanged.

(d)In the "Select Air Quality Grids" panel, next to the "Baseline File" field, click Open.
The Open window will appear. Navigate to the "PM25_RIA" folder under the "Air
Quality Grids" folder, select
"Baseline_PM25_RIA_2020_cmaq_grid_15_Annual_65_Daily.aqg", and click Open.

(e)Repeat these steps for the "Control File", this time selecting
"Control_PM25_RIA_2020_cmaq_grid_14_Annual_35_Daily.aqg".

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Figure 5-2. Configuration Settings window - General parameters.

Background: The other settings in this window may be changed when you are doing your
own studies. The Point Mode versus the Latin Hypercube Points options allow you to
generate either an average incidence estimate or a range of results. With the Point Mode
option, BenMAP uses the mean values of the inputs to the health impact functions, and
generates a single “point estimate” of the change in adverse health effects; this is useful
for quick analyses. With the Latin Hypercube Points option, BenMAP estimates a
distribution of incidence results that expresses the variability in the incidence estimates;
this option reports specific percentiles along the estimated incidence distribution. The
greater the number of chosen points, the greater the number of estimates and hence the
greater the time needed by BenMAP to process the results. The Population DataSet and
Population Year specify the population data that will be used in the health impact
functions. The Population DataSet should match the grid definition of your baseline and
control files. The Threshold indicates the air quality level below which the program will
not calculate benefits. That is, air quality metrics below the threshold will be replaced with
the threshold value.

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(f) Before continuing on to select health impact functions, we should do some quality
assurance (QA) on the aqg files. Specifically, we want to look at the AQ deltas. In the
Configuration Settings window (Figure 5-2), click on Map Grids. This will open a
new BenMAP GIS window.

(g)In the BenMAP GIS window, uncheck the "Control Grid" and "Baseline Grid" in the
"Layers" panel (on the left side). Double-click on the "Delta" layer, which will open the
Display Options window.

In the Display Options window, uncheck "Grid Outline" and set the Variable to
"QuarterlyMean". Click OK.

Back in the BenMAP GIS window, overlay a State reference layer. Your GIS
window should now look similar to Figure 5-3.

Figure 5-3. Mapping delta AQ

(h)Exercise (5.1): Using the Create Layer Statistics button, what are the maximum and
mean for the QuarterlyMean of PM2.5? Using the Build query button, which states have
a QuarterlyMean greater than 1.0 µg/m3?

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Answer:

(i) After you have completed the above exercise, click Close in the BenMAP GIS window
to return to the Configuration Settings window. At this point we have set all the general
parameters for our configuration. Note: we did not modify the latin hypercube points,
population year, or threshold. Click Next.

(j) This will open a new Configuration Settings window (Figure 5-4). This window
describes the specific health impact functions that were selected in the configuration
file. We will also use this window to select new health impact functions for our new
configuration. This window is divided into two panels:

Available CR Functions: This describes all the available functions that are appropriate
for this type of AQ data. In our case, these are all the PM2.5 functions. The left-hand
panel is the "Tree". It describes the hierarchy between endpoint groups (major groupings
of adverse health effects) and endpoints (specific adverse health effects). You can
expand any section by clicking on the plus sign next to the heading, or collapse a section
by clicking on the minus sign next to a heading. To see the specific health functions,
you need to expand the endpoint heading of choice. The right-hand panel is the "Data"
panel. The data are all the details of the specific health functions: the author of the
study, location where the study was done, the specific function that BenMAP uses to
calculate that adverse health effect, whether there is a qualifier to the health function,
etc. A complete description of each column can be found in the User's Manual. The
scroll bar at the bottom of the “Available CR Functions” panel is for panning across the
"Data" columns.

Selected CR Functions: This describes the functions that have been chosen for this
specific configuration. The left-hand panel is "Function Identification", which contains
all the columns necessary to uniquely identify the function. The scroll bar at the bottom
of the “Selected CR Functions” panel is for panning across the "Function Identification"
columns. We recommend focusing on Endpoint, Author, Year and Qualifier. The
right-hand panel is "Function Parameters". These parameters are used by the health
functions and some of them can be edited by the user. For example, you might change
the age range ("Start Age" and "End Age") for a specific health impact function if you
were interested in studying the impact on a certain demographic.

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Figure 5-4. Configuration Settings window - Initial functions.

Tip: When looking at the CR functions, it is often useful to change the order and/or width
of the columns. To reorder the columns, click and hold your cursor on the variable name
at the top of a column, then drag the column either to the right or to the left. Release your
cursor when you have moved the column over the desired location – BenMAP will then
rebuild the tree structure using the newly specified variable order. To resize a column,
either double click on the right edge of the desired column (maximizes the column) or
click on the edge of the column and drag it to the right or left until it is the appropriate
size.

(k)Before adding new functions to our configuration, we will look at the current set of
selected health impact functions:

(1)In the "Tree" panel, expand the DataSet "Complete Version2". This should reveal
the available endpoint groups. You can expand any endpoint group to see the

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available endpoints within that endpoint group. You can also expand a specific
endpoint so that you can see the specific health functions for that particular
endpoint. For example, expand the endpoint group "Emergency Room Visits,
Respiratory" and the revealed endpoint "Emergency Room Visits, Asthma" to
reveal the specific health impact functions.

(2)Exercise (5.2): How many health functions are there for the "Emergency Room
Visits, Asthma" endpoint? Who are the author(s) for these functions/studies? What
are the differences between these functions? (After you have completed this
exercise, you might want to collapse the "Emergency Room Visits, Respiratory"
endpoint group. This will reduce the clutter in the top panel.)

Answer:

(3)Exercise (5.3): What are the endpoints under the "Hospital Admissions, Respira­
tory" endpoint group? How many functions are there under the "HA, Chronic Lung
Disease" endpoint and who are their authors? Note: You might have to expand the
width of the Endpoint column to make sure you have the right one.

Answer:

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(4)Exercise (5.4): Who is the author of the mortality function used in our current
configuration? Hint: Look at the "Function Identification" panel. If you look at the
available mortality functions, how many of them are by this author? Looking at the
Qualifier column, what differentiates this author's functions? Which of the
functions are we using in our current configuration? Hint: We recommend
reorganizing the columns in the "Data" panel so that you have Author, Start Age,
End Age, Qualifier, and Function next to each other (see previous Tip).

Answer:

(l) In the next series of steps, we will add new health functions to our configuration. We
will add an additional mortality function, some hospital admission functions, and some
acute myocardial infarction (AMI) functions. You will note that in many cases there will
be multiple functions for the same endpoint by the same author. In most cases these will
be differentiated by the content of the Qualifier column. In all of our cases, we will
select the function that does not have a threshold or other qualifier.

(1)We will start by adding a new "Mortality, All Cause" endpoint health function.
Select the function that has Woodruff as the author and no qualifier (no threshold).
To add it to our configuration, simply click on the specific row and drag it to the
"Selected CR Functions" panel (Figure 5-5).

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Figure 5-5. Adding a new health impact function.

Tip: If you mistakenly add the wrong health impact function, you can delete it by
highlighting the particular function in the "Selected CR Functions" panel and clicking
Delete on your keyboard.

(2)After moving a function into the configuration, you need to decide whether you
want to change any of the "Function Parameters", i.e., the inputs to the health
function. In the Woodruff case, we want to set the "Incidence DataSet" (i.e., the
background incidence rate for mortality). Click on the "Incidence DataSet" cell for
the Woodruff study. Use the drop-down menu to select "2020 Mortality Incidence"
(Figure 5-6). In other words, we are using the incidence rate for mortality that has
been projected to the year 2020.

Note: In this case there is an available incidence rate dataset for 2020. For

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other endpoints (e.g. Chronic Bronchitis), the background incidence rates are
only available for 2000 because they have not been projected to 2020.

Figure 5-6.Changing Function Parameters - the incidence rate.

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(3)Exercise (5-5): Compare the Pope and Woodruff mortality studies in the
“Available CR Functions” panel. What is the age range for each study? Write down
the functions for each study. Note: compare the respective Pope and Woodruff
functions that you selected.

Answer:

(4)Next we will add a health function for hospital admission due to pneumonia. Under
the "Hospital Admissions, Respiratory" endpoint group, expand the "HA,
Pneumonia" endpoint. Select the function by Ito without a threshold shown in the
qualifier column. Simply click on the appropriate function with your mouse and
drag it to the "Selected CR Functions" panel.

Note: In this case the incidence dataset has already been selected. If you try to
select another dataset you will see that 2000 is the only available dataset. In
other words, the incidence and prevalence for hospital admissions due to
pneumonia has not been projected to 2020.

(5)Next we will add health functions for hospital admissions due to chronic lung
disease. Under the endpoint "HA, Chronic Lung Disease", add the functions by Ito
and Moolgavkar (without threshold). Note: Make sure you are not using the
endpoint "HA, Chronic Lung Disease (less Asthma)".

(6)Exercise (5-6): Compare the Ito and Moolgavkar studies. How do their specific
functions compare? What is the beta (regression coefficient) for each study? Bonus
question: Which function is more sensitive to changes in AQ?
Answer:

(7)Finally, we will add health functions for AMI. Under the "Acute Myocardial

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Infarction" endpoint group and "Acute Myocardial Infarction, nonfatal" endpoint,

select the Peters study (no threshold). Here, we will do something slightly different.
Drag four copies of the Peters function to the "Selected CR Functions" panel. The
age range for this function is 18 to 99 years. We want to look at the effect on a
more specific demographic—that is, we want to break this into four age ranges.

Starting with the first Peters function, select the "End Age" cell in the
"Function Parameters" panel. Edit the cell to 44. The new age range for the
first Peters function is now 18 to 44, inclusive.

For the next Peters function, modify the Start Age to 45 and the End Age to
54. For the remaining Peters functions, change the age range to 55-64 and
65-99, respectively. After modifying the age ranges, your Configuration
Settings window should look similar to Figure 5-7.

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Figure 5-7. Four additional AMI functions with modified age ranges.

(8)You have completed adding all the new health functions to your configuration. You
should now have 12 functions in your "Selected CR Functions" panel (Figure 5-7).
Double check to be sure all of the selected functions have an empty qualifier cell
(check in the "Function Identification" panel by moving the bottom scroll bar until
the Qualifier column is visible, note that the Pope function will say "no threshold").

(m)When you have set up all the health impact functions as instructed above, you are ready
to save the new configuration and generate the health incidence results. Click Run. This
will bring up a Save Configuration window (Figure 5-8).

We want to save this new configuration (so that it can be re-used), so click Save.
This will bring up a Save As window. Under the "Configurations" folder, in the

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"File name" field, type in the new configuration file name,

"PM25_RIA_2020_course_modified", and click Save. A Progress window will
appear.

Figure 5-8. Save Configuration window.

(n)After the configuration is saved, you will be returned to the Save Configuration window
(Figure 5-8). Now run the configuration by clicking OK. This will bring up another
Save As window. Here we will save the configuration results (cfgr). Under the
"Configuration Results" folder, save the results as
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily".

The calculation of the results will begin and a Progress window will appear. The
calculation of the results may take a few minutes. When the calculations are
finished, you will be returned to the main BenMAP window.

Tip: If you are not ready to run this configuration, click Cancel. If you generated
a configuration, you can open the configuration and run it to generate valua
results at a later time.

Analysis:
The rest of the exercises in Section 5.2 focus on analyzing the results of our BenMAP run.
Specifically, we will look at the newly created health incidence configuration file (cfg) and
results file (cfgr). A good habit to get into is to quality-assure both your configuration and
your results. Some things to check include whether you have the right functions and
parameters selected and whether the results seem reasonable.

(a)First, we will look at the newly created configuration file (cfg) using the audit trail.
From the main BenMAP window, click on the "Report" graphic in the right-hand panel.

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Select the "Audit Trail Reports" in the Select Report Type window and click OK. Under
the "Configurations" folder, select the new configuration,
"PM25_RIA_2020_course_modified.cfg" and click Open.

(a)Exercise (5.7): What is the population year used in this configuration? How many
health functions (CR functions) were used? What are the location and the incidence rate
dataset used in the Woodruff mortality function? Hint: if you added the functions in the
same order as the lab, the Woodruff study should be "CR Function 4". When you are
done with this exercise, click OK to close the Audit Trail Report window.

Answer:

(b)Using the Tools menu in the main BenMAP window, open a BenMAP GIS window.
Click on Open a File, then select “Configuration Results (*.cfgr)”. Under the
"Configuration Results" folder, open our newly created file,
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily.cfgr".

(c)In the Edit GIS Field Names window, provide more meaningful names for your health
incidence results, then click OK. Here are suggested names: MortPope, ChronBronc,
ER, AcutResp, MortWood, HAPneum, HAChrIto, HAChrMool, AMI18, AMI45,
AMI55, AMI65. Note: BenMAP GIS field names cannot exceed 10 characters in length
and cannot include commas.

(d)Exercise (5.8): Compare the Pope and Woodruff mortality results. How do the
maximum values compare? The Pope and Woodruff health impact functions are
calculating avoided mortalities for different subgroups within the population. What is
the Pope result measuring versus the Woodruff result? Do they have similar spatial
patterns?

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Answer:

(e)Exercise (5.9): Compare the Ito and Moolgavkar Hospital Admissions due to Chronic
Lung Disease results. How do the maximum values compare? How do their respective
populations compare (by "population", we mean the population variable POP1, POP2,
etc. that correspond to the appropriate heath incidence result)? The spatial patterns of
the two results are identical while their magnitudes differ. How do you explain this?
Hint: Look back at Exercise 5.6.

Answer:

(f) Exercise (5.10): Compare the AMIs (heart attacks) for various age groups. What are the
maximum values for the AMI18 and AMI65 functions? What are the population
maximum values for these two functions? Why do you think that the value of AMI18 is
less than the value of AMI65? After you are done with the above exercises, close the
BenMAP GIS window by clicking Close.

Answer:

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(g)From the main BenMAP window, click on the "Report" graphic in the right-hand panel.
Select "Raw Incidence Results" in the Select Report Type window and click OK. Under
the folder "Configuration Results", open our results file,
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily.cfgr".

In the “C-R Function Fields” panel within the “Column Selection” panel of the
Configuration Results Report window (Figure 5-9), select Endpoint, Author, Start
Age, and End Age. In the “Result Fields” panel, deselect Delta and Variance.

As you select or deselect items in the “Column Selection” panel, your choices are
reflected in the “Preview” panel in the bottom half of this window, which displays
a preview of the columns that will be included in the results report when you save
the file.

Figure 5-9. Report window for raw incidence results.

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Background: Some of the key columns that can be included in results reports are the
following: the "mean" is the mean of the Latin Hypercube points for this result; the
"point estimate" is the single point estimate for this result; "percentiles" are the
individual Latin Hypercube points for this result; the "baseline" is the number of
individuals experiencing this adverse health effect due to all causes (typically incidence
rate  population); the "percent of baseline" is the relative change in adverse health
effects due to the control scenario we are considering (point estimate/baseline); the
"population" is the population used in the particular health function at this grid cell.

(h)Now that you have chosen all the columns to include in your results report, you can save
the report. From the Configuration Results Report window, type Ctrl-S. Under the
"Reports" folder, save the file as
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily". After the file
has been saved, close the window by clicking Done.

Use Windows Explorer to navigate to the "Reports" folder. Double-click on the

newly created csv file and it should open in Excel. Note: if you are using an
earlier version of Excel, it may give you an error message saying that it could not
load the complete file. Click OK in the warning window.

(i) Exercise (5.11): All of the following questions refer to the grid cell 14, 63 (column,
row) for the endpoint "Minor Restricted Activity Days" (within the endpoint group
"Acute Respiratory Symptoms"). What is the background incidence (the total number of
minor restricted activity days due to all causes) for this particular grid cell? Hint: the
column is called "Baseline". What is the change in adverse health effects (i.e., the
number of minor restricted activity days avoided) under the control scenario? We know
that the heath impact functions have an underlying statistical function that gives us a
range of results. What is the estimate of the change in adverse health effects at the 5th
percentile? What is the estimate at the 95th percentile? When you are finished with this
exercise, close the Excel window.

Answer:

A.1.5.2 Example: PM2.5 Control 2020 14/35 Adjusted

The goal of this exercise is to re-use our newly modified health incidence configuration
(from Section 5.2) and create health incidence results for the adjusted control scenario RIA

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2020 14 annual, 35 daily µg/m3. Note: in the following instructions, we refer to "adjusted"
and "nonadjusted" results, AQ data, and/or configurations. The "nonadjusted" data and
configuration are from Section 5.2. The "adjusted" are from this Section (5.3).
Procedures: The following is a list of the necessary steps. We have abbreviated the
instructions because they are very similar to the steps you just completed in Section 5.2.

(a) Open "Incidence Estimation" from the main BenMAP window, Custom Analysis
side.

(a) Select "Open Existing Configuration", and Click Go!. Choose the newly created
configuration "PM25_RIA_2020_course_modified.cfg" under the
"Configurations" folder and open it.

(a) In the Configuration Settings window, change the baseline and control aqg files.
Under the "PM25_RIA" folder, select the
"Baseline_PM25_RIA_2020_cmaq_grid_15_Annual_65_Daily_adjusted.aqg" as
the baseline and the
"Control_PM25_RIA_2020_cmaq_grid_14_Annual_35_Daily_adjusted.aqg" as
the control. Leave the rest of the settings the same.

(a) Quality-assure the aqg files. Click on the Map Grids button. In the new GIS
window that opens, select only the "Delta" layer and in the Display Options
window display the QuarterlyMean.

(a) Exercise (5.12): What are the maximum and mean for the delta QuarterlyMean of
PM2.5? Which states have a delta QuarterlyMean greater than 1.0 µg/m3. Compare
your answers to Exercise 5.1. Which scenario (adjusted or nonadjusted) do you
predict will have greater number of avoided adverse health incidences? Explain
your answer.

Answer:

(a) After returning to the Configuration Settings window, click Next.

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(a) Review your selected health functions. There should be 12 of them. Make sure
they are the same functions you used in the last example then run the example by
clicking Run.

(a) Do not save the configuration. There is no need to save it because the only
changes were to the baseline and control files. Do create the health incidence
results by clicking OK. Under the "Configuration Results" folder, save the results
as
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_adjusted".
The calculation of the results will begin and a Progress window will appear. The
calculation may take a few minutes.

Analysis: Now we will look at the newly created health incidence results file (cfgr). Because
we have already checked the cfg file in Section 5.2, we do not need to quality-assure this
configuration file again.

(a) Click on the right-hand "Report" graphic in the main BenMAP window. Use the
Select Report Type window to open an audit trail for the new health incidence results
file,
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_adjusted.cfg
r".

(b) Exercise (5.13): What is the population year used in this cfgr? How many health
functions (C-R functions) were used? How many Latin Hypercube points are used
in calculating the C-R functions’ statistical distribution?

Answer:

(c) Open a BenMAP GIS window then open the same health incidence results file
under the "Configuration Results" folder.

(d) Exercise (5.14): Compare the Pope and Woodruff mortality results. How do the
maximum values compare? How do these results compare to the nonadjusted
results (see Exercise 5.8)?

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Answer:

(e) Exercise (5.15): Compare the AMIs for various demographics. What are the
maximum values for the AMI18 and AMI65 functions? What are the population
maximum values for the two functions? How do these results compare to the
nonadjusted results (see Exercise 5.10)?

Answer:

(f) From the main BenMAP window, follow the steps needed to create a raw
incidence results report from the same health incidence results file. Select the same
results columns as before (see Figure 5-8).

Save the report under the "Reports" folder as

"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_adjusted".
Then open the new csv file in Excel.

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(g) Exercise (5.16): All of the following questions refer to the grid cell 14, 63
(column, row) for the endpoint "Minor Restricted Activity Days" (within the
endpoint group "Acute Respiratory Symptoms"). What is the background
incidence (the total number of minor restricted activity days due to all causes) for
this particular grid cell? What is the change in adverse health effects (i.e. the
number of minor restricted activity days avoided) under the control scenario? We
know that the heath impact functions have an underlying statistical function that
gives us a range of results. What is the estimate of the change in adverse health
effects at the 5th percentile? What is the estimate at the 95th percentile? How do
these results compare to the nonadjusted results (see Exercise 5.11)?

Answer:

(h) Close the Excel file and any open BenMAP windows. This completes the "Health
Incidence" lab. In the next lab, “Aggregation, Pooling, and Valuation,” we will
take our health incidence results and calculate the corresponding monetized
benefits due to these health effect changes.
A.1.6 Section 6. Aggregation, Pooling, and Valuation
In this section, you will create an aggregation, pooling, and valuation (APV) configuration
and use it to produce new valuation results. You will create two separate sets of valuation
results based on the same configuration and two similar, but distinct, control strategies.
Creating valuation results has four main stages:
(1)Select a health incidence results file (cfgr) and set up pooling for similar results
(i.e. combining similar results together into one result).
(2)Select specific valuation functions and pool similar valuations.
(3)Select additional parameters for the valuation functions, and decide on the
aggregation (e.g. summing results from county level to state level) for the health
incidence results and the valuation results.
(4)Save all the settings from the first three stages as a configuration file (apv), which
can be re-used later with other health incidence results if desired. Finally, run the
aggregation, pooling, and valuation configuration, which will create a valuation
results file (apvr).

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A reduction in air quality level is usually associated with lowering the risk for adverse
health effects for a population. This reduction in risk is usually not the same for all
individuals, and there is a need to translate the reduction in risk to a quantifiable economic
value. BenMAP relies upon published studies where the unit value of such a reduction in
risk has been calculated for various health effects. Since multiple studies are sometimes
available for a given health incidence, the user needs to choose between them, or adopt
techniques to pool (statistically combine) the different functions in an appropriate manner.
In this section, we will learn how to pool the results and monetize the reduction in risk for
adverse health effects due to changes in air quality levels.
Note: For many of the health endpoints (e.g., mortality), there are many different valuation
functions that you could choose to include in your configuration. In addition, there are
multiple ways to pool your health incidence and valuation results. This lab has you select
specific functions and teaches you how to differentiate these valuation functions and
modify certain parameters. This lab does not teach you how to determine which valuation
functions and pooling options are the best for a particular study. To determine the best
choices for a particular analysis, we recommend that you read the appendices
accompanying BenMAP that describe the specific studies that correspond to the specific
valuation functions and/or that you discuss your choices with an economist.

A.1.6.1 Example: PM2.5 Control 2020 14/35

The goal of this exercise is to create a new aggregation, pooling, and valuation configuration
(apv) and produce valuation results for the control scenario RIA 2020 14 annual, 35 daily
µg/m3.

Procedures:

(a) In the main BenMAP window, begin the process of creating an apv configuration
by clicking on the graphic titled "Pooling, Aggregation, and Valuation" in the
right-hand panel, under the “Step 3” heading. This will open the APV
Configuration Creation Method window (Figure 6-1).

Figure 6-1. APV Configuration Creation Method window

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(b) In the APV Configuration Creation Method window (above), select "Create New
Configuration for Aggregation, Pooling, and Valuation". Click Go!. An Open
window will appear.

We first have to select the health incidence results that this apv will be based on:
the results that we created in Section 5.2. In the "Configuration Results" folder,
select
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily.cfgr" file
and click Open. This will open the Incidence Pooling and Aggregation window
(Figure 6-2).

Figure 6-2. APV Incidence Pooling and Aggregation window

(c) This window is where we will combine (pool) similar health incidence results
together. Before we begin pooling, let us look at the main features of this window.
First, the "Configuration Results File Name(s)" field near the bottom of the
window shows the health incidence results (cfgr) that you just selected for this
apv. If you want to use a different cfgr, you would use the Browse button to locate
it. We will do this later, in the second example for this lab.

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The "Target Grid Type" is the grid definition used to generate the selected health
incidence results; it always matches the cfgr input's grid. The "Available Incidence
Results" panel has an expandable hierarchical tree that lists each of the health
incidence results in the cfgr file. The "Select Pooling Methods" panel has one or
more pooling windows. The pooling windows are where you will select individual
health incidence results that you may want to pool. These selected results (whether
or not they have been pooled) will then be available for valuation (next window).
The Add and Delete buttons add new pooling windows or remove pooling
windows that have already been created.

(d) First, change the name of the pooling window. (For our configuration, there will
be only one pooling window.) Click in the "Pooling Window Name" field within
the "Select Pooling Methods" panel. Change the text "Pooling Window 1" to
"Main Pooling Window".

(e) In the "Available Incidence Results" panel, expand "PM2.5" by clicking on the
plus [+] sign. This will reveal the available endpoint groups. You can expand any
endpoint group to see the available endpoints within that endpoint group. In turn,
you can expand a specific endpoint so that you can see the specific health
incidence results available for that endpoint.

We will begin by expanding the "Chronic Bronchitis" endpoint group and

endpoint. Notice that the health incidence result is identified in the tree using the
reference that describes the study used to derive the underlying health incidence
function. Click on the chronic bronchitis result "Abbey D. E., B. E. Ostro, F.
Pertersen and R. J. Burchette. 1995. …" and drag it to the "Main Pooling
Window" (Figure 6-3). That is all it takes—you have added the first health
incidence result.

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Figure 6-3. Adding a health incidence result to a pooling window

Tip: By hovering the cursor over the Available Incidence, you can see a more complete
description of these studies.

(f) For the "Emergency Room Visits, Respiratory" endpoint group, add the health
incidence result "Norris G., et al. …" to the "Main Pooling Window". Again,
simply click on the specific result from the "Available Incidence Results" panel
and drag it to the pooling window.

(g) For the "Acute Respiratory Symptoms" endpoint group, add the health incidence
result "Ostro, B. D. and S. Rothschild …" to the "Main Pooling Window". At this
point you should have three endpoints with their corresponding three health
incidence results in the pooling window (Figure 6-4).

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Figure 6-4. Initial three health incidence results in the pooling window

Tip: If you mistakenly add the wrong health incidence result, you can delete it by
highlighting the particular function in the "Select Pooling Methods" panel and clicking
Delete on your keyboard. The Delete button in the Select Pooling Methods panel will remove
the whole pooling window. Typically, you would not want to do this.

(h) For the rest of the endpoint groups, we will add multiple health incidence results
per group. In the "Available Incidence Results" panel, expand the "Mortality"
endpoint group. Drag the "Pope et al.,…" result into the "Main Pooling Window".
Repeat for the "Woodruff, T.J., J. Grillo…" result (Figure 6-5).

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Figure 6-5. Addition of mortality health incidence results to the pooling window

(i) Now, please note a couple of points about the present state of the pooling window.
First, we have begun to create a hierarchy. Under the "Mortality" endpoint group
we have one endpoint, "Mortality, All Cause". Under this endpoint we have two
health incidence results, "Pope" and "Woodruff". You can use the scroll bar to pan
across the various columns of data describing the specific results (similar to what
you did in the "Available CR Functions" panel of the health incidence
“Configuration Settings” window (Figure 5-7)).

Second, a "None" appeared in the Pooling Method column of the "Main Pooling
Window" in the "Mortality" row. When there are multiple health incidence results
under a single endpoint group, BenMAP allows you to pool the results. Unlike the
other endpoint groups, the "Mortality" group has two results; therefore, you have
the option of pooling them. By default, the pooling is set to "None"—that is, no
pooling. We do want to use pooling, but before setting up the pooling we are going
to add the rest of the health incidence results for the remaining endpoint groups.

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Tips: (1) You can grab a whole group of endpoints and add all of their respective results
to the pooling window at once. (2) You do not need to add all of the available health
incidence results to your pooling window(s). If you are not interested in pooling or valuing
a particular result, do not add it to a pooling window.

(j) For the "Hospital Admissions, Respiratory" endpoint group, add these three items
to the pooling window:

 the "Ito" results for the "HA, Pneumonia" endpoint

 Both the "Ito" and the "Moolgavkar" results for the "HA, Chronic Lung
Disease" endpoint.

(k) For the "Acute Myocardial Infarction" endpoint group, add the four age-specific
"Peters" results to the pooling window (Figure 6-6). Note: although the four
functions seem to be missing in Figure 6-6, they are in the pooling window. You
need to use the scroll bar in the right hand panel to see the specific "Start Age"
column.

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Figure 6-6. All health incidence results added to the pooling window, with no pooling

(l) The "Main Pooling Window" has four places we could potentially pool the results
(indicated by the red arrows in Figure 6-6).

(m) Starting with the "Mortality" endpoint group, click on the "None" in the
corresponding Pooling Method column. A drop-down menu will appear that lists
all the possible pooling methods. Select the "Sum (Dependent)" method (Figure
6-7). This will cause the results from the Pope and Woodruff studies to be
summed together to create a single mortality result.

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Figure 6-7. Adding a pooling method for the mortality results

Background: In the mortality case, we are using Sum because the results from the two
studies are distinct from each other. The number of avoided adult mortalities (Pope) does
not overlap with the number of avoided infant mortalities (Woodruff)—i.e., they are
distinct age groups. See "Pooling Approaches" in the appendices.

(n) Now we will add pooling to the “Hospital Admissions, Respiratory” results. There
are two levels of pooling that can be done in this endpoint group, because it
contains multiple endpoints (“HA, Pneumonia” and “HA, Chronic Lung Disease”),
and one of those endpoints contains multiple results (“Ito” and “Moolgavkar”).
Starting with the bottom of the hierarchy, we will combine the "HA, Chronic Lung
Disease" endpoint's results ("Ito" and "Moolgavkar"). After combining those
results into a single result, we will take this new, pooled result and combine it with
the "HA, Pneumonia" endpoint to create a single, combined result for the whole

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endpoint group.

First, click the "None" corresponding to the "HA, Chronic Lung Disease"
endpoint. Select the "Random / Fixed Effects" pooling method from the
drop-down menu. This combines the two results into one pooled result for the
"HA, Chronic Lung Disease" endpoint.

Next, click the "None" next to "Hospital Admissions, Respiratory" endpoint

group. Select the "Sum (Dependent)" pooling method (Figure 6-8). With this step,
we have pooled the different endpoint results into one result for the endpoint
group.

Figure 6-8. Adding pooling methods for the hospital admission results

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Background: In calculating the combined HA chronic lung disease results, we are looking
at overlapping populations (same endpoint, same age range); therefore, we want to use
Random/Fixed Effects to combine their distributions. In contrast, when we pool the HA
endpoint group, we are looking at nonoverlapping populations: pneumonia versus chronic
lung disease (i.e., different endpoints). Therefore, we want to pool the pneumonia and
chronic lung disease distributions by doing a Sum. See "Pooling Approaches" in the
appendices.

(o) The "Random / Fixed Effects" pooling method has advanced settings. To access
these settings, double-click on the "Random / Fixed Effects" cell in the Pooling
Method column. This will bring up an Advanced Pooling Options window (Figure
6-9). There are multiple options for customizing this type of pooling (See the
user's guide for specifics). We will not change the existing settings in this window.
Click OK to close it.

Figure 6-9. Advanced Pooling Options window

(p) The "Acute Myocardial Infarction" endpoint group is the final group for which
pooling could be done. In this configuration, however, we will not pool the four
age-specific AMI results. Leaving the results unpooled will allow us to take
advantage of age-specific valuation functions in the next stage of the APV
configuration setup. In other words, we will have four separate AMI results to
value instead of one single, combined result. To not pool the results, leave the
"Pooling Method" for the AMI endpoint group as "None".

We have now finished setting up the health incidence results pooling, which is the
first of the four stages in creating valuation functions (see the stages list at the
beginning of Section 6). Your pooling window should look like Figure 6-8.

(q) Exercise (6.1): If you were going to pool the four AMI results, which pooling
method would you use? Why?

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Answer:

(r) Now we move on to the second stage of creating valuation functions: choosing the
specific valuation functions and pooling similar valuations. Click Next in the
Incidence Pooling and Aggregation window. This will open the Select Valuation
Methods, Pooling, and Aggregation window (Figure 6-10).

Figure 6-10. Select Valuation Methods, Pooling, and Aggregation window

(s) This window is where we will apply valuation functions to our health incidence
results and combine (pool) similar valuation results together. Before beginning, let
us look at the main features of this window. The "Valuation Methods" panel has
an expandable hierarchical tree that lists the available valuation functions, based

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on the incidence results in this configuration. The right-hand panel contains the
pooling windows that were defined in the previous step. In our case, there is only
one pooling window, "Main Pooling Window". If there had been three pooling
windows created in the previous health incidence pooling step, then we would
have three pooling windows in the Select Valuation Methods, Pooling, and
Aggregation window.

The "Variable DataSet" field at the top of the window defines specific variables
used in the valuation functions. The "Skip QALY Valuation" checkbox at the
bottom of the window determines whether or not we will configure and run QALY
(Quality Adjusted Life Years) functions. In our case we will not be calculating
QALY since we are interested in quantifying the benefits in dollars.

Background: In the context of air pollution benefit analysis, the QALY represents the
combined mortality and morbidity benefits of some air quality change. This combined
metric is calculated by counting: (1) the number of life years gained; (2) the number of life
years lived without some chronic condition. In step 2, the life years are weighted
according to the severity of the condition (the "quality" of that year), such that a year in
near perfect health might be counted as 0.9, but a year lived with chronic bronchitis might
be counted as 0.5.

(t) In the "Valuation Methods" panel, expand "EPA Standard Valuation Functions".
This will reveal the available endpoint groups. You can expand any endpoint
group to see the available endpoints within that group. In turn, you can expand a
specific endpoint so that you can see the specific valuation functions available for
that endpoint.

We will begin by expanding the "Chronic Bronchitis" endpoint group and

endpoint. You will see six COI (Cost Of Illness) and one WTP (Willingness To
Pay) functions. We will add the WTP function for average bronchitis severity ages
30 to 99. Click on the "WTP: average severity | 30-99" and drag it to the "Main
Pooling Window" to the "Chronic Bronchitis" endpoint group's row (Figure 6-11).
That is all it takes—you have added the first valuation function.

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Figure 6-11. Adding a valuation function for chronic bronchitis to the pooling window

Tip: By hovering your cursor over the valuation functions, you can read their full
names. If you drag and drop a function and nothing happens, then you probably
tried to drop it into the wrong endpoint. Retry with the correct endpoint.

(u) Next we will add a valuation function for acute respiratory symptoms. Under the
"Acute Respiratory Symptoms" endpoint group in the Valuation Methods column,
expand the "Minor Restricted Activity Days" endpoint. Add the WTP valuation
function for one day of lost work based on a contingent valuation (CV) study for
ages 18 to 99 by clicking on the "WTP: 1 day, CV studies| 18-99" function and
dragging it to the corresponding row in the "Main Pooling Window" (i.e. the
"Acute Respiratory Symptoms" endpoint group).

(v) Next we will add a valuation function for mortality. Under the "Mortality"
endpoint group, expand the "Mortality, All Cause" endpoint. Add the value of a
statistical life (VSL) function that ranges from $1-10 million with a normal

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distribution by clicking and dragging the function "VSL, based on range $1 to $10
million, normal distribution, | 0-99" to the pooling window (Figure 6-12).

Figure 6-12. Initial three valuation functions in the pooling window

Background: Recall that in Section 6.2(m), we pooled the two underlying mortality
results to make this single, combined result to which we have just assigned a valuation
function. Because we pooled the health incidence results, we need only one valuation
function to calculate the value of mortality. If we had not pooled the results, we would
need at least one valuation function for each of the mortality results. The same holds
true for the HA endpoint group (see next step).

(w) Under the "Hospital Admissions, Respiratory" endpoint group, expand the "HA,
All Respiratory" endpoint. Add the valuation function for cost of illness (COI)
medical costs and wage loss ages 65 to 99. Recall that in Section 6.2(n) we
combined the individual HA chronic lung disease and pneumonia results to create
a pooled result containing all respiratory results for ages 65 to 99.

(x)

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Tip: You can click Previous to return to the Incidence Pooling and Aggregation window
if you want to inspect the underlying health incidence results or the incidence pooling.
You will not lose your present valuation configuration. When you are done exploring the
incidence results, click Next to return to the Select Valuation Methods, Pooling, and
Aggregation window.

(y) For the rest of the endpoint groups, we will be adding multiple valuation functions
per group. Expand the "Emergency Room Visits, Respiratory" endpoint group and
then the "Emergency Room Visits, Asthma" endpoint. Add the COI Smith
valuation function. Repeat for the COI Standford study (Figure 6-13).

Note: A "None" appeared in the Pooling Method column across from the endpoint
group "Emergency Room Visits, Respiratory". Similar to the incidence pooling
window, this indicates that we could potentially pool these two valuation
functions. We will do this pooling in a later step.

Figure 6-13. Adding two emergency room visits valuation functions to the pooling

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window

(z) Next we will add valuation functions to the AMI health incidence results. We will
add age-specific valuation functions to each of the age-specific health incidence
results. To see the age-specific results, use the scroll bar for the pooling window to
pan until you can see the Start Age column.

In the “Valuation Methods” panel, expand "Acute Myocardial Infarction". We will

add two valuation functions per age range: one function by Russell and the other
by Wittels. We will use the COI function for 5 years of medical costs and 5 years
of wages loss with a 3% discount rate (DR). Add the valuation function "COI: 5
yrs med, 5 yrs wages, 3% DR, Russell (1998) | 25-44" to the AMI health incidence
result for ages 18 - 44 (i.e., start age = 18).

Repeat for "COI: 5 yrs med, 5 yrs wages, 3% DR, Wittels (1990) | 25-44" (Figure
614).

Note: As happened with the endpoint group "Emergency Room Visits,

Respiratory", “None” appeared in the Pooling Method column next to the 18 to 44
result. Again, this indicates that these two valuation functions could be pooled.

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Figure 6-14. Adding two age specific AMI valuation functions to the pooling window

Tip: If you mistakenly add the wrong valuation function, you can delete it by highlighting
the particular function in the right hand pooling window panel and clicking Delete on
your keyboard.

(aa) Continue to add one Russell and one Wittels function for each of the remaining
age ranges (i.e., 45-54, 55-64, and 65-99) (Figure 6-15).

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Figure 6-15. All valuation functions added to the pooling window

(ab) The "Main Pooling Window" now has six places we could potentially pool the
results (indicated by the red arrows in Figure 6-15). The pooling procedure is the
same as the one we used earlier in the Incidence Pooling and Aggregation
window.

(ac) Starting with the "Emergency Room Visits, Respiratory" endpoint group, click on
the "None" in the corresponding Pooling Method column. A drop-down menu will
appear that lists all the possible pooling methods. Select the "Subjective Weights"
method.

Background: You generally use subjective weights when you have overlapping
populations (same endpoint and same age range). Unlike the random/fixed effects method,
you explicitly determine the relative weights of the two (or more) distributions in
calculating the combined distribution. For example, if you want to emphasize one study
over another, you would give it a greater weight. We will assign these weights later, after
all pooling methods have been selected.

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(ad) For each of the AMI age ranges, we will pool together the Russell and Wittels
age-specific valuation functions. Click on the "None" for the start age of 18 in the
Pooling Method column (make sure that you are not selecting the "None" in the
row above this one, which is for the entire the endpoint group), then select
"Subjective Weights" (Figure 6-16).

Repeat this step for each of the other three age ranges, choosing "Subjective
Weights" in every case.

Figure 6-16. Adding “Subjective Weights” pooling to the specific AMI valuation
functions

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(ae) At this point we have combined the two valuations for each age range. Now we
want to “move up a level” in the hierarchy and combine the four age ranges. Click
the "None" in the same row as the AMI endpoint group, then select "Sum
(Dependent)" (Figure 6-17). This will create one valuation result for the entire
endpoint group.

Figure 6-17. Adding “Sum (Dependent)” pooling to the AMI endpoint group

(af) Finally, we need to set the specific weights to be used in the subjective weights
pooling methods. Double-click on any of the "Subjective Weight" pooling method
cells. The Select Subjective Weights window will open (Figure 6-18).

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The default weight for each of the component functions is 0.5, i.e., the valuation
functions are being weighted equally. We will leave the default weights for AMI's
four poolings.

For the emergency room (ER) pooling, we want to give more weight to the Smith
valuation function. Edit the Weights column so that the Smith function is 0.60 and
the Standford is 0.40. Click OK to set these weights and return to the Select
Valuation Methods, Pooling, and Aggregation window.

Figure 6-18. Changing the weights for “Subjective Weights” pooling of ER visits

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(ag) Exercise (6.2): Why did we use “Sum (Dependent)” pooling for the AMI endpoint
group instead of “Random/fixed Effects” pooling?

Answer:

(ah) At this point we have set up the pooling for health incidence results (Stage 1 in
creating valuation functions), and have set up the specific functions and the
pooling for similar valuations (Stage 2). Moving on to Stage 3, we need to set
some additional parameters for the valuation functions, and decide on the
aggregation levels for the health incidence results and the valuation results. We
will then save all these settings from the three stages as a configuration (apv).

In the Select Valuation Methods, Pooling, and Aggregation window, click the
Advanced button. This will open the APV Configuration Advanced Settings
window (Figure 6-19).

Under the "Aggregation and Pooling" tab, use the drop-down menus to select
"State" as the aggregation level for the incidence and valuation results. In other
words, the results will be aggregated from CMAQ 36 km grid cells to states
(minimum spatial unit).

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Figure 6-19. Advanced settings: Changing the aggregation level and the inflation dataset

(ai) Under the "Currency and Income" tab set the "Inflation DataSet" to "EPA Standard
Inflators" and make sure the "Currency Year" is set to 2000. Then, set the
"Income Growth Adjustment DataSet" to "Income Elasticity (3/21/2007). Change
the "Year" to 2020, the same year used in our aqg files created earlier in the
training. Then select all of the "Endpoint Groups" by clicking on the first group,
holding down the Shift key and clicking on the last group (Figure 6-20).

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Figure 6-20. Advanced settings: Setting the income growth adjustment parameters

(aj) Since, as noted earlier, we are not doing anything in this training with QALY
weights (the third tab in the window), click OK. This will return you to the Select
Valuation Methods, Pooling, and Aggregation window.

The last parameter you need to set is the "Variable DataSet" at the top of the
window. Use the drop-down menu to select "EPA Standard Variables" (Figure
6-21). Note: If you do not set the "Variable DataSet" you cannot save and run the
configuration (next step).

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Figure 6-21. Setting the variable dataset

Background: The variable dataset includes variables that are used in calculating the
valuation—for example, median income and average house size. Many of these variables
are provided at the county level.

(ak) When you have set up all the valuation functions and pooling as instructed above,
you are ready to move to Stage 4 of creating valuation results: saving the new
configuration file (apv) and generating the valuation results file (apvr).

Click Next. This will bring up a Save Aggregation, Pooling, and Valuation
Configuration window (Figure 6-22). We do want to save this new configuration
(so that it can be re-used), so click Save.

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This will bring up a Save As window. Under the "Configurations" folder, in the
"File name" field, type in the new configuration file name,
"PM25_RIA_2020_course_modified_state", and click Save.

Figure 6-22. Save Aggregation, Pooling, and Valuation Configuration window

(al) After the APV configuration is saved, you will be returned to the Save
Aggregation, Pooling, and Valuation Configuration window (Figure 6-22). Now
run the configuration by clicking OK. This will bring up another Save As window.
Here we will save the valuation results (apvr). Under the "Configuration Results"
folder, save the results as
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_state".

The calculation of the results will begin and a Progress window will appear. The
calculation of the results may take a few minutes. When the calculations are
finished, you will be returned to the main BenMAP window.

Tip: If you are not ready to run this configuration, click Cancel. If you generated a
configuration, at a later time you can open the configuration and run it to generate
valuation results at a later time.

Background: The process of creating an aggregation, pooling, and valuation configuration

(apv) is more restrictive than the process of creating a health incidence configuration (cfg)
(discussed in Section 5). If you change the number or type of health incidence results used
in an APV process, you have to re-create the health incidence pooling. If you change the
health incidence pooling, you have to re-create the valuation functions and pooling.

Analysis:
The rest of the exercises in Section 6.2 focus on analyzing the results of our BenMAP run.

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Specifically, we will look at the newly created aggregation, pooling, and valuation config­
uration file (apv) and results file (apvr). Recall from Section 5 that quality-assuring both
your configuration and your results is a good idea.
(a) First, we will use the audit trail to look at the newly created configuration file
(apv). From the main BenMAP window, click on the "Report" graphic in the
right-hand panel. Select the "Audit Trail Reports" in the Select Report Type
window and click OK. Under the "Configurations" folder, select the new
configuration, "PM25_RIA_2020_course_modified_state.apv" and click Open.
(b) Exercise (6.3): What is the income growth adjustment year? For the incidence
pooling, what are the pooling methods for the mortality and HA endpoint groups?
What is the pooling method and advanced pooling method for the "HA, Chronic
Lung Disease" endpoint? For the valuation pooling, what is the pooling method for
the ER and AMI endpoint groups? What is the population year? When you are
done with this exercise, click OK to close the Audit Trail Report window.

Answer:

(c) Using the "Tools" menu in the main BenMAP window, open a BenMAP GIS
window. Open the "APV Configuration Results (*.apvr)" and select the "Pooled
Incidence Results". Under the "Configuration Results" folder, open our newly
created file,
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_state.apvr
".

(d) In the Edit GIS Field Names window, provide more meaningful names for your
health incidence results then click OK. Here are some suggested names:
ChronBronc, ER, AcutResp, Mortality, HA, AMI18, AMI45, AMI55, AMI65.

Note: As you would expect, the individual results have been pooled together (for
example, the Pope and Woodruff results have been pooled into one mortality
result).

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(e) Exercise (6.4): What are the numbers of avoided mortalities in California,
Pennsylvania, and Illinois? How many acute respiratory symptoms were avoided
in the same states?

Answer:

(f) Exercise (6.5): Compare the AMI (heart attacks) for various age groups. What are
the maximum values for the AMI18 and AMI65 functions?

Answer:

(g) Next we will overlay a pooled valuation map for the same apvr. From the same
GIS window, open "APV Configuration Results (*.apvr)" and select "Pooled
Valuation Results". Under the "Configuration Results" folder, open our newly
created file,
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_state.apvr
".

(h) In the Edit GIS Field Names window, provide more meaningful names for your
valuation results. Some suggested names are ChronBronc, ER, AcutResp,
Mortality, HA, AMI.

(i) In the Valuation Sums Layer window, add a sum for mortality and morbidity. For
morbidity, check the following endpoint groups: chronic bronchitis, ER, acute
respiratory symptoms, HA, AMI. Use "Dependent" as the summation type.

Remember to edit the "GIS Field Name" to "morbidity" and "mortality",

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respectively. Make the "Control_PM25_RIA…(Pooled Valuation Results 0)" layer

the active layer; simply right-click on that layer and select "Move Up".

(j) Exercise (6.6): What are the monetized benefits for the avoided acute respiratory
symptoms in California, Pennsylvania, and Illinois? Now make the "Pooled
Valuation Results Sums" layer active. What are the monetized benefits for the
avoided morbidity events in the same states? What are the monetized benefits for
the avoided mortalities in the same states? In comparing your answers to those for
Exercise 6.5, what conclusion can you draw about the mortality valuation function
versus the acute respiratory symptoms valuation function? When you are done
with this exercise, close the GIS window.

Answer:

(k) Create a new report for our valuation results. From the main BenMAP window,
click on "Report" in the right-hand panel and then select the "Incidence and
Valuation Results: Raw; Aggregated and Pooled" type. Under the "Configuration
Results" folder, open our newly created file,
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_state.apvr
". For the result type, select "Pooled Valuation Results".

In the APV Configuration Results Report window (Figure 6-23), select the
"Endpoint Group" within the "Pooled Valuation Method Fields" panel. In the
"Results Fields" panel, uncheck the "Variance". In the "Display Options" panel,
reduce the "Digits After Decimal Point" to 0. The “Preview” panel in the bottom
half of this window will reflect your choices.

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Figure 6-23. Pooled valuation report.

(l) Now that you have chosen all the columns to include in your valuation results
report, you can save the report. From the APV Configuration Results Reports
window, type Ctrl-S. Under the "Reports" folder, save the file as
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_state_valu
e".

After the file has been saved, close the window by clicking Done. Use Windows
Explorer to navigate to the "Reports" folder. Double-click on the newly created
csv file and it should open in Excel.

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(m) Exercise (6.7): All of the following questions refer to California, FIPS code 6 (i.e.,
column = 6, row = 1). What is the point estimate of the monetized benefit for the
number of avoided AMIs? What is the estimate of the monetized benefit for AMIs
at the 0.5 percentile? What is the estimate at the 99.5 percentile? When you are
finished with this exercise, close the Excel window.

Answer:

A.1.6.2 Example: PM2.5 Control 2020 14/35 Adjusted

The goal of this exercise is to re-use our newly created aggregation, pooling, and valuation
configuration (apv) (Section 6.2) and produce valuation results for the adjusted control
scenario RIA 2020 14 annual, 35 daily µg/m3.
Procedures:
(a)In the main BenMAP window, click on the graphic titled "Pooling, Aggregation, and
Valuation" in the right-hand panel. This will open the APV Configuration Creation
Method window

(a)In this window, select "Open Existing Configuration file for Aggregation, Pooling, and
Valuation". Under the "Configurations" folder, select the newly created configuration
"PM25_RIA_2020_course_modified_state.apv" and click Open.

(a)In the Incidence Pooling and Aggregation window that opens, we will change the input
health incidence file (cfgr). Click the Browse button next to the "Configuration Results
File Name(s)" field. Under the "Configuration Results" folder, select the health
incidence file
“Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_adjusted.cfgr”.

(a)Review your health incidence pooling window, "Main Pooling Window". The pooling
configuration should be identical to our previous example (see Figure 6-8).

(a)Click Next. The Select Valuation Methods, Pooling, and Aggregation window will
appear. Review your valuation functions and pooling. The configuration should be
identical to our previous example (see Figure 6-17). Click on Advanced to confirm that
these settings are the same as before (see Figure 6-19 and Figure 6-20). When you are
done reviewing the configuration, click Next.

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(a)Do not save the configuration. There is no need to save since the only change was to
the health incidence results file (cfgr). Do create the valuation results (apvr) by clicking
OK. Under the "Configuration Results" folder, save the results as
"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_state_adjusted"
.

The calculation of the results will begin and a Progress window will appear. The
calculation may take a few minutes.

Analysis: Now we will look at the newly created aggregation, pooling, and valuation results
file (apvr).

(a)Open an audit trail for the new valuation results file,

"Control_PM25_RIA_2020_modified_cmaq_grid_14_annual_35_daily_state_adjusted.apvr".

(a)Exercise (6.8): What is the population year used in this apvr? What are the weights
used for pooling the two ER valuation functions?

Answer:

(a)Open a BenMAP GIS window, then open the same valuation results file (apvr). Map the
"Pooled Incidence Results".

(a)Exercise (6.9): What are the numbers of avoided mortalities in California,

Pennsylvania, and Illinois? How many acute respiratory symptoms were avoided in the
same states? How do these results compare to the nonadjusted results (see Exercise
6.4)?

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Answer:

(a)Overlay the "Pooled Valuation Results" for the same apvr. Edit the GIS field names. In
the Valuation Sums Layer window, create sums for morbidity and mortality the same
way you did above Exercise 6.6. Make the "Control_PM25_RIA…(Pooled Valuation
Results 0)" layer the active layer.

(a)Exercise (6.10): What are the monetized benefits for the avoided acute respiratory
symptoms in California, Pennsylvania, and Illinois? Now make the "Pooled Valuation
Results Sums" layer active. What are the monetized benefits for the avoided morbidity
events in the same states? What are the monetized benefits for the avoided mortalities in
the same states? How do these results compare to the nonadjusted results (see Exercise
6.6)? When you are done with this exercise, close the GIS window.

Answer:

(a)Create a new report for the valuation results file. After selecting the report type and
opening the file, you should select the results type, "Pooled Valuation Results".

In the APV Configuration Results Report window, select the "Endpoint Group"
within the "Pooled Valuation Method Fields" panel. In the "Results Fields" panel,
uncheck the "Variance". In the "Display Options" panel, reduce the "Digits After
Decimal Point" to 0.

Under the "Reports" folder, save the file as "Control_PM25_RIA_2020_modified_

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cmaq_grid_14_annual_35_daily_state_adjusted_value". Open the csv file in Excel.

(a)Exercise (6.11): All of the following questions refer to California, FIPS code 6 (i.e.,.
column = 6, row = 1). What is the point estimate of the monetized benefit for the
number of avoided AMIs? What is the estimate of the monetized benefit for AMIs at the
0.5 percentile? What is the estimate at the 99.5 percentile? How do these results
compare to the nonadjusted results (see Exercise 6.7)? When you are finished with this
exercise, close the Excel window.

Answer:

A.1.6.3 Example: Modifying One-Step Analysis Parameters

The goal of this exercise is to modify the One-Step Analysis to use our newly created
health incidence and aggregation, pooling, and valuation configurations.
Procedures:
(a)From the main BenMAP window, select "One Step Analysis" from the "Parameters"
menu (Figure 6-24).

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Figure 6-24. Parameters menu in the main BenMAP window.

(a)This will open the One Step Setup Parameters window (Figure 6-25). Here you can
select the health incidence (cfg) and valuation configuration (apv) files that will be used
in the One-Step Analysis approach.

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Figure 6-25. Modifying configurations for One-Step Analysis

(a)Select "PM 2.5" from the Pollutant drop-down menu. Click the Browse button to the
right of the CFG File Name box. In the Open window, under the "Configurations"
folder, select "PM25_RIA_2020_course_modified.cfg" and click Open. This will return
you to One Step Setup Parameters window.

Click the Browse button to the right of the APV File Name box, so that you can
select the new aggregation, pooling, and valuation configuration. In the Open
window, under the "Configurations" folder, select
"PM25_RIA_2020_course_modified_state.apv" and click Open. This will again
return us to One Step Setup Parameters window.

We have the option of changing the currency year, but in our case leave the
"Currency Year" as 2000. Finally, click Save. The next time you run One-Step
Analysis, it will use these new configurations.

(a)This completes the “Aggregation, Pooling, and Valuation” lab. In the next lab, "Adding
New Datasets & Independent Study", we will add the necessary data to do a
metropolitan scale analysis of Detroit. After adding the new datasets, we will use our
new configurations (from Sections 5 and 6) to create health incidence and valuation
results for our new domain.
A.1.7 Section 7. Adding New Datasets & Independent Study
In this section, you will add new datasets to BenMAP and run a local-scale benefit analysis

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in Detroit, Michigan.
BenMAP contains pre-loaded data necessary to perform a health impact assessment that
will meet most users’ analytical needs. However, you can also import your own datasets
into BenMAP when the pre-loaded datasets are not adequate for your analysis. For
example, you can add new population datasets, new grid definitions, new health impact
and valuation functions, and new background incidence rates for specific health endpoints.
If you decide to conduct either a local-scale analysis or a non-U.S. analysis, you will likely
need to add new datasets to model the benefits and adequately reflect those local factors. In
other words, the U.S. national datasets may not be the best available data or functions for
your study.
In this section, you will add new datasets to conduct an entire benefit analysis for a change
in air quality in the Detroit metropolitan area. Below are a few key aspects of the analysis:
 Our model area is the greater Detroit metropolitan area, partially covering three counties:
Wayne, Oakland, and Macomb.
 The air quality grid cells are 1 km by 1 km.
 The air quality model data are for 2020.
 The control scenario models a 14.5 µg/m3 annual PM2.5 standard for the core of the
metropolitan region.
Unlike our previous national studies, this lesson uses a finer-resolution grid,
Detroit-specific population data, and Detroit-specific background incidence rates for
hospital admissions due to asthma.

A.1.7.1 Example: Adding Datasets for Detroit

The goal of this exercise is to add the necessary datasets so that we can conduct a
local-scale analysis in Detroit. Specifically, we will add a new 1-km grid definition, a new
population dataset for Detroit, and new background incidence for asthma hospital
admissions for Detroit.
Procedures:
(a)From the main BenMAP window, select "Modify Setup" from the Tools menu (Figure
7-1).

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Figure 7-1. Choosing “Modify Setup”

(b)This will open the Manage Setup window (Figure 7-2). Through this window, you can
modify many of the datasets, parameters, and functions used in BenMAP. Specifically,
you can add to or change any of the following 11 categories of data: grid definitions,
pollutants, monitor datasets, incidence/prevalence datasets, population datasets, C-R
function datasets, variable datasets, inflation datasets, valuation datasets, income growth
adjustments, and QALY distribution datasets. To modify any one of these, you can click
the Edit button below the appropriate list.

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Figure 7-2. Manage Setup window

(c)We will start by adding a new grid definition. Click Edit below the Grid Definitions
list. This will open the Manage Grid Definitions window (Figure 7-3). Here you can add
new grid definitions or you can delete or edit existing grid definitions.

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Figure 7-3. Manage Grid Definitions window

Tip: You can use the Edit button to view other grid definitions. Simply highlight the
particular grid in the Available Grid Definitions list and click Edit. Make sure you do not
accidentally save any changes while you are viewing the definition. You can use this
same technique to view other datasets that have already been loaded (e.g., "Pollutants").

(d)We will add a new grid definition for Detroit. In the Manage Grid Definitions window,
click the Add button. This will open a Grid Definition window (Figure 7-4). Here we
can define our new grid.

Note: When adding a series of new datasets, you should generally load the new
grid definition first. Adding other datasets (e.g. adding population data) will
typically depend on the new grid definition.

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Figure 7-4. Grid Definition window

(e)We will define the new grid based on an ESRI shapefile. First, we will set the name of
the new grid. Edit the Grid ID field by changing the text to "Detroit CMAQ 1km".

Next we load our shapefile. Click the "Shapefile Grid" tab. Next to the Load
Shapefile field, click the browse button. Under the folder "Inputs" and the
subfolder "Detroit", select the file "Detroit_grid.shp" and click Open. This will
return you to the Grid Definition window.

Click Preview to view your new grid (Figure 7-5).

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Figure 7-5. Loading and previewing the Detroit CMAQ 1km grid

(f) Click OK. This will return you to the Manage Grid Definitions window. Scroll through
the list of available grid definitions to confirm that your new grid is included then click
OK. This will return you to the Manage Setup window. Note: It may take a minute or
two to complete the loading of the new grid (indicated by the Manage Setup window
becoming active again).

Confirm that the new definition is in the Manage Setup window’s grid definitions
list. If it is, then you have successfully added a new grid definition.

(g)Next we will add a new background incidence rates dataset. This new dataset will have
specific rates for Detroit instead of national averages. However, for the purposes of this
lesson, the dataset will include only the "HA, Asthma" endpoint. Click Edit below the
Incidence/Prevalence DataSets list. This will open the Manage Incidence DataSets
window (Figure 7-6). Here you can add new background incidence rates datasets or you
can delete or edit existing background incidence rates datasets.

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Figure 7-6. Manage Incidence DataSets window

(h)Click the Add button. This will open an Incidence DataSet Definition window (Figure
7-7) that we will use to define our new background incidence rates dataset.

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Figure 7-7. Incidence DataSet Definition window

(i) Edit the DataSet Name field by changing the text to "2004 HA Incidence Detroit". Click
the Load From Database button. This will open a Load Incidence/Prevalence DataSets
window. Using the Grid Definition drop-down menu, select the "Detroit CMAQ 1km"
grid definition (Figure 7-8).

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Figure 7-8. Load Incidence/Prevalence Database window

(j) Next to the Database field, click Browse. In the new Open window, set the Files of type
to "Excel Files". Under the folder "Inputs" and the subfolder "Detroit", select the file
"background_incidence_Detroit" and click Open.

(k)This will open a Select a Table window. Here you will select the particular Excel sheet
(within the Excel file) that contains the new background incidences rates data Using the
drop-down menu, select "Sheet1$" (Figure 7-9)

Figure 7-9. Select a Table window

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(l) Click OK. This will return you to the Load Incidence/Prevalence Database window.
Click OK in that window to return to the Incidence Dataset Definitions window, where
fields have now been filled in from the dataset you loaded. Explore some of the
background incidence rates by highlighting various age ranges in the "DataSets
Incidence Rates" panel and using the scrollbar in the right-hand panel (Figure 7-10).

Figure 7-10. Loading and viewing the Detroit background incidence rates

(m)Click OK. This will return you to the Manage Incidence DataSets window. Scroll
through the list of available datasets to confirm that your new background incidence
rates dataset is included, then click OK. This will return you to the Manage Setup
window. Note: It may take a minute or two to complete the loading of the new dataset
(indicated by the Manage Setup window becoming active again).

Confirm that the new dataset is in the Manage Setup window’s incidence/prevalence
datasets list. If it is, then you have successfully added a new background incidence rates
dataset.

(n)Next we will add a new population dataset. This new dataset will have more specific
population information for the Detroit area than the national datasets. Click Edit below
the Population DataSets list. This will open the Manage Population DataSets window
(Figure 7-11). Here you can add new population datasets or you can delete (but not edit)
existing population datasets.

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Note: The population datasets are relatively large, so it may take a few minutes to
display each of the windows discussed here.

Figure 7-11. Manage Population DataSets window

(o)Click the Add button. This will open a Load Population DataSet window (Figure 712).

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Figure 7-12. Load Population DataSet window

(p)Edit the Population DataSet Name field by changing the text to "Detroit CMAQ 1km".
In the Population Configuration field, use the drop-down menu to select "United States
Census". For the Grid Definition field, use the drop-down menu to select "Detroit
CMAQ 1km".

Background: The “Population Configuration” defines the age range, race, and
gender variables in your population database. It is critical that the definitions in the
population configuration match those used in the development of the database.

(q)Next to the Database field, click the Browse button. In the new Open window, set the
Files of type to "Text Files". Under the folder "Inputs" and the subfolder "Detroit",
select the file "Detroit_Pop" and click Open. This will return you to the Load
Population DataSet window (Figure 7-13).

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Figure 7-13. Setting the population configuration and the grid definition

(r) Click OK. A Progress window will appear. It will take a few minutes to load the
population dataset. When it is loaded, you will be returned to the Manage Population
DataSets window, where the fields have now been filled in from the dataset you loaded.
Explore your new population dataset by highlighting "Detroit CMAQ 1km" in the
Available DataSets list and using the horizontal and vertical scrollbars on the right-hand
panel (Figure 7-14).

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Figure 7-14. Loading and viewing the Detroit population dataset

(s)Click OK. This will return you to the Manage Setup window. Note: It may take a
minute or two to complete the loading of the new dataset (indicated by the Manage
Setup window becoming active again). Confirm that the new dataset is in the Manage
Setup window's population datasets list. If it is, then you have successfully added a new
population dataset.

(t) You have now finished adding the necessary datasets for our Detroit study. From the
Manage Setup window, click OK. This will return you to the main BenMAP window.

Analysis:
The rest of Section 7.2 focuses on analyzing one of the new datasets for Detroit.

(a)We will focus on the new population data for Detroit. Using the "Tools" menu in the
main BenMAP window, open a BenMAP GIS window. Open the "Population" dataset
(Figure 7-15).

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Figure 7-15. Mapping population data

(b)This will open a Select Population Data window. Using the drop-down menus, select
"Detroit CMAQ 1km" as the population dataset and 2020 as the population year (Figure
7-16). Click OK. A Progress window will appear. It may take a few minutes for your
population data layer to appear in the "Layers" panel.

Figure 7-16. Select Population Data window

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(c)Display the population data for African-American females, ages 30 to 34

(B_F_30TO34).

Select the "Detroit CMAQ 1km" as the reference layer. Now, change the reference
layer to the county grid. This will automatically zoom out to the national domain.
Zoom back in to the Detroit area (Figure 7-17).

Figure 7-17. Detroit study area

Background: The following are example demographic codes in the Detroit dataset:
N_M_40TO44 = Native American male 40 to 44 years; B_F_50TO54 =
African-American female 50 to 54 years; A_M_60TO64 = Asian-American male 60
to 64 years; W_F_50TO54 = white female 50 to 54 years; O_M_1TO4 = other male
1 to 4 years.

(d)Exercise (7.1): Compare the different demographics from the Detroit population
dataset. How does the spatial pattern of African-American females 30 to 34 differ from
the spatial pattern of white females 30 to 34?

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Answer:

A.1.7.2 Independent Study: Detroit Benefits Analysis

The goal of this exercise is to model the health effects and the subsequent monetized
benefits of a change in air pollution (PM2.5 concentrations) for the Detroit region.
Procedures:
The following steps should be thought of as general guidance on how to complete the
Detroit benefit analysis. Unlike the earlier labs, this lab does not give detailed instructions
on how to complete each stage of the model run and analysis for the Detroit study. If
needed, you may refer to previous labs for more detailed instructions on specific steps.

(a) Create a baseline and control aqg from the corresponding model data. You will
find two model datasets in the "Detroit" subfolder under the "Inputs" folder. Both
datasets are for the 2020 model year and are on the "Detroit CMAQ 1km" grid.
The control scenario has some areas reduced to 14.5 µg/m3 annual average PM2.5
concentrations. Be sure to clearly name your files so that you know which file is
the control and which is the baseline.

(b) Open and modify the health incidence configuration created in Section 5. Change
the population dataset to your new Detroit population dataset. Change the baseline
and control to your Detroit baseline and control.

Add a new function for the "HA, Asthma" endpoint (no threshold). Set the new
"HA, Asthma" function’s incidence rate to the Detroit-specific background
incidence rates dataset. Save a new health incidence configuration and create a
results file.

(c) Re-create the apv configuration (from Section 6) using your new Detroit health
incidence results. Because we are adding a new incidence endpoint, you will have
to start from scratch (see Figures 6-8, 6-19, 6-20, and 6-21 for reference). Include
the new "HA, Asthma" incidence result in your "Hospital Admission, Respiratory"
pooling.

In selecting the valuation function for "Hospital Admissions, Respiratory", take

into account your new age range for your pooled results (i.e., look at the age
ranges of the health impact functions that make up the pooled result). Aggregate
your health incidence and valuation results to the county level. Save the apv

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configuration and create a results file. This completes the modeling portion of the
Detroit study.

Analysis:
We provide a series of exercises to guide your analysis of the results from the Detroit
study.

(a) Exercise (7.2): What pooling type did you use to combine "HA, Pneumonia",
"HA, Asthma", and "HA, Chronic Lung Disease" together? Why?

Answer:

(b) Exercise (7.3): Compare the total adult population (30-99) from the mortality
incidence to the demographic population (Exercise 7.1). How does the “total”
population’s spatial pattern differ from the patterns for the two demographics
(African-American females ages 30 to 34 and white females ages 30 to 34)?

Answer:

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(c) Exercise (7.4): Why are the aggregated incidence results a significant
underestimate of the total change in incidence for the three counties? Hint: look at
the extent of the nonaggregated domain.

Answer:

(d) Exercise (7.5): What is the total (over the three counties) monetized value for
avoided premature mortalities? What is the total monetized value for avoided
acute respiratory symptoms? What are the total health incidence results for these
two endpoints?

Answer:

(e) Exercise (7.6): Answer the following questions using the totals for each county:
What are number of "Hospital Admissions, Respiratory" avoided? What are the
number of "HA, Asthma" avoided? What is the background incidence for "HA,
Asthma"?

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Answer:

(f) Exercise (7.7): What is the total (summed over endpoints) monetized benefit for
each county? Give the mean and confidence intervals (0.5th and 99.5th percentiles).

Answer:

Synthesis Questions:
The following questions are meant to help you synthesize what you have learned as you
have worked through the entire body of BenMAP course material. They draw from
multiple labs and course slides.

(a) Exercise (7.8): Would you expect the benefits to increase or decrease if you used a
later population year? Why?

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Answer:

(b) Exercise (7.9): Would you expect the monetized benefits to be higher or lower if
you used a later currency year? Why?

Answer:

(c) Exercise (7.10): Why might your results differ if you used a national incidence
baseline instead of a local incidence baseline for the "HA, Asthma" endpoint?

Answer:

(d) Exercise (7.11): If some of the health incidence results extended beyond the
analysis year (in our case, 2020), should we discount these monetized benefits?

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Answer:

(e) Exercise (7.12): Unlike in our configuration, EPA generally uses more than one
study to model adult mortality. They also do not tend to pool their mortality
results. Why might you not want to pool adult mortality and instead report a range
for your incidence results?

Answer:

(f) Exercise (7.13): Is BenMAP better suited to perform national (large-scale)

analyses or local (urban-scale) analyses? Why?

Answer:

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(g) Exercise (7.14): What are some of the benefits of reducing air pollution that
BenMAP does not currently quantify?

Answer:

(h) Exercise (7.15): Do you think that valuation estimates would be higher if we used
willingness-to-pay (WTP) studies or cost-of-illness (COI) studies?

Answer:

(i) Exercise (7.16): What are some of the sources of uncertainty in a BenMAP
analysis?

Answer:

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A.1.8 Answers to Training Exercises

Section 2 Answers
(2.1) D24HourMean = 10.56 µg/m3; QuarterlyMean =10.44 µg/m3; lat/lon = (47.35, -68.32).

(2.2) States of Alabama, California, Georgia, Illinois, Michigan, Pennsylvania, Ohio,

Tennessee

(2.3) QuarterlyMean maximum = 28.32 µg/m3; minimum = 2.76 µg/m3

(2.4) D8HourMax maximum = 67.68 ppb; minimum = 17.19 ppb

States of Arizona, California, South Carolina, Tennessee, Utah.

(2.5) No, because the CMAQ grid is a regular grid, whereas the state and other political
grids have irregular borders.

(2.6) States of California, Montana, Oregon.

(2.7) The age range is 30 to 99 years.

(2.8) States of California, Oregon, Pennsylvania, Washington.

(2.9) The number of acute respiratory symptoms avoided is much greater than the number
of mortalities avoided.

(2.10) Because the health incidence values are a function of both delta and population.
Therefore, a high delta in a low population area will still have a small health incidence
change. In contrast, a relatively low delta in a high population area may have a large
health incidence change—in other words, significantly fewer people having that health
incidence.

(2.11) Incidence of mortality: 213; incidence of acute respiratory symptoms: 188,303.

Valuation of mortality: $1.4 billion; valuation of morbidity $66 million.
This means that even though there are far fewer mortalities, they are valued at a much
higher rate than the morbidity incidences (as one would expect).

(2.12) Population year 2020.

CMAQ 36 km

(2.13) 0-17 years.

Norris, G., et al.

Section 3 Answers
(3.1) States of Arizona, California, Idaho, Maryland, Montana, Nevada, Ohio, Oregon,

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Pennsylvania, Utah, Washington, West Virginia, Wyoming.

(3.2) No, because the C-R functions are based on deltas and population. The human
population in the ocean is 0, so both the incidence and valuation over the ocean will be
0.

(3.3) Initially: County, State, Report_regions, and Nation grids.

After setting Incidence to State, grids at the same scale or coarser are then available.

(3.4) endpoint = Mortality, All Cause

author = Pope et al.
incidence aggregation = valuation aggregation = County

(3.5) The CMAQ 36km Nation Overlap grid.

Because aggregation occurs in the valuation step, the aggregated health incidence data
is in the apvr file, not the cfgr file.

(3.6) States of California, Washington, Oregon, Utah, Michigan, Ohio, Pennsylvania, New
Jersey, New York, Maryland, and Virginia.

(3.7) The County grid.

(3.8) State code = 6, FIPS code = 37 (Los Angeles County); avoided mortalities = 132.76

(3.9) health incidence maximum = 66.68; sum = 1707.67

pooled incidence maximum = 132.76; sum = 1707.67

(3.10) State code = 6, FIPS code = 37 (Los Angeles County); mortality = $876 million;
morbidity = $38 million
National mortality: $11.27 billion; National morbidity: $403 million.

(3.11) For col 1, row 9, mortality has the greatest standard deviation = 247,031
Chronic bronchitis has the greatest coefficient of variation = 16.587/13,520 = 1.23

(3.12) The delta for the 14/35 analysis is significantly larger. For example, a larger portion
of the states have more than 0.2 µg/m3difference.

(3.13) Illinois: 227 mortality for 14/35 scenario, 3.75 mortality for 15/35 scenario.
California: 559 mortality for 14/35 scenario, 573 mortality for 15/35 scenario.
Overall, the 14/35 scenario has more states showing significant numbers of avoided
mortalities, especially in the East, whereas the 15/35 scenario has some western states
with slightly greater reductions (e.g., California, Oregon, Washington). Total number
of mortalities avoided for the lower 48 states is 4,787 for the 14/35 scenario and 1,707
for the 15/35 scenario.

(3.14) California: $3.69 billion saved in prevented mortality, $147 million saved in prevented
morbidity.

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Illinois: $1.5 billion saved in prevented mortality, $50 million saved in prevented
morbidity.
$31.6 billion mortality and $1.1 billion morbidity for the 14/35 scenario versus $11.2
billion mortality and $403 million morbidity for the 15/35 scenario. In other words,
our intuition was correct that the 14/35 scenario had higher benefits than the 15/35
scenario.

Section 4 Answers
(4.1) The adjusted aqg's have no values greater than 15 µg/m3. In comparison, the
non-adjusted aqg's do have regions with annual values greater than 15 µg/m3.

(4.2) The VNA AQG is much smoother, because it uses distance weighting to smooth the
AQG between monitor locations.

(4.3) Neighbor scaling type = inverse distance;

Rollback region = California (6), Oregon (41), Pennsylvania (42), and Washington
(53);
Rollback method = percentage, the percentage of rollback = 0.1 (i.e. 10%)

(4.4) California, Ohio, West Virginia, Maryland, Georgia, and Alabama.

(4.5) Region 1: using peak shaving for inter and intraday rollback. Rolling back to a
standard (attainment test) of 35 µg/m3 on the D24HourMean metric and an ordinality
of 1.
Region2: using incremental rollback, reducing all monitors by an increment of 4 µg/m3
.

(4.6) The Western states have a generally constant delta. This makes sense because we
applied an incremental change (a constant reduction) to all the monitors in the region.
In contrast, the East Coast has been reduced to a standard. Therefore, only areas that
were over the standard (35 µg/m3 daily mean) will be reduced. We see that the most
significant changes are in Pennsylvania and to a lesser degree in Georgia.
If we look at the eastern edge of the West coast states, we notice that the delta is not
constant across each state. Initially, we might expect the deltas to be constant across
the state, because we applied an incremental change to all the monitors. However, the
AQG is the result of interpolating from the monitors to the grid cells. Therefore, on
the eastern edge we are interpolating between monitors that did have a rollback and
those areas that had no change.

Section 5 Answers
(5.1) QuarterlyMean maximum = 1.67 µg/m3.
QuarterlyMean mean = 0.11 µg/m3 (misleading because includes model domain over
the ocean).

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Washington, California, Oregon, Georgia, Pennsylvania, West Virginia.

(5.2) Two functions.

Both functions are by Norris.
Differences include a qualifier (10 µg/m3 threshold), Beta and P1Beta (standard
deviation), and C (C=10 for the threshold function).

(5.3) Endpoint: "HA, Chronic Lung Disease (less Asthma)". "HA, Chronic Lung Disease",
HA, Pneumonia", "HA, Asthma".
Four functions: two by Ito and two by Moolgavkar.

(5.4) Pope.
Three functions are by Pope.
The three functions have different thresholds (0, 7.5, and 10 µg/m3).
The current configuration uses the 0 µg/m3 threshold Pope function.

(5.5) Pope age range 30-99 years, Woodruff age range 0-0 years.
 1 
1   Q   In c P o p
Pope function =  e 
 1 
1    In c P o p
 1  In ce  Q  In c
Woodruff function =

(5.6) Ito and Moolgavkar have the same functional form.

Ito's β = 0.001169.
Moolgavkar's β = 0.00183.
Bonus: Moolgavkar is more sensitive to changes in AQ. An equal change in AQ will
result in a larger change in the health incidence from Moolgavkar's function compared
1
 Q
to Ito's function. Mathematically, the larger β, the smaller the value of e , and
hence the larger the value of the whole function.

(5.7) Population year = 2020.

12 Concentration-Response (C-R) functions.
Woodruff location is 86 cities and incidence dataset is 2020 Mortality Incidence Rates

(5.8) Pope maximum = 66.78 premature deaths (ages 30-99) avoided.

Woodruff maximum = 0.15 premature deaths (infant) avoided.
Similar but not the exact same spatial patterns.

(5.9) Ito maximum = 3.01.

Moolgavkar maximum = 4.73.
Moolgavkar population is the same as the Ito population.
They have identical inputs. The only difference between the two functions is the β;
therefore, the Moolgavkar study is more sensitive to changes in AQ.

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(5.10) AMI18 maximum = 3.63, population maximum = 2,434,707.

AMI65 maximum = 65.36, population maximum = 988,819.
Although the population for the 18-44 group is much greater than the population for
the 65-99 group and the functions are the same, the incidence results are much smaller
for the 18-44 age group. This implies that the incidence rate for younger group is
much smaller than the incidence rate for the older group. This result reflects our
intuition.

(5.11) baseline = 5,452.946.

point estimate = 4.7457.
5th percentile = 4.0085.
95th percentile = 5.4827.

(5.12) QuarterlyMean maximum = 4.56 µg/m3.

QuarterlyMean mean = 0.32 µg/m3.
California, Washington, Oregon, Idaho, Wyoming, Montana, Utah, Pennsylvania,
West Virginia.
Compared to Exercise 5.1, the adjusted control has much larger AQ delta values and
larger geographic areas of significant delta, especially in the West.
The adjusted scenario should have a significantly larger change in adverse health
effects because it has a significantly larger change in AQ.

(5.13) Population year = 2020.

12 CR functions.
Number of Latin Hypercube Points = 10.

(5.14) Pope maximum = 196.13.

Woodruff maximum = 0.52.
The adjusted results are greater than the nonadjusted results.

(5.15) AMI18 maximum = 11.13, population maximum = 2,434,707.

AMI65 maximum = 189.75, population maximum = 988,819.
The adjusted results are greater than the nonadjusted results. The adjusted population
is equal to the nonadjusted population. There was also a change in spatial pattern. For
the adjusted results, most of the significant results are in the West.

(5.16) baseline = 5452.946.

point estimate = 11.302.
5th percentile = 9.5474.
95th percentile = 13.0561.
The adjusted baseline equals the nonadjusted baseline. The adjusted mean is greater
than the nonadjusted mean. The adjusted statistical spread and values are greater than
the nonadjusted statistical spread and values.

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Section 6 Answers
(6.1) Sum (Dependent) because the health incidence populations are nonoverlapping
(distinct age groups).

(6.2) We used Sum (Dependent) because the four AMI valuation results are for
nonoverlapping populations (distinct age groups).

(6.3) Income growth adjustment year = 2020.

HA pooling and mortality pooling both use Sum (Dependent).
HA Chronic Lung Disease pooling uses Random / Fixed Effects, with advanced
pooling using round weight to two digits.
ER endpoint group valuation pooling = Subjective Weights
AMI endpoint group valuation pooling = Sum (Dependent)
Population year = 2020.

(6.4) California mortalities = 560, acute respiratory symptoms = 503,139.

Pennsylvania mortalities = 342, acute respiratory symptoms = 184,340.
Illinois mortalities = 227, acute respiratory symptoms = 163,566.

(6.5) AMI18 maximum = 30.

AMI65 maximum = 555.

6.6) California acute respiratory = $25.4 million, morbidity = $289.6 million,

mortality = $3.7 billion.
Pennsylvania acute respiratory = $9.3 million, morbidity = $141.6 million,
mortality = $2.3 billion.
Illinois acute respiratory = $8.3 million, morbidity = $106.1 million,
mortality = $1.5 billion.
The mortality incidence numbers are far smaller than the acute respiratory symptom
numbers, but the mortality valuation is far greater than the acute respiratory valuation.
Therefore, the mortality valuation function (VSL) must be much larger than the acute
respiratory symptoms function.

(6.7) AMI point estimate = $79.3 million.

0.5th percentile = $14.6 million.
99.5th percentile = $193.5 million.

(6.8) Population year = 2020.

Smith subjective weight = 0.60, Standford subjective weight = 0.40.

(6.9) California mortalities = 2,295, acute respiratory symptoms = 2.1 million.

Pennsylvania mortalities = 365, acute respiratory symptoms = 196,460.
Illinois mortalities = 231, acute respiratory symptoms = 166,252.
The adjusted health incidence results are greater than the nonadjusted results,
especially in the West.

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6.10) California acute respiratory = $107.2 million, morbidity = $1.19 billion,

mortality = $15.15 billion.
Pennsylvania acute respiratory. = $9.9 million, morbidity = $151 million,
mortality = $2.41 billion.
Illinois acute respiratory = $8.4 million, morbidity = $108 million,
mortality = $1.53 billion.
The adjusted valuation results are greater than the nonadjusted results, especially in
the West.

(6.11) AMI point estimate = $320 million.

0.5th percentile = $59.7 million.
99.5th percentile = $772 million.
The adjusted mean is greater than the nonadjusted mean. The adjusted statistical
spread and values are greater than the nonadjusted statistical spread and values.

Section 7 Answers
(7.1) African-American females age 30-34 are concentrated in the central and eastern band
of our domain (Northern Wayne Co.). White females age 30-34 are more concentrated
in the northern (southern Oakland and Macomb Co.) and southwestern (central Wayne
Co.) parts of our domain.

(7.2) We used sum (dependent) to combine together the various "HA" endpoints. We used
random/fixed effects to combine together the Ito and Moolgavkar "HA, Chronic Lung
Disease" results into one result. The sum (dependent) pooling makes sense for the
three endpoints because the populations are distinct, nonoverlapping. On the other
hand, the two "HA, Chronic Lung Disease" results are for an overlapping population;
therefore, the random/fixed effects pooling is appropriate.

(7.3) The spatial pattern of total adult population is more spatially homogeneous than the
pattern of the demographic data. It appears to be more similar to the combination of
the African-American female and white female spatial patterns than to either of the
individual demographic patterns.

(7.4) The aggregated incidence results are a significant underestimate of the total change in
incidence for the three counties because the "Detroit CMAQ 1km" grid does not cover
the entire spatial extent of the three counties. In other words, we are characterizing the
whole county's incidence change based on a subset of the county, i.e., based on a
subset of the population.

(7.5) Total monetized mortality benefit = $1.75 billion

Total monetized acute respiratory symptoms benefit = $8.64 million
Total mortality incidence results = 264
Total acute respiratory symptoms results = 170,868

(7.6) Macomb (FIPS 99):"HA, Respiratory " = 9.4, "HA, Asthma" = 0.85, "HA, Asthma"

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baseline = 201.3
Oakland (FIPS 125): "HA, Respiratory " = 35.6, "HA, Asthma" = 3.77, "HA, Asthma"
baseline = 608.3
Wayne (FIPS 163): "HA, Respiratory " = 115.0, "HA, Asthma" = 36.5, "HA, Asthma"
baseline = 3,954.3

(7.7) Macomb (FIPS 99) total monetized benefit: mean = $119 million, 0.5th = -$7.68
million, 99.5th = $347 million
Oakland (FIPS 125) total monetized benefit: mean = $464 million, 0.5th = -$29.2
million, 99.5th = $1.37 billion
Wayne (FIPS 163) total monetized benefit: mean = $1.28 billion, 0.5th = -$81.1
million, 99.5th = $3.75 billion

(7.8) For most areas, a later population year would mean a greater population. Because most
of the health impact functions are proportional to population, a greater population
would mean a greater benefit.

(7.9) A later currency year would generally mean that the monetized benefits would be
higher. The later the currency year, generally the greater the inflation, and hence the
less the purchasing power of an individual dollar. Therefore, the same benefit in a
later currency year would equal a greater number of dollars.

(7.10) A national background incidence rate would not reflect the local incidence rates for
specific health endpoints. A local background incidence rate would likely more closely
reflect the local population characteristics than the national average. The background
incidence rates are an important variable in the underlying health impact function.

(7.11) The AMI functions calculate a change in benefits beyond 2020. The AMI results are
for five years of medical costs and five years of opportunity costs. Because these costs
span five years (2020-2025), the benefits should be discounted back to 2020. We use a
discount rate to reflect our tendency to value future costs less than present costs. In
other words, if the combined costs were incurred only in 2020, we would value these
costs more than if these same costs were spread over five later years.

(7.12) By not pooling their adult mortality results, EPA is reporting a range of reasonable
results. You can think of the different mortality results as spanning the minimum to
maximum estimations of the health incidence results. In other words, a range provides
a window between the worst- and best-case scenarios.

(7.13) It depends. If you use only the national and regional-level health data pre-loaded in
BenMAP, it is better suited for national-scale analyses. Most of the input datasets have
been developed with a national or at least regional perspective. For example, many of
the health incidence functions were studied using large populations spread across
multiple cities and states. As one goes to a more local scale, the default health
incidence functions, valuation functions, and background incidence rates may become
less and less representative of the local population. In addition, if the scale becomes

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very small, then the populations become very small. If you have a small population,
then the sample size may become problematic, which undermines the statistical
functions used in BenMAP.
In contrast, imagine that you are able to find high quality local health incidence
functions, valuation functions, and background incidence rates for your particular
study area. You would expect that BenMAP would give more representative results
from these specific functions and datasets that have been "tuned" to your particular
study area than it would for a national analysis.

(7.14) BenMAP does not quantify the following benefits of reducing air pollution: improved
ecosystem health, climatological benefits, improved visibility and consequentially
improved aesthetics, and the reductions of pollution damages to infrastructure and
buildings. However, with the addition of appropriate impact functions, it would be
possible to use BenMAP to quantify these endpoints.

(7.15) The valuation estimates would probably be higher if we used WTP functions instead
of COI functions. COI functions do not include the cost of pain and suffering in the
estimate of monetized value. WTP functions attempt to capture both COI and the cost
of pain and suffering.

(7.16) There are many sources of uncertainty in a human health benefit analysis. EPA has
attempted to quantify some sources of uncertainty in BenMAP. For example, the
uncertainty in the regression coefficients for the health impact functions and the
underlying distribution are included in the valuation functions. Other uncertainties
have not been quantified. For example, there is significant uncertainty in the baseline
and control AQG, in the geographic variability of functions (i.e., which functions are
really regional or local and do not translate to other areas), in the differences between
personal exposure and outdoor pollution concentrations, and in the background
incidence rates.
A.2 CityOne
Below is a very simple tutorial using the CityOne setup available at the BenMAP website
(http://www.epa.gov/air/benmap/). The tutorial is based on a hypothetical scenario where
ambient PM2.5 concentrations are reduced by 25 percent in 2003. The steps in this analysis
are as follows:
Step 1. Data Files Needed for Training
Step 2. Create Air Quality Grids for the Baseline & Control Scenario
Step 3. Specify Configuration Settings
Step 4. Select Health Impact Functions
Step 5. Specify Aggregation, Pooling and Valuation
Step 6. Generate Reports
Step 7. View Your Reports
Step 8. Map Your Results

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Each step is explained in detail below.

A.2.1 Step 1. Data Files Needed for Training

To do this training you need to download the CityOne files from the BenMAP website:
http://www.epa.gov/air/benmap/. The data are most easily accessible if loaded in using the
Data Import tool, which is discussed in the here in the chapter on loading data.

A.2.2 Step 2. Create Air Quality Grids for the Baseline and Control Scenarios
Click on the Create Air Quality Grids button to begin inputting the air quality data
needed by BenMAP. This will open up the window where you will input the air quality
data. In general, you need two air quality grids to conduct a benefit analysis, one for a
baseline scenario and one for the policy you are evaluating (the control scenario). We will
be creating our baseline and control scenarios together, through the Monitor Rollback air
quality grid creation method.

Select Monitor Rollback from the list and click on Go!

This will take you to the Monitor Rolback Settings: (1) Select Monitors screen where
you will enter the information about the air quality monitoring data you want to use.
Choose PM2.5 from the Pollutant drop-down menu. On the Library tab, choose CityOne
Monitors from the Monitor DataSet drop-down menu, and choose 2003 from the
Monitor Library Year drop-down list. Finally, in the Rollback Grid Type choose
Metropolitan Area.

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When your window looks like the window above, click Next.
This will take you to the Monitor Rolback Settings: (2) Select Rollback Regions and
Settings window where you will choose the type of rollback for the CityOne metropolitan
area.

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Click Add Region. This will bring up the Select Region Rollback Type window.

In the Select Region Rollback Type window you may select from three rollback options.
Select the Percentage Rollback option as shown above. Click OK.

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In the box of Rollback Parameters for Region 1, type 25 in the Percent box. (This will
reduce each of the monitors in the CityOne area by 25 percent.) Then click on the Select
All box. When your window looks like the window above, click Next.
This will take you to the Monitor Rolback Settings: (3) Additional Grid Settings
window, the final step in creating rollback grids.
Choose the Voronoi Neighborhood Averaging interpolation method. Leave the scaling
method as None. From the Grid Type drop-down list choose County. Leave the box
checked next to Make Baseline Grid (in addition to Control Grid). This option will
cause BenMAP to create a baseline scenario air quality grid using the monitors selected in
the previous step, but without rolling their values back. BenMap will create a second grid
with the rolled back monitors, which will serve as our control scenario air quality grid.

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When your window looks like the window above, click Go!.
BenMAP will now prompt you to save the baseline air quality grid. Make sure you are in
the Air Quality Grids subfolder in the BenMAP directory and then save the file as: PM2.5
CityOne County Baseline 2003 VNA.aqg (you do not have to enter the “.aqg” extension).

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BenMAP will now prompt you to save the control air quality grid. Again, make sure you
are in the Air Quality Grids subfolder in the BenMAP directory and then save the file as:
PM2.5 CityOne County 25 Pct Rollback 2003 VNA.aqg (you do not have to enter the
“.aqg” extension).

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BenMAP will now create baseline and control air quality grids that you can use in your
benefit analysis. When the progress bar is complete, BenMAP will return to the main
BenMAP screen.

A.2.3 Step 3. Specify Configuration Settings

On the main BenMAP screen, click on the Create and Run Configuration button. In the
following box, select Create New Configuration and click Go!.

This will bring up the Configuration Settings form, where you will enter the basic
information about your analysis before selecting the health effects you wish to estimate.

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In the Baseline File field, you can either enter the path for your baseline air quality grid, or
click Open. For this example, click Open and browse to the Air Quality Grids folder.
Select PM2.5 CityOne County Baseline 2003 VNA and click Open.
Next, click on Open next to the Control File field and select PM2.5 CityOne County 25
Pct Rollback 2003 VNA and click Open.
This specifies that you want to conduct a benefit analysis of the difference between the
baseline and control scenarios for which we created air quality grids in Step 2.
In the Settings section of this window, there are several fields which set the overall scope
of the analysis.
In the Population DataSet field, select CityOne Tract Population from the drop down
menu. This tells BenMAP that you want your analysis to use tract-level population data
from this dataset when calculating health impacts.
In the Population Year field, enter 2005 or select 2005 from the drop down menu. This
tells BenMAP that you want your analysis to use 2005 populations when calculating health
impacts.
In the Latin Hypercube Points field, enter 10 or select 10 from the drop down menu.
This tells BenMAP that you want to estimate the percentiles of the distribution of health
endpoint incidence using Latin Hypercube Sampling with 10 percentiles of the distribution,
representing the 5th, 15th, 25th, and so on up to the 95th percentile.
Leave the Run in Point Mode box unchecked.
Leave the Threshold field blank. This tells BenMAP that you want to estimate benefits
associated with all changes in PM2.5, regardless of where those changes occur along the
range of PM2.5 concentrations. Selecting a non-zero threshold means that you would only
want to calculate benefits for changes occurring above the threshold.

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When your window looks like the above, click Next.

This will bring up the next page of the Configuration Settings form, where you can select
health impact functions from a set of available health impact functions.

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(Note: This screen can be resized if you are having trouble seeing all of the information.
Individual columns can also be resized. Just click on the border of a column and drag to
increase or decrease its width.)

A.2.4 Step 4. Select Health Impact Functions

In this screen, you can select health impact functions to use in your analysis. For this
example, we are going to estimate the change in incidence of three health endpoints
associated with PM2.5: acute bronchitis, acute myocardial infarctions (heart attacks), and
emergency room visits for asthma. To select a health impact function, you must drag it
from the upper box (Available C-R Functions) in the window to the lower box (Selected
C-R Functions). You can drag groups of health impact functions over, or drill down and
drag over individual functions.
For acute bronchitis, drill down until you see the function by the Author Dockery et al.
Drag the function into the lower panel of the window. You should see a new row with the
Endpoint Group Acute Bronchitis.

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For acute myocardial infarctions (AMI), drag the entire Endpoint Group titled Acute
Myocardial Infarction to the lower panel (do not drill down). This will include the full set
of age-specific health impact functions for AMI.
For asthma emergency room visits, also drag over the entire the Endpoint Group titled
Emergency Room Visits, Respiratory.
You should now have seven health impact functions listed in the lower panel: one acute
bronchitis function, five AMI functions, and one ER visit function.

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BenMAP will then prompt you to save your file. Click Save. Browse to the
Configurations subfolder within the BenMAP directory and save the file as: PM25
Example Configuration.cfg (you do not need to include the “.cfg” extension).
When you have saved the configuration file, click OK to run the configuration.
BenMAP will prompt you to “Save Configuration Results to File”. Browse to the
Configuration Results subfolder within the BenMAP directory and save the file as: PM2.5
CityOne County 25 Pct Rollback 2003 VNA Example.cfgr (you do not need to include the
“.cfgr” extension)
Once you have entered the filename, BenMAP will begin calculating the change in
incidence for the set of health impact functions you have selected. The run may take a few
minutes to finish; a progress bar will let you know how it is proceeding. When BenMAP
is finished running your configuration, it will return to the main BenMAP screen.

A.2.5 Step 5. Specify Aggregation, Pooling and Valuation

This step allows you to take the incidence results that BenMAP just produced and place an
economic valuation on them. Although not covered in this tutorial, this is also where you
can select the geographic level of aggregation and combine individual incidence results

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into pooling groups.

From the main screen, click on the Aggregation, Pooling and Valuation button. This
will bring up a menu screen with two choices: Create New Configuration for Aggregation,
Pooling and Valuation, or Open Existing Configuration for Aggregation, Pooling and
Valuation (*.apv file).

Select Create New Configuration for Aggregation, Pooling and Valuation and click on
Go!.
BenMAP will prompt you to open a Configuration Results File. Browse to the
Configuration Results subfolder and select PM2.5 CityOne County 25 Pct Rollback 2003
VNA Example.cfgr. Then click on Open.

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BenMAP will then open the Incidence Pooling and Aggregation window with the results
from running your configuration. You should see a window that looks like the following:

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Click on each of the results groups (acute bronchitis, acute myocardial infarction, and
emergency room visits) and drag them to the right panel.
For this example, we are not pooling any of the incidence results (although we will pool
valuations in the next window), so just click on Next at the bottom of the window.
This will take you to the Select Valuation Methods, Pooling, and Aggregation window.

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A) Select a value for acute bronchitis

To select a valuation method for acute bronchitis, drill down the Acute Bronchitis
valuation group until you see individual valuation methods. Click on the WTP: 6 day
illness, CV studies | 0-17 method and drag it onto the Acute Bronchitis endpoint group in
the right hand panel. You should see the method appear under acute bronchitis in the
Valuation Method column in the right hand panel.
B) Select values for acute myocardial infarctions (heart attacks)
To select valuation methods for acute myocardial infarctions, drill down the AMI valuation
group until you see a (long) list of individual valuation methods. You might find it easier
to expand the column width of the Valuation Methods column (drag the right hand edge of
the column to the right to make it wider). We will be working with the valuation estimates
from two studies, Wittels and Russell. For each of the studies, there are a number of age
specific valuations. There are also two different discount rates (the discount rate is the rate
at which future medical costs are discounted to the present). Drag the age-specific
valuation estimates from Wittels for the 3 percent discount rate (COI, 5 yrs med, 5 yrs
wages, 3% DR, Wittels (1990) | age) to each matching age-specific line in the right hand
panel (Pooling Window 1). You may have to scroll over in the right hand panel to see the
Low Age column.
Note that you will need to drag some age-specific valuation estimates to multiple lines in

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the pooling window, since there is not a perfect match between the available age-specific
valuation estimates and the age groups for which the incidence of heart attacks was
estimated. For example, you will have to drag the valuation estimate for the 25 to 44 age
group to both the 25 to 35 age group and the 35 to 45 age group in the pooling window.
Now repeat this process using the Russell 3 percent discount rate valuation estimates.
When you are finished, you should have two valuation estimates for each AMI age group,
and your pooling window should look like the one below.

Now you can pool the valuation results for heart attacks in each age group using the unit
values from both Wittels and Rusell. In order to do so, you must select a pooling method.
BenMAP lets you select from several different pooling methods. For this example, you
will be using subjective weights. In other applications, you may wish to use fixed or
random effects weights.
To set the pooling method for each age group result, click on the Pooling Method field in
the row ABOVE each pair of valuation methods (where it says None) and use the drop
down menu to select Subjective Weights. You must repeat this for EACH age group in
order for pooling to take place over all age groups.
In addition to pooling the results over the two valuation methods, we also need to
aggregate the results into a total estimate across age groups. In order to do so, in the row

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with Endpoint Group (Endpoint Group = Acute Myocardial Infarction) click in the
Pooling Method field and select Sum (Dependent) from the drop down menu.
Your screen should look like the following:

This pooling configuration for acute myocardial infarctions will assign a starting set of
equal weights to each valuation method for the set of five age groups, and then create an
overall estimate of acute myocardial infarctions by summing the age-specific pooled
estimates, treating the distributions for each age group as dependent (i.e. a draw from the 5
th percentile of the 45 to 54 age group will be added to the draw from the 5th percentile of

the 55 to 64 age group and so on).

C) Select values for asthma emergency room visits
To select values for asthma ER visits, drill down the Emergency Room Visits, Respiratory
heading to the Emergency Room Visits, Asthma, and then to the valuation approach
Standford et al, 1999 | 0 - Max. Drag this to the Emergency Room Visits entry in the right
hand panel.
D) Choose variable dataset
In the Variable Dataset drop-down menu, choose CityOne Variables. (BenMAP requires
that there be a variable dataset be chosen before going to the next step.)

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Your completed screen should look like the one below.

E) Entering subjective weights

Once you have completed this step, click on Run. BenMAP will now bring up a window
to allow you to enter subjective weights.
BenMAP assigns a default equal weight to each selected valuation method. You can
change these weights by clicking in the weight cells. However, for this exercise, you
should leave them at 0.5 for each study. Click on OK at the bottom of the screen. You
should see a save dialog box. Click on Save to save your APV configuration. Save the file
as PM25 Direct example APV.

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Click on OK to start the pooling and aggregation. First you will be prompted to enter a
filename for the aggregation, pooling, and valuation configuration file that you just created.
Enter PM25 Example Configuration.apv and click Save.
Then you will be prompted to enter a filename for the aggregation, pooling, and valuation
results. Enter PM2.5 CityOne County 25 Pct Rollback 2003 VNA Example.apvr and click
Save. When the progress bar disappears, you will be returned to the main BenMAP
screen.

A.2.6 Step 6. Generate Reports

You may view your results within BenMAP, either in the preview window in the Create
Reports button or through the mapping functions. Alternatively, you may export the
results to a comma separated values file (*.csv), or a shapefile (*.shp) which can be viewed
in a GIS program such as ESRI’s ArcView product.

A) Generate a Pooled Incidence Results report.

A Pooled Incidence Results report contains the incidence results you previously
generated, using the aggregation level and pooling that you specified in the Incidence
Pooling and Aggregation window. Previously, in Step 5, we did not specify any pooling
of incidence results (although valuations were pooled), so in this case the Pooled
Incidence Results report will look just like the Aggregated Incidence Results report. If
some incidence results had been pooled, the two reports would be different.

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Click on the Create Reports button from the main BenMAP screen. This will bring up
the Select Result Type window.

Select Incidence and Valuation Results: Raw, Aggregated and Pooled. Click OK. This
will bring up a window where you can select a results file. Chose the PM2.5 CityOne
County 25 Pct Rollback 2003 VNA Example.apvr file, and click Open. This will bring up
the Choose a Result Type window.

In the Choose a Result Type window, choose Pooled Incidence Results. Then click OK.
This will bring up the APV Configuration Results Report, where you can customize your
report display and select the fields you want to see in the report. In the Pooled C-R
Function Fields box, check off Endpoint Group and Qualifier.

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When your window looks like the window above, then go to the File menu and choose
Save. In the Save As window that appears, type in the file name and browse to the location
where you want to store the exported file. The Reports subfolder is a good location to
keep exported reports. Type in the name, PM2.5 CityOne County 25 Pct Rollback 2003
VNA Example Health.csv in the box and click Save. You can now open the report in
another application, such as a spreadsheet or database program.

B) Generate a Pooled Valuation Results report.

This report is similar to the Pooled Incidence Results report, and uses the valuation
pooling you previously specified. Click on the Create Reports button from the main
BenMAP screen. This will bring up the Select Report Type window. Select Incidence
and Valuation Results: Raw, Aggregated and Pooled. Click OK. This will bring up a
window where you can select a results file. Chose the PM2.5 CityOne County 25 Pct
Rollback 2003 VNA Example.apvr file, and click Open. This will bring up the Choose a
Result Type window.

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In the Choose a Result Type window, choose Pooled Valuation Results. Then click OK.
This will bring up the APV Configuration Results Report window, where you can
customize your report display and select the fields you want to see in the report. In the
Pooled Valuation Methods Fields box, check off Endpoint Group.

When your window looks like the window above, then go to the File menu and choose
Save.
In the Save As window that appears, type in the file name and browse to the location
where you want to store the exported file. The Reports subfolder is a good location to
keep exported reports. Type in the name, PM2.5 CityOne County 25 Pct Rollback 2003
VNA Example Valuation.csv in the box and click Save. You can now open the report in
another application, such as a spreadsheet or database program.

A.2.7 Step 7. View Your Reports

BenMAP generates comma separated values files (*.csv) that can be read by various
spreadsheet and database applications, such as Microsoft Excel.

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A.2.8 Step 8. Map Your Results

You can also map any of the results that you have generated so far. This includes the air
quality grids, population data, incidence results, and valuation results. In this example, we
will look at the air quality grid for the base scenario, and view our incidence results. For
more information on these and other mapping functions, see Chapter 9.
To use the BenMAP mapping functionality, go to the Tools menu and choose GIS /
Mapping. The BenMAP GIS window will appear, with buttons at the top for managing
files and navigating the map.

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To see the name of each button, simply hold the cursor over it. Click on the Open a file
button, and select Air Quality Grid from the drop-down menu. Browse to the file PM2.5
CityOne County 25 Pct Rollback 2003 VNA.aqg file and click Open.
The name of the file will appear in the left-hand panel under Layers. Double-click on the
name and a small box will appear with Display Options for viewing this layer. Here you
can select the variable contained in the layer (file) that you want to view. In the air quality
grid, the variables that are available are the Quarterly Mean and the Daily Mean
(D24HourMean). Select D24HourMean for the annual mean of the Daily Mean in the
Variable. In this box, you can also change the colors in the map display, and the
maximum and minimum values displayed.

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When done choosing your display options, click OK. You should see a map like the one
below.

To see tract outlines, select County from the Reference Layer drop-down menu at the top
of the screen. You may also use the other reference layers: Metropolitan Area and Tract.
However, since the results have been calculated at the county level in this example, the
county reference is generally most appropriate.

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Now you can look at a geographical display of the incidence results you created for cases
of bronchitis, acute myocardial infarctions, and emergency room visits. Click on the Open
a file button at the top of the screen and select APV Configuration Results, then Incidence
Results. In the next window, select PM2.5 CityOne County 25 Pct Rollback 2003 VNA
Example.apvr, then click Open. BenMAP will load your incidence results and display
them in a table. Because GIS programs can typically only accommodate field names that
are 10 characters or less, there is a new column at the end of the table labeled Gis Field
Name. Here you can name your variables, as shown in the table below.

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When you are satisfied with the variable names, click OK. The new layer will show in the
BenMAP GIS window on top of the first layer. If the previous layer is still checked, then it
will appear, but underneath the new layer. Uncheck the box next to the bottom (previous)
layer to hide it. Your screen should look like the one below.

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Like the previous layer, double click on the name to bring up the Display Options box.
Under Variable you will see a list of the variable names you defined in the previous step.
Select Myo65up, uncheck the Grid Outline box, and click OK. The viewer will now
display the annual increase in the number of acute myocardial infarctions for people ages
65 and up, as calculated between the base and control scenarios. You can use the Display
Options to select other variables to view or change how the values are displayed.

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Appendix B: Monitor Rollback Algorithms

This Appendix details the rollback procedures that you can perform on monitor data. The
rollback procedure is a quick way to determine the monitor levels that would exist under
various kinds of changes that you can specify. This includes three basic types of rollbacks:
Percentage, Increment, and Rollback to Standard.
Once a set of monitors has been selected, the user may define one or more non-overlapping
rollback regions. A region is simply a set of states with an associated set of rollback
parameter values. Three rollback types are available:
 Percentage Rollback. Monitor values are reduced the same percentage.
 Incremental Rollback. Monitor values are reduced by the same fixed increment.
 Rollback to a Standard. Monitor values are reduced so that attainment of a specified
standard is reached.
Each of these rollback types has different rollback parameters associated with it.

B.1 Percentage Rollback

Percentage Rollback involves setting only two parameters - a percentage and a
background level. The rollback procedure is similarly straightforward - each observation
at each monitor in the region has the portion of its value which is above background level
reduced by percentage.

Example: Background Level: 35; Percentage: 25

Initial Observations at a monitor in rollback region:

20 20 25 59 35 51 83 35 30 67 87 79 63 35 35

If we select the background level of 35, we first calculate the portion of each observation
that is above background level, that is, we subtract the background level from the initial
observation level. Observations below background level are given a value of 0.

Observation portions above background level:

0 0 0 24 0 16 48 0 0 32 52 44 28 0 0

When we apply the rollback percentage, each observation portion gets reduced by 25%.

Reduced portions above background level:

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0 0 0 18 0 12 36 0 0 24 39 33 21 0 0

Then, each reduced portion is added to the background level of 35. Zero values are
replaced by the initial observations.

Reduced Observations:

20 20 25 53 35 47 71 35 30 59 74 68 56 35 35

B.2 Incremental Rollback

Incremental Rollback similarly involves setting only two parameters - an increment and a
background level. The rollback procedure is quite similar to the percentage rollback
procedure - each observation at each monitor in the region has the portion of its value
which is above background level reduced by increment. The reduced values are not
allowed to become negative, however - that is, they are truncated at zero.

Example: Background Level: 35; Increment: 25

Initial Observations:

20 20 25 59 35 51 83 35 30 67 87 79 63 35 35

Observation portions above background level:

0 0 0 24 0 16 48 0 0 32 52 44 28 0 0

Reduced portions above background level:

0 0 0 0 0 0 23 0 0 7 27 19 3 0 0

Reduced Observations:

20 20 25 35 35 35 58 35 30 42 62 54 38 35 35

B.3 Rollback to a Standard

Rollback to a Standard has two groups of parameters - those associated with the
Attainment Test, which determines whether a monitor is in attainment (meets the
standard), and those associated with the Rollback Methods, which are used to bring out of

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attainment monitors into attainment.

The Attainment Test parameters are Metric, Ordinality, and Standard. A monitor is
considered in attainment if the nth highest value of the metric specified by Metric is at or
below the value specified by Standard, where n is the value specified by Ordinality. For
example, if Metric is TwentyFourHourDailyAverage, Ordinality is two, and Standard is
eighty five, a monitor will be considered in attainment if the second highest value of
TwentyFourHourDailyAverage is at or below eighty five.
Supported metrics for pollutants with hourly observations (Ozone) include
FiveHourDailyAverage, EightHourDailyAverage, TwelveHourDailyAverage,
TwentyFourHourDailyAverage, OneHourDailyMax, and EightHourDailyMax. Supported
metrics for pollutants with daily observations (PM10, PM2.5) include
TwentyFourHourDailyAverage and AnnualAverage. For Annual Average, Ordinality
does not apply, since there is only a single metric value to work with.
The Rollback Method parameters are Interday Rollback Method, Interday
Background Level, Intraday Rollback Method, and Interday Background Level.
These four parameters determine the rollback procedures used to bring out of attainment
monitors into attainment. The Interday Rollback Method and Background Level are
used to generate target values for the metric specified by the Attainment Test. The
Intraday Rollback Method and Background Level are used to adjust hourly
observations to meet the target metric values generated in the previous step. As such, the
Intraday Rollback Method and Background Level are used only for pollutants with
hourly observations (ozone).

B.3.1 Interday Rollback - Generating Target Metric Values

Because standards are defined on metrics, not directly on observations, the first step in
rolling back out of attainment monitors is generating target metric values. There are four
supported rollback methods for Interday Rollbacks - Percentage, Incremental, Peak
Shaving, and Quadratic. Each of these rollback methods requires some preprocessing of
the initial monitor metric values. We will discuss this preprocessing first, and then go
through Percentage, Incremental, and Peak Shaving rollbacks in turn. Quadratic rollback
is more complicated than these first three, and has its own section.
The Interday Background Level specifies the portion of each metric value which cannot be
affected by human intervention - we call this portion the non-anthropogenic portion.
Whatever portion is left over after subtracting out the background level is referred to as the
anthropogenic portion. The anthropogenic portion of the initial monitor metric values is
the only part which will be affected by the Interday Rollback Method.
BenMAP calculates an out of attainment value by determining the particular monitor
metric value which caused the monitor to be out of attainment - this value is the nth
highest value of the metric specified by the Attainment Test metric, where n is the
Attainment Test ordinality. BenMAP then calculates an anthropogenic out of attainment
value by subtracting the Interday Background Level from the out of attainment value.

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BenMAP also calculates an anthropogenic standard by subtracting the Interday

Background Level from the Attainment Test standard. Finally, BenMAP calculates a set of
anthropogenic metric values and a set of non-anthropogenic metric values using the
following procedure on each initial monitor metric value:
IF the metric value is less than or equal to the Interday Background Level,
non-anthropogenic metric value = metric value
anthropogenic metric value = 0
ELSE
non-anthropogenic metric value = Interday Background Level
anthropogenic metric value = metric value - Interday Background Level

B.3.1.1 Interday Rollback - Percentage

To generate target metric values using Percentage rollback, BenMAP calculates the
percentage required to reduce the anthropogenic out of attainment value to exactly the
anthropogenic standard. This percentage reduction is then applied to all of the
anthropogenic metric values. Finally, these reduced anthropogenic metric values are added
to the non-anthropogenic metric values to give the final target metric values.

Example:
Initial Metric Values:
30 35 50 10 80 44 67 88 90 70 50 30 55 90 80 85
0

Attainment Test: Highest value of metric <= 70

Interday Background Level: 40
Out of Attainment Value: 100
Anthropogenic Out of Attainment Value: 60 (= 100 - 40)
Anthropogenic Standard: 30 (= 70 - 40)
Percentage Reduction Required: 50% (=(60-30)/60)

Non-Anthropogenic Metric Values:

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30 35 40 40 40 40 40 40 40 40 40 30 40 40 40 40

Anthropogenic Metric Values:

0 0 10 60 40 4 27 48 50 30 10 0 15 50 40 45

Reduced Anthropogenic Metric Values:

0 0 5 30 20 2 14 24 25 15 5 0 8 25 20 23

Target Metric Values:

30 35 45 70 60 42 54 64 65 55 45 30 48 65 60 63

B.3.1.2 Interday Rollback - Incremental

To generate target metric values using Incremental Rollback, BenMAP calculates the
increment required to reduce the anthropogenic out of attainment value to exactly the
anthropogenic standard. This incremental reduction is then applied to all of the
anthropogenic metric values (but - they are not allowed to fall below zero). Finally, these
reduced anthropogenic metric values are added to the non-anthropogenic metric values to
give the final target metric values.

Example:
Initial Metric Values:
30 35 50 10 80 44 67 88 90 70 50 30 55 90 80 85
0

Attainment Test: Highest value of metric <= 70

Interday Background Level: 40
Interday Rollback Method: Incremental
Out of Attainment Value: 100
Anthropogenic Out of Attainment Value: 60
Anthropogenic Standard: 30 (=70 - 30)
Incremental Reduction Required: 30

Non-Anthropogenic Metric Values:

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30 35 40 40 40 40 40 40 40 40 40 30 40 40 40 40

Anthropogenic Metric Values:

0 0 10 60 40 4 27 48 50 30 10 0 15 50 40 45

Reduced Anthropogenic Metric Values:

0 0 5 30 20 2 14 24 25 15 5 0 8 25 20 23

Target Metric Values:

30 35 45 70 60 42 54 64 65 55 45 30 48 65 60 63

B.3.1.3 Interday Rollback - Peak Shaving

To generate target metric values using Peak Shaving rollback, BenMAP simply truncates
all anthropogenic metric values at the anthropogenic standard. These reduced
anthropogenic metric values are added to the non-anthropogenic metric values to give the
final target metric values.

Example:
Initial Metric Values:
30 35 50 10 80 44 67 88 90 70 50 30 55 90 80 85
0

Attainment Test: Highest value of metric <= 70

Interday Background Level: 40
Interday Rollback Method: Peak Shaving
Anthropogenic Standard: 30

Non-Anthropogenic Metric Values:

30 35 40 40 40 40 40 40 40 40 40 30 40 40 40 40

Anthropogenic Metric Values:

0 0 10 60 40 4 27 48 50 30 10 0 15 50 40 45

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Reduced Anthropogenic Metric Values:

0 0 10 30 30 4 27 30 30 30 10 0 15 30 30 30

Target Metric Values:

30 35 50 70 70 44 67 70 70 70 50 30 55 70 70 70

B.3.2 Intraday Rollback - Adjusting Hourly Observations

Once a set of target metric values has been calculated for a pollutant with hourly
observations (e.g., Ozone), BenMAP must adjust the hourly observations so that they
produce the target metric values. There are three supported rollback methods for Intraday
Rollback - Percentage, Incremental, and Quadratic. Each of these rollback methods
requires some preprocessing of the initial monitor observations, and each can require
multiple iterations to hit the target metric values. We will discuss this preprocessing and
iteration first, and then go through Percentage and Incremental rollbacks in turn. Quadratic
rollback is more complicated than these first two, and has its own section.
For various reasons, each of the Intraday Rollback methods can fail to hit the target metric
values during a single pass through the rollback procedure (these will be discussed in detail
below). As such, each of the rollback methods uses an iterative approach to get within a
threshold of each of the target metric values - currently this threshold is 0.05. The iterative
approach works as follows:
For each target metric value, BenMAP calculates the current value of the Attainment Test
metric. For the first iteration, the metric value will be calculated using unadjusted hourly
observations. For subsequent iterations, the metric value will be calculated using the
current values of the adjusted hourly observations.
If the difference between the metric value and the target metric value is less than or equal
to 0.05, the rollback procedure is finished. Otherwise, another iteration is required.
The Intraday Background Level specifies the portion of each observation which cannot be
affected by human intervention - we call this portion the non-anthropogenic portion.
Whatever portion is left over after subtracting out the background level is referred to as the
anthropogenic portion. The anthropogenic portion of the initial monitor observations is the
only part which will be affected by the Intraday Rollback Method.
In a way analogous to the Interday Rollback procedure, BenMAP calculates the
twenty-four hourly anthropogenic observations and the twenty-four hourly
non-anthropogenic observations using the following procedure for each hourly
observation:

IF the current value of the observation is less than or equal to the Intraday Background
Level,

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non-anthropogenic observation = observation

anthropogenic observation = 0
ELSE
non-anthropogenic observation = Intraday Background Level
anthropogenic observation = observation - Intraday Background Level

Given (i) an Attainment Test Metric (e.g., EightHourDailyMax), (ii) an Intraday

Background Level, and (iii) a target metric value for the day, BenMAP proceeds to adjust
hourly observations in the following steps:

1. Calculate the Attainment Test metric (e.g., the 8-hour daily maximum);
2. Identify the “window” – i.e., the set of hours used to calculate the metric (e.g., if the
8-hour daily maximum is achieved in the first 8 hours, then the window is comprised of
the first 8 hours);
3. Calculate the non-anthropogenic hourly observations (=min(hourly observation,
Intraday Background Level));
4. Calculate the anthropogenic hourly observations (=hourly observation - Intraday
Background Level);
5. Calculate the non-anthropogenic metric value (= the metric using the
non-anthropogenic hourly observations in the “window”);
6. Calculate the anthropogenic metric value (= the metric using the anthropogenic hourly
observations in the “window”);
7. Calculate the anthropogenic target metric value (= the target metric value minus the
non-anthropogenic metric value);
8. Calculate the reduction required to get the anthropogenic metric value down to the
anthropogenic target metric value;
9. Adjust all anthropogenic hourly observations by the reduction calculated on the
previous step;
10. Calculate the adjusted hourly observations (= the adjusted anthropogenic hourly
observation + the non-anthropogenic hourly observation).

B.3.2.1 Intraday Rollback - Percentage

Below, we present two examples of a percentage-based Intraday Rollback. In one
example, a single iteration is needed, and in the second example, two iterations are

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required because a number of the monitor values fall below the assumed background level.

B.3.2.1.1 Example: All Hourly Observations Exceed the Intraday Background (Single Iteration)

If all of the hourly observations in a day are greater than the Intraday Background Level,
then the above procedure is straightforward and can be accomplished in a single iteration.
We illustrate with the following example. Suppose that:
Metric = EightHourDailyMax,
Target metric value for a given day = 85
Intraday Background Level = 40.
And that the hourly observations on that day are:
530 45 50 60 45 45 45 60 70 100 100 100 100

100 100 100 100 60 45 50 45 45 47 47

Based on these observations, we see that the 8-hour daily maximum = 110.
Assuming a background level of 40, then the Anthropogenic hourly observations are:
490 5 10 20 5 5 5 20 30 60 60 60 60 60

60 60 60 20 5 10 5 5 7 7

Then, we know:
Anthropogenic metric value = 70.
Non-anthropogenic metric value = 40.
Anthropogenic target metric value = 45.
Percentage reduction required = ((70-45)/70) = 35.7%
All of the hourly anthropogenic observations are reduced by 35.7%. The average of the
first 8 values (the window on which the Test metric is based) will be exactly 45, the
anthropogenic target metric value. Finally, the adjusted hourly observations are calculated
by adding the non-anthropogenic hourly observation to the adjusted hourly anthropogenic
observations.

B.3.2.1.2 Example: Some Hourly Observations are Below the Intraday Background (Multiple Iterations Required)

In the above example, the anthropogenic target metric value was met on a single iteration

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because all of the hourly observations were greater than the Intraday Background Level. In
this case, a simple percent reduction of all hourly values will produce an average in the
window that is equal to the anthropogenic target metric value. If some of the hourly
observations in a day are less than or equal to the Intraday Background Level, however,
then BenMAP uses an iterative procedure. On each iteration, it adjusts hourly observations
using the 10-step method given above. It then compares the new metric value to the target
metric value. If the difference is less than or equal to 0.05 ppb, the rollback procedure is
finished. Otherwise, another iteration is required. The iterative procedure is illustrated in
the following example.
Suppose that:
Metric = EightHourDailyMax,
Target metric value for a given day = 85
Intraday Background Level = 40.

Suppose also that the hourly observations on that day are:

530 20 25 60 35 35 40 60 70 100 100 100 100

100 100 100 100 60 33 40 30 30 25 20

Then, we know that the 8-hour daily maximum = 100.6.

Non-Anthropogenic Hourly Observations, Iteration One:
40 20 25 40 35 35 40 40 40 40 40

40 40 40 40 40 40 40 33 40 30 30 25 20

Anthropogenic Hourly Observations, Iteration One:

490 0 0 20 0 0 0 20 30 60 60 60 60 60

60 60 60 20 0 0 0 0 0 0

Non-Anthropogenic Metric Value: 34.4 (EightHourDailyMax - calculated over the same

eight hour window as the initial metric value was calculated over)
Anthropogenic Metric Value: 66.3
Anthropogenic Target Metric Value: 50.6
Percentage Reduction Required: 23.6%

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Reduced Anthropogenic Hourly Observations, Iteration One:

374 0 0 15 0 0 0 15 23 46 46 46

46 46 46 46 46 15 0 0 0 0 0 0

Reduced Hourly Observations, Iteration One:

414 20 25 55 35 35 40 55 63 86 86 86 86

86 86 86 86 55 33 40 30 30 25 20

Reduced Metric Value (EightHourDailyMax): 85.8

Target Metric Value (EightHourDailyMax): 85

Non-Anthropogenic Hourly Observations, Iteration Two:

40 20 25 40 35 35 40 40 40 40 40 40 40

40 40 40 40 40 33 40 30 30 25 20

Anthropogenic Hourly Observations, Iteration Two:

374 0 0 15 0 0 0 15 23 46 46 46 46

46 46 46 46 15 0 0 0 0 0 0

Non-Anthropogenic Metric Value: 40 (EightHourDailyMax - calculated over the same

eight hour window the initial metric value was calculated over)
Anthropogenic Metric Value: 45.8
Anthropogenic Target Metric Value: 45
Percentage Reduction Required: 1.9%

Reduced Anthropogenic Hourly Observations, Iteration Two:

368 0 0 15 0 0 0 15 23 45 45 45 45 45

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45 45 45 15 0 0 0 0 0 0

Reduced Hourly Observations, Iteration Two:

408 20 25 55 35 35 40 55 63 85 85 85 85 85

85 85 85 55 33 40 30 30 25 20

Reduced Metric Value (EightHourDailyMax): 85

The above example, in addition to illustrating the Intraday Percentage Rollback, also
illustrates one reason why the iterative procedure can be necessary. When using the
EightHourDailyMax metric in the Attainment Test, it is possible for the window over
which the maximum eight hour average occurs to move after a single pass through the
rollback procedure. When this happens, it becomes necessary to go through additional
iterations to hit the target metric value.

B.3.3 Intraday Rollback - Incremental

To adjust hourly observations using Incremental rollback, BenMAP calculates the
increment required to reduce the anthropogenic metric value to exactly the anthropogenic
target metric value. This incremental reduction is then applied to all of the anthropogenic
observations (but - they are not allowed to fall below zero). Finally, these reduced
anthropogenic observations are added to the non-anthropogenic observations to give the
final reduced observations.
Example:
Initial Hourly Observations:
20 20 25 60 35 35 40 70 35 30 65 90 76

65 35 35 54 60 33 40 30 30 25 20

Initial Metric Value (EightHourDailyMax): 60

Target Metric Value (EightHourDailyMax): 55
Intraday Background Level: 40
Intraday Rollback Method: Incremental

Non-Anthropogenic Hourly Observations, Iteration One:

20 20 25 40 35 35 40 40 35 30 40 40 40

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40 35 35 40 40 33 40 30 30 25 20

Anthropogenic Hourly Observations, Iteration One:

0 0 0 20 0 0 0 30 0 0 25 50 36

25 0 0 14 20 0 0 0 0 0 0

Non-Anthropogenic Metric Value (EightHourDailyMax): 38.8

Anthropogenic Metric Value (EightHourDailyMax): 21.3
Anthropogenic Target Metric Value (EightHourDailyMax): 16.3
Incremental Reduction Required: 5.0

Reduced Anthropogenic Hourly Observations, Iteration One:

0 0 0 15 0 0 0 25 0 0 20 45 31

20 0 0 9 15 0 0 0 0 0 0

Reduced Hourly Observations, Iteration One:

20 20 25 55 35 35 40 65 35 30 60 85 71

60 35 35 49 55 33 40 30 30 25 20

Reduced Metric Value (EightHourDailyMax): 56.25

Target Metric Value (EightHourDailyMax): 55

Non-Anthropogenic Hourly Observations, Iteration Two:

20 20 25 40 35 35 40 40 35 30 40 40 40

40 35 35 40 40 33 40 30 30 25 20

Anthropogenic Hourly Observations, Iteration Two:

0 0 0 15 0 0 0 25 0 0 20 45 31

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20 0 0 9 15 0 0 0 0 0 0

Non-Anthropogenic Metric Value (EightHourDailyMax): 38.8

Anthropogenic Metric Value (EightHourDailyMax): 17.5
Anthropogenic Target Metric Value (EightHourDailyMax): 16.3
Incremental Reduction Required: 1.25

Reduced Anthropogenic Hourly Observations, Iteration Two:

0 0 0 14 0 0 0 24 0 0 19 44 30

19 0 0 8 14 0 0 0 0 0 0

Reduced Hourly Observations, Iteration Two:

20 20 25 54 35 35 40 64 35 30 59 84 70

59 35 35 48 54 33 40 30 30 25 20

Reduced Metric Value (EightHourDailyMax): 55.3

Target Metric Value (EightHourDailyMax): 55

This example should actually continue for one further iteration, with a new Incremental
Reduction of 0.3. This illustrates another reason why the iterative procedure can be
necessary - for incremental reductions, the prohibition against values becoming negative
can cause target metric values to not be met. Incremental reductions thus very often
require multiple iterations.

B.3.4 Interday and Intraday Rollback - Quadratic

Quadratic rollback is based on an algorithm developed by Horst and Duff . The idea
behind quadratic rollback is to reduce large values proportionally more than small values
while just achieving the standard - that is, the out-of-attainment value should be more or
less at the standard after the rollback (some small amount of error is involved).
The original quadratic rollback algorithm is designed to roll back hourly observations
given a desired peak value. That is, it assumes that the Attainment Test metric is the
one-hour average and the Attainment Test ordinality is one. As such, the algorithm was
modified slightly to allow for ordinalities other than one to be used.

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The basic formula for quadratic rollback is:

Reduced Observation = [ 1 - ( A + B * Initial Observation ) ] * Initial Observation

where:
i ranges over the days being reduced.
A=1-V
V = Min( 1, Vi )
Vi = ( 2 * Maximum Observation Value * Standard ) / Xi
Xi = ( 2 * Maximum Observation Value * Metricsi ) - Metricsi2
B = Max( 0, [( V * Out of Attainment Value - Standard ) / Out of Attainment Value2] )

B.3.4.1 Quadratic Rollback - Interday

Because Quadratic Rollback was originally designed to adjust hourly observations to meet
a daily metric standard, it is slightly complicated to use it to generate target metric values.
First, Quadratic Rollback calculates the anthropogenic out of attainment value by
subtracting the Intraday Background Level from the out of attainment value. Note that this
differs from the other interday rollback methods, which subtract the Interday Background
Level from the out of attainment value. Similarly, the anthropogenic standard is calculated
by subtracting the Intraday Background Level from the standard.
The anthropogenic observations and non-anthropogenic observations are then calculated.
For pollutants which have daily observations (PM10, PM2.5) the anthropogenic metric
values are used (see above for their calculation). For pollutants which have hourly
observations (Ozone), Quadratic Rollback loops through each metric value and calculates
the twenty four corresponding anthropogenic observations and non-anthropogenic
observations as follows:

IF the metric value is at or below the Interday Background Level,

For each observation,
non-anthropogenic observation = observation
anthropogenic observation = 0
ELSE

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For each observation,

IF the observation is at or below the Intraday Background Level
non-anthropogenic observation = observation
anthropogenic observation = 0
ELSE
non-anthropogenic observation = Intraday Background Level
anthropogenic observation = observation - Intraday Background
Level

A new set of anthropogenic metric values is then calculated by generating the Attainment
Test metric from the anthropogenic observations. The Quadratic Rollback algorithm is
then called, passing in the anthropogenic metric values as Metrics, anthropogenic
observations as Observations, anthropogenic standard as Standard, and anthropogenic out
of attainment value as Out of Attainment Value. The result is a set of reduced
anthropogenic observations. These are then added together with the non-anthropogenic
observations to give a final set of reduced observations.
Then, if Quadratic Rollback was also selected as the Intraday Rollback method, these
observations are used as the final reduced observations for the monitor. Otherwise, metric
targets are generated from these hourly observations, and the observations themselves are
discarded

B.3.4.2 Quadratic Rollback - Intraday

Quadratic Rollback can also be used to adjust hourly observations to meet metric targets
generated via a different rollback method. In this case, the algorithm is used to adjust each
set of twenty four hourly observations to meet the corresponding metric target. Intraday
Quadratic Rollback uses the normal set of anthropogenic observations as Observations, a
single normal anthropogenic metric value as Metrics, and the normal anthropogenic metric
target as Standard. Intraday Quadratic Rollback tends to always slightly miss its metric
target, so it is not run in an iterative fashion as the other Intraday Rollback Methods are
(doing so would sometimes result in an infinite loop).

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Appendix C: Air Pollution Exposure Estimation

Algorithms
BenMAP has grouped individuals into what we refer to as “population grid-cells,” where
the grid-cells typically conform to some type of grid used in an air quality model, such as
the REMSAD air quality model, or just the counties of the United States. For each type of
grid, the population is built in each grid-cell by aggregating census block data. In the next
step, BenMAP estimates the air pollution exposure for each grid-cell, with the assumption
that people living within a particular grid-cell experience the same air pollution levels.
You have a variety of approaches to estimate the exposure to air pollution for the people
living within a given population grid-cell. Perhaps the simplest approach is to use model
data directly, and to assume that the people living within a particular model grid-cell
experience the level estimated by the model. An alternative approach is to use air
pollution monitoring data, where you may choose the closest monitor data to the center of
a grid-cell or take an average of nearby monitors. In a third general approach, you may
combine both modeling and monitoring data to estimate exposure.
When combining modeling and monitoring data, BenMAP scales or adjusts the monitoring
data with modeling data. The advantage of modeling data is that they can provide
predictions for years in which monitoring data are not available, as well as to provide
predictions in areas of the country for which monitoring data are not available. And the
advantage of monitor data is that they are based on actual observations. Combining both
sources of information, allows BenMAP to make more informed predictions.
The goal of estimating exposure is to provide the necessary input for
concentration-response functions, so that BenMAP can estimate the impact of air pollution
on adverse health effects. Table C-1 lists the types of metrics commonly used in
concentration-response functions. In the case of air pollution metrics calculated on a daily
basis, such as the one-hour maximum and the 24-hour average, it is often the case that
there are missing days of data. Air quality modeling is often conducted on a subset of the
days in the year, and air quality monitors often miss a number of observations through out
the year. To account for missing days, BenMAP represents the distribution of daily
metrics with a certain number points or “bins,” where each bin represents a certain range of
the distribution, with the underlying assumption that missing days have the same
distribution as the available data. For example, for analyses of the United States the
Environmental Protection Agency has typically used 153 bins to represent the ozone
season from May through September, and for particulate matter they have used 365 bins to
represent the year. In addition to being able to account for incomplete or missing data, and
using bins to represent the distribution provides a uniform approach that allows for easy
comparison of different monitors.

Table C-1. Metrics Typically Used in Concentration-Response Functions for Criteria

Air Pollutants

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Measurement Metric Name Metric Description

Frequency
Daily Daily Average Daily average
(e.g., PM2.5,
PM10) Annual Average Average of four quarterly averages. The four quarters are defined
as: Jan-Mar, April-June, Jul-Sep, Oct-Dec.
Annual Median Median of values through out the year.
Hourly 1-hour Daily Max Highest hourly value from 12:00 A.M. through 11:59 P.M.
(e.g., Ozone)
8-hour Daily Average of hourly values from 9:00 A.M. through 4:59 P.M.
Average
12-hour Daily Average of hourly values from 8:00 A.M. through 7:59 P.M.
Average
24-hour Daily Average of hours from 12:00 A.M. through 11:59 P.M.
Average

C.1 Direct Modeling

When using direct modeling data to estimate exposure, BenMAP assumes that the people
living within a particular air pollution model grid-cell experience the same air pollution
levels. BenMAP then estimates the air pollution metrics of interest, as defined for each
pollutant. (See the section on defining pollutants in the Loading Data chapter.)
Generally modeling data providing hourly observations are complete for any given day.
However, it is common to have missing days of modeling data during the course of a year.
Given the estimated metrics from the available data, BenMAP then represents the
distribution of daily metrics with the number of days specified for each pollutant. By
calculating bins with the available days, BenMAP assumes that the distribution of missing
days is similar to the distribution of available data.

C.2 Closest Monitor

When using the closet monitor to represent air pollution levels at a population grid-cell,
BenMAP identifies the center of the population grid-cell, and then chooses the monitor
that is closest to the center. In the simplest case, BenMAP assigns the closest monitor to a
population grid-cell, uses the monitoring data to calculate the annual and daily air pollution
metrics, and then calculates the bins that represent the distribution of the daily metrics.
The annual metrics and the binned daily metrics are then used in the calculation of health
effects.
The figure below presents nine population grid-cells and three monitors, with the focus on
identifying the monitor closest to grid-cell “E.” In this example, the closest monitor
happens to be 10 miles away from the center of grid-cell E, and the data from this monitor
would be used to estimate air pollution levels for the population in this grid-cell. An
analogous procedure would be used to estimate air pollution levels in the other grid-cells
(A, B, C, D, F, G, H, and I).

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To capture some of the information generated by air pollution models, BenMAP can also
scale the data from the closest monitor with air pollution modeling data. BenMAP
includes two types of scaling – “temporal” and “spatial” scaling. We discuss each below.

C.2.1 Closest Monitor – Temporal Scaling

With temporal scaling, BenMAP scales monitoring data with the ratio of the future-year to
base-year modeling data, where the modeling data is from the modeling grid-cell
containing the monitor. In the case of pollutants typically measured hourly, such as ozone,
BenMAP scales the hourly monitor values, calculates the annual and daily metrics of
interest, and then bins the daily metrics. In the case of pollutants typically measured daily,
BenMAP scales the daily values, calculates the annual metrics of interest, and then bins the
daily metric.
Consider the case in the figure below. To forecast air pollution levels for 2030, BenMAP
would multiply the 1995 monitor value (80 ppb) by the ratio of the 2030 model value (70
ppb) to the 1995 model value (95 ppb):
Forecast2030 = Monitor Value 1995 * (Model Value D, 2030 / Model Value D, 1995)

Forecast2030 = 80 ppb * (70 ppb / 95 ppb) = 58.9 ppb.

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In this example, we have examined the adjustment of a single monitor value with the ratio
of single model values. The approach is essentially the same when there are multiple
monitor values and multiple model values.

C.2.2 Closest Monitor – Spatial Scaling

With spatial scaling, we are estimating a monitor value for the center of each population
grid-cell. We start by choosing the closest monitor to the center of each population
grid-cell, and then we scale this closest monitor with modeling data. In particular,
BenMAP multiplies the monitoring data with the ratio of the base-year modeling data for
the destination grid-cell to the base-year modeling data for grid-cell containing the
monitor. The spatial scaling occurs in the same fashion as with temporal scaling. In the
case of pollutants typically measured hourly, such as ozone, BenMAP scales the hourly
monitor values, calculates the annual and daily metrics of interest, and then bins the daily
metrics. In the case of pollutants typically measured daily, BenMAP scales the daily
values, calculates the annual metrics of interest, and then bins the daily metric.
To estimate air pollution levels for 1995 in grid-cell “E” below, BenMAP would multiply
the 1995 closest monitor value (80 ppb) by the ratio of the 1995 model value for grid-cell
“E” (70 ppb) to the 1995 model value for grid-cell “D” (95 ppb):
Forecast1995 = Monitor Value1995 * (Model Value E, 1995 / Model Value D, 1995)

Forecast1995 = 80 ppb * (85 ppb / 95 ppb) = 71.6 ppb.

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C.2.3 Closest Monitor – Temporal and Spatial Scaling

Combining both temporal and spatial scaling, BenMAP first multiplies monitoring data
with both the ratio of the future-year to base-year modeling data, where the modeling data
is from the modeling grid-cell containing the monitor. This gives a temporary forecast for
2030. BenMAP then multiplies this temporary forecast with the ratio of the future-year
modeling data for the destination grid-cell to the future-year modeling data for grid-cell
containing the monitor. As seen below, this simplifies to multiplying monitoring data with
both the ratio of future-year modeling data from the destination grid-cell to the base-year
modeling data from the grid-cell containing the monitor. Again, as described for temporal
and spatial scaling, BenMAP first scales the hourly and daily values, generates the metrics
of interest and then bins the daily metrics.
To forecast air pollution levels for 2030 in the figure below, BenMAP would multiply the
1995 monitor value (80 ppb) by the ratio of the 2030 model value (70 ppb) to the 1995
model value (95 ppb):
Temporary Forecast 2030 = Monitor Value 1995 * (Model Value D, 2030 / Model
Value D, 1995)

Temporary Forecast 2030 = 80 ppb * (70 ppb / 95 ppb) = 58.9 ppb.

Forecast 2030 = Temporary Forecast 2030 * (Model Value E, 2030 / Model Value D,
2030)

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Forecast 2030 = 58.9 ppb * (60 ppb / 70 ppb) = 50.5 ppb.

Note that through cancellation, this equation simplifies to:

Forecast 2030 = Monitor Value 1995 * (Model Value E, 2030 / Model Value D, 1995)

C.3 Voronoi Neighbor Averaging (VNA)

Like the closest monitor approach, the Voronoi Neighbor Averaging (VNA) algorithm
uses monitor data directly or in combination with modeling data. However, instead of
using the single closest monitor to estimate exposure at a population grid-cell, the VNA
algorithm interpolates air quality at every population grid cell by first identifying the set of
monitors that best “surround” the center of the population grid-cell.

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In particular, BenMAP identifies the nearest monitors, or “neighbors,” by drawing a

polygon, or “Voronoi” cell, around the center of each BenMAP grid cell. The polygons
have the special property that the boundaries are the same distance from the two closest
points.

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BenMAP then chooses those monitors that share a boundary with the center of grid-cell
“E.” These are the nearest neighbors, BenMAP uses these monitors to estimate the air
pollution level for this grid-cell.

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To estimate the air pollution level in each grid-cell, BenMAP calculates the metrics for
each of the neighboring monitors, and then calculates an inverse-distance weighted average
of the metrics. The further the monitor is from the BenMAP grid-cell, the smaller the
weight.
In the figure below, the weight for the monitor 10 miles from the center of grid-cell E is
calculated as follows:

The weights for the other monitors would be calculated in a similar fashion. BenMAP
would then calculate an inverse-distance weighted average for 1995 air pollution levels in
grid-cell E as follows:
Forecast 1995 = 0.35*80 ppb + 0.24*90 ppb+ 0.24*60 ppb + 0.18*100 ppb = 81.2 ppb .

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C.3.1 VNA | Temporal Scaling

Like the closest monitor approach, the Voronoi Neighbor Averaging (VNA) algorithm uses
monitor data directly or in combination with modeling data. However, instead of using
the single closest monitor to estimate exposure at a population grid-cell, the VNA
algorithm interpolates air quality at every population grid cell by first identifying the set of
monitors that best “surround” the center of the population grid-cell.

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In particular, BenMAP identifies the nearest monitors, or “neighbors,” by drawing a

polygon, or “Voronoi” cell, around the center of each BenMAP grid cell. The polygons
have the special property that the boundaries are the same distance from the two closest
points.

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We then choose those monitors that share a boundary with the center of grid-cell “E.”
These are the nearest neighbors, we use these monitors to estimate the air pollution level
for this grid-cell.

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To estimate the air pollution level in each grid-cell, BenMAP calculates the annual and the
binned daily metrics for each of the neighboring monitors, and then calculates an
inverse-distance weighted average of the metrics. The further the monitor is from the
BenMAP grid-cell, the smaller the weight.
In the figure below, the weight for the monitor 10 miles from the center of grid-cell E is
calculated as follows:

The weights for the other monitors would be calculated in a similar fashion. BenMAP
would then calculate an inverse-distance weighted average for 1995 air pollution levels in
grid-cell E as follows:
Forecast 1995 = 0.35*80 ppb + 0.24*90 ppb+ 0.24*60 ppb + 0.18*100 ppb = 81.2 ppb .

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Note that BenMAP is calculating an inverse-distance weighted average of the annual

metrics and the binned daily metrics. Alternatively, BenMAP could calculate an
inverse-distance weighted average of the hourly and daily observations, calculated the
annual and daily metrics, and then binned the daily metrics.

C.3.2 Voronoi Neighbor Averaging (VNA) – Spatial Scaling

BenMAP can also combine VNA with spatial scaling. For each of the neighbor monitors,
BenMAP multiplies the monitoring data with the ratio of the base-year modeling data for
the destination grid-cell to the base-year modeling data for grid-cell containing the
monitor. The spatial scaling occurs in the same fashion as with temporal scaling. In the
case of pollutants typically measured hourly, such as ozone, BenMAP scales the hourly
monitor values, calculates the annual and daily metrics of interest, and then bins the daily
metrics. In the case of pollutants typically measured daily, BenMAP scales the daily
values, calculates the annual metrics of interest, and then bins the daily metric.
Consider the example in the figure below. To forecast air pollution levels for 1995,
BenMAP would multiply the 1995 monitor value by the ratio of the 1995 model value to
the 1995 model value:

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C.3.3 Voronoi Neighbor Averaging (VNA) – Temporal & Spatial Scaling

Combining both temporal and spatial scaling, BenMAP multiplies monitoring data with
the ratio of the future-year to base-year modeling data, where the future-year modeling data
are from the destination grid-cell and the base-year modeling data are from the grid-cell
containing the monitor. One the hourly and daily monitoring data are scaled, BenMAP
generates the metrics of interest, bins the daily metrics, and then uses the metrics to
estimate adverse health effects in the population grid-cell.
The figure below gives an example of combining temporal and spatial scaling.

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C.4 Fixed Radius

When using the fixed radius option to represent air pollution levels at a population
grid-cell, BenMAP identifies all monitors within a specified distance of the center of the
population grid-cell, calculates the metrics at each monitor, and then calculates a weighted
average of the metrics using the algorithms described for VNA. When no monitors are
within the specified distance, BenMAP assigns the closest monitor to a population
grid-cell, and calculates the metrics using the algorithms described for the closest monitor
approach.

C.5 Temporal and Spatial Scaling Adjustment Factors

As presented in the preceding examples of temporal and spatial scaling, the closest monitor
, VNA, and fixed radius approaches can use model data to scale monitor observations. In
the examples above, we scaled single monitor values with the ratio of single model values.
In fact, however, the scaling involves multiple monitor values and multiple model values.
To proceed with the scaling, BenMAP takes the modeling values and splits them into
groups, depending on how the pollutant is defined. (See the section on defining pollutants
in the Loading Data chapter.) The United States setup has defined ozone to have a default
of 10 adjustment factors for the ozone season, where the first group represents the first 10
percent of the model observations; the second group represents the observations between
the 10th and 20th percentile; and so on through the tenth group, which represents the
observations between the 90th and 100th percentiles. BenMAP then averages the values in
each group. The United States setup has defined particulate matter to have five adjustment
factors for each of the four seasons in the year, where the first group in each season
represents the first 20 percent of the model observations; the second group represents the
observations between the 20th and 40th percentiles; and so on. Then, as for ozone model
values, BenMAP averages the particulate matter model values in each group.
BenMAP treats the monitor values in a similar way. It sorts the monitor values from low
to high, and divides them into the same number groups as there are scaling factors.

C.5.1 Calculation of Scaling Factors

In developing scaling factors for the standard United States setup, BenMAP sorts the
modeling data into either 10 groups or 20 groups, depending on the pollutant (e.g., 10 for

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ozone and 20 for particulate matter, 5 for each of the 4 seasons). Given the number of
groups, BenMAP then determines how to assign the model values. In determining to
which group a value belongs, BenMAP assigns a two-digit "percentile" to each value.
With values in a given grid-cell sorted from low to high, the percentile for each value will
equal: (the observation rank number minus 0.5) divided by (the total number of values)
multiplied by (100). If there are 250 hourly values, the first hourly value will have a
percentile = (1-0.5)/(250)*(100) = 0.20%; the 27th value will have a percentile =
(27-0.5)/(250)*(100) = 10.60%; and so on.
Each data group is represented by "group-lo" and "group-hi" values. These are the
minimum and the maximum percentiles in each group, where group-lo equals: (group rank
minus 1) multiplied by (100) divided by ( the number of groups); and group-hi equals:
(group rank) multiplied by (100) divided by ( the number of groups) minus 0.001. If there
are ten groups: the first group will have: group-lo = (1-1)/100*10 = 0.000%, and group-hi
= (1/100*10)-0.001 = 9.999% ; the second group will have: group-lo = (2-1)/100*10 =
10.000%, and group-hi = (2/100*10)-0.001 = 19.999% ; and so on to the tenth group,
which will have: group-lo = (10-1)/100*10 = 90.000%, and group-hi = (10/100*10)-0.001
= 99.999%. BenMAP assigns each observation to a particular group with the following
algorithm: if "group-lo" <"percentile" < "group-hi", then assign the observation to that data
group.
Below we give some examples of the calculations that BenMAP performs when scaling.

C.5.1.1 Example: PM2.5 Scaling Factors in U.S. Setup

After preparing the PM2.5 model and monitor data, BenMAP calculates the following:

where:
adjusted monitor = predicted daily PM2.5 level, after
adjustment by model data (μg/m3)
monitor = observed daily PM2.5 monitor level
(μg/m3)
i = day identifier
j = model season/quintile group (1 to
20)
k = grid cell identifier for population
grid cell
l = grid cell identifier for grid cell
containing monitor

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base = base-year (e.g., 2000)

future = future-year (e.g., 2020)
REMSAD = representative model
season/quintile value (μg/m3)

After adjusting the monitor values to reflect air quality modeling, BenMAP calculates for
each monitor the PM2.5 metrics needed to estimate adverse health effects. In the case of
VNA, BenMAP then calculates a weighted average (e.g., inverse-distance weighted
average) of the neighbors identified for each population grid cell:

where:
population grid cell = inverse distance-weighted PM2.5
metric at population grid cell (μg/m3)
adjusted monitor = predicted PM2.5 metric, after
adjustment by model data (μg/m3)
m = monitor identifier
base = base-year (e.g., 2000)
future = future-year (e.g., 2020)
weight = inverse-distance weight for monitor

After generating the bins for both the baseline and control scenarios, BenMAP uses these
to calculate the change in air quality needed in most health impact functions to calculate
the change in adverse health effects. To calculate the change in air quality, BenMAP
subtracts the baseline value in the first bin from the control value in the first bin, and so on
for each of the bins created for the daily PM2.5 average.

C.5.1.2 Example: Ozone Scaling in U.S. Setup

After preparing the ozone model and monitor data, BenMAP calculates the following:

where:

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adjusted monitor = predicted hourly ozone level,

after adjustment by model data
(ppb)
monitor = observed hourly ozone monitor
level (ppb)
i = hour identifier
j = model decile group (1 to 10)
k = grid cell identifier for population
grid cell
l = grid cell identifier for grid cell
containing monitor
base = base-year (e.g., 1996)
future = future-year (e.g., 2030)
CAMX = representative model decile
value (ppb)

After adjusting the monitor values to reflect air quality modeling, BenMAP calculates for
each monitor the ozone metrics needed to estimate adverse health effects. In the case of
VNA, BenMAP then calculates a weighted average (e.g., inverse-distance weighted
average) of the neighbors identified for each population grid cell:

where:
population grid cell = inverse distance-weighted ozone
metric at population grid cell (ppb)
adjusted monitor = predicted ozone metric, after
adjustment by model data (ppb)
m = monitor identifier
future = future-year (2020, 2030)
weight = inverse-distance weight for
monitor

After generating the bins for both the baseline and control scenarios, BenMAP can use
these to calculate the change in air quality needed in most C-R functions to calculate the

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change in adverse health effects. To calculate the change in air quality, BenMAP subtracts
the baseline value in the first bin from the control value in the first bin, and so on for each
of the bins created for the daily ozone metrics.

C.6 Binned Metrics

When estimating air pollution exposure, it will often happen that metrics are often not
available for each day in the year. To remedy this, BenMAP calculates representative
values or bins with the available daily metrics, under the assumption that the missing days
have a similar distribution. Each bin represents a day. In the case where there are 365
bins, the set of bins represents the entire year.
When combining air pollution metrics from multiple monitors, BenMAP first calculates
the bins for the daily metrics, and then combines the bins, such as with some form of VNA
. Once BenMAP has calculated binned exposure measures for both a baseline and a
control scenario, BenMAP then takes the difference between the two scenarios for each
bin – taking the difference between the baseline value in the first bin and the control value
in the first bin, and so on for each of the bins.

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Appendix D: Deriving Health Impact Functions

This Appendix provides of an overview regarding the health impact functions that
BenMAP uses to estimate the impact of a change in air pollution on adverse health effects.
It provides a description of the particular types of health impact functions that BenMAP
uses.
The functional form of the relationship between the change in pollutant concentration, Dx,
and the change in population health response (usually an incidence rate), Dy depends on
the functional form of the C-R function from which it is derived, and this depends on the
underlying relationship assumed in the epidemiological study chosen to estimate a given
effect. For expository simplicity, the following subsections refer simply to a generic
adverse health effect, “y” and uses particulate matter (PM) as the pollutant – that is, Dx = D
PM – to illustrate how the relationship between Dx and Dy is derived from each of several
different C-R functions.
Estimating the relationship between DPM and Dy can be thought of as consisting of three
steps:

(1) choosing a functional form of the relationship between PM and y (the C-R function),
(2) estimating the values of the parameters in the C-R function assumed, and
(3) deriving the relationship between DPM and Dy (the health impact function) from the
relationship between PM and y (the C-R function).

Epidemiological studies have used a variety of functional forms for C-R functions. Some
studies have assumed that the relationship between adverse health and pollution is best
described by a linear form, where the relationship between y and PM is estimated by a
linear regression in which y is the dependent variable and PM is one of several
independent variables. Log-linear regression and logistic regression are other common
forms.
Note that the the log-linear form used in the epidemiological literature is often referred to
as “Poisson regression” because the underlying dependent variable is a count (e.g., number
of deaths), believed to be Poisson distributed. The model may be estimated by regression
techniques but is often estimated by maximum likelihood techniques. The form of the
model, however, is still log-linear.

D.1 Overview
The relationship between the concentration of a pollutant, x, and the population response,
y, is called the concentration-response (C-R) function. For example, the concentration of
the pollutant may be fine particulate matter (PM2.5) in μg/m3 per day, and the population
response may be the number of premature deaths per 100,000 population per day. C-R
functions are estimated in epidemiological studies. A functional form is chosen by the

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researcher, and the parameters of the function are estimated using data on the pollutant
(e.g., daily levels of PM2.5) and the health response (e.g., daily mortality counts). There are
several different functional forms, discussed below, that have been used for C-R functions.
The one most commonly used is the log-linear form, in which the natural logarithm of the
health response is a linear function of the pollutant concentration.
For the purposes of estimating benefits, we are not interested in the C-R function itself,
however, but the relationship between the change in concentration of the pollutant, Dx, and
the corresponding change in the population health response, Dy. We want to know, for
example, if the concentration of PM2.5 is reduced by 10 μg/m3, how many premature
deaths will be avoided? The relationship between Dx and Dy can be derived from the C-R
function, as described below, and we refer to this relationship as a health impact function.
Many epidemiological studies, however, do not report the C-R function, but instead report
some measure of the change in the population health response associated with a specific
change in the pollutant concentration. The most common measure reported is the relative
risk associated with a given change in the pollutant concentration. A general relationship
between Dx and Dy can, however, be derived from the relative risk. The relative risk and
similar measures reported in epidemiological studies are discussed in the sections below.
The derivation of the relationship of interest for BenMAP – the relationship between Dx
and Dy – is discussed in the subsequent sections.

D.2 Review Relative Risk and Odds Ratio

The terms relative risk and odds ratio are related but distinct. Table D-1 provides the basis
for demonstrating their relationship.

Table D-1. Relative Risk and Odds Ratio Notation

Exposure Fraction of Population Adverse Effect Measure

Affected Not Affected Relative Risk Odds

Baseline Pollutant y0 1-y0 y0/(1-yc)

Exposure y0/yc
Control Pollutant Exposure yc 1-yc yc/(1-yc)

The “risk” that people with baseline pollutant exposure will be adversely affected (e.g.,
develop chronic bronchitis) is equal to y0, while people with control pollutant exposure
face a risk, yc, of being adversely affected. The relative risk (RR) is simply:

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The odds that an individual facing high exposure will be adversely affected is:

The odds ratio is then:

This can be rearranged as follows:

As the risk associated with the specified change in pollutant exposure gets small (i.e., both
y0 and ycapproach zero), the ratio of (1-yc) to (1-y0) approaches one, and the odds ratio
approaches the relative risk. This relationship can be used to calculate the pollutant
coefficient in the C-R function from which the reported odds ratio or relative risk is
derived, as described below.

D.3 Linear Model

A linear relationship between the rate of adverse health effects (incidence rate) and various
explanatory variables is of the form:

where α incorporates all the other independent variables in the regression (evaluated at
their mean values, for example) times their respective coefficients. The relationship
between the change in the rate of the adverse health effect from the baseline rate (y0) to the
rate after control (yc) associated with a change from PM0 to PMc is then:

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For example, Ostro et al. (1991, Table 5) reported a PM2.5 coefficient of 0.0006 (with a
standard error of 0.0003) for a linear relationship between asthma and PM2.5 exposure.

The lower and upper bound estimates for the PM2.5 coefficient are calculated as follows:

It is then straightforward to calculate lower and upper bound estimates of the change in
asthma.

D.4 Log-linear Model

The log-linear relationship defines the incidence rate (y) as:

or, equivalently,

where the parameter B is the incidence rate of y when the concentration of PM is zero, the
parameter β is the coefficient of PM, ln(y) is the natural logarithm of y, and α = ln(B).
Other covariates besides pollution clearly affect mortality. The parameter B might be
thought of as containing these other covariates, for example, evaluated at their means.
That is, B = Boexp{ß1x1 + ... + ßnxn}, where Bo is the incidence of y when all covariates
in the model are zero, and x1, ... , xn are the other covariates evaluated at their mean
values. The parameter B drops out of the model, however, when changes in y are
calculated, and is therefore not important.
The relationship between DPM and Dy is:

This may be rewritten as:

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where y0 is the baseline incidence rate of the health effect (i.e., the incidence rate before
the change in PM).
The change in the incidence of adverse health effects can then be calculated by multiplying
the change in the incidence rate, Dy, by the relevant population (e.g., if the rate is number
per 100,000 population, then the relevant population is the number of 100,000s in the
population).
When the PM coefficient (β) and its standard error (σβ) are published (e.g., Ostro et al.,
1989), then the coefficient estimates associated with the lower and upper bound may be
calculated easily as follows:

Epidemiological studies often report a relative risk for a given DPM, rather than the
coefficient, β (e.g., Schwartz et al., 1995, Table 4). Recall that the relative risk (RR) is
simply the ratio of two risks:

Taking the natural log of both sides, the coefficient in the C-R function underlying the
relative risk can be derived as:

The coefficients associated with the lower and upper bounds (e.g., the 2.5 and 97.5
percentiles) can be calculated by using a published confidence interval for relative risk, and
then calculating the associated coefficients.
Because of rounding of the published RR and its confidence interval, the standard error for
the coefficient implied by the lower bound of the RR will not exactly equal that implied by
the upper bound, so an average of the two estimates is used. The underlying standard error
for the coefficient (σβ) can be approximated by:

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D.5 Logistic Model

In some epidemiological studies, a logistic model is used to estimate the probability of an
occurrence of an adverse health effect. Given a vector of explanatory variables, X, the
logistic model assumes the probability of an occurrence is:

where β is a vector of coefficients. Greene (1997, p. 874) presents models with discrete
dependent variables, such as the logit model. See also Judge et al. (1985, p. 763). This
may be rewritten as:

The odds of an occurrence is:

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The odds ratio for the control scenario (oddsc) versus the baseline (odds0) is then:

The change in the probability of an occurrence from the baseline to the control (Dy),
assuming that all the other covariates remain constant, may be derived from this odds ratio:

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Multiplying by:

gives:

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 Appendix D: Deriving Health Impact Functions

The change in the number of cases of the adverse health effect is then obtained by
multiplying by the relevant population:

When the coefficient (β) and its standard error (σβ) are published (e.g., Pope et al., 1991,
Table 5), then the coefficient estimates associated with the lower and upper bound may be
calculated easily as follows:

Often the logistic regression coefficients are not published, and only the odds ratio
corresponding to a specified change in PM is presented (e.g., Schwartz et al., 1994). It is
easy to calculate the underlying coefficient as follows:

The coefficients associated with the lower and upper bound estimates of the odds ratios are
calculated analogously.
The underlying standard error for the coefficient (σβ) can be approximated by:

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Sometimes, however, the relative risk is presented. The relative risk does not equal the
odds ratio, and a different procedure should be used to estimate the underlying coefficient.
Note that ESEERCO (1994, p. V-21) calculated (incorrectly) the underlying regression
coefficient for Abbey et al. (1993, Table 5) by taking the logarithm of the relative risk and
dividing by the change in TSP.
The relative risk (RR) is simply:

where y0 is the risk (i.e., probability of an occurrence) at the baseline PM exposure and yc
is the risk at the control PM exposure.
When the baseline incidence rate (y0) is given, then it is easy to solve for the control
incidence rate (yc):

The odds ratio, may then be calculated:

Given the odds ratio, the underlying coefficient (β) may be calculated as before:

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The odds ratio and the coefficient calculated from it are dependent on the baseline and
control incidence rates. Unfortunately, it is not always clear what the baseline and control
incidence rates should be. Abbey et al. (1995b, Table 2) reported that there are 117 new
cases of chronic bronchitis out of a sample of 1,631, or a 7.17 percent rate. In addition,
they reported the relative risk (RR = 1.81) for a new case of chronic bronchitis associated
with an annual mean concentration “increment” of 45 μg/m3 of PM2.5 exposure.
Assuming that the baseline rate for chronic bronchitis (y0) should be 7.17 percent, the
question becomes whether the “increment” of 45 μg/m3 should be added to or subtracted
from the existing PM2.5 concentration. If added the control incidence rate (yc) would be
greater than the baseline rate (y0), while subtraction would give a control rate less than the
incidence rate. In effect, one might reasonably derive two estimates of the odds ratio:

An alternative is to simply assume that the relative risk (1.81) is reasonably close to the
odds ratio and calculate the underlying coefficient. It is easy to show that the relative risk
equals:

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 Appendix D: Deriving Health Impact Functions

Assuming that:

It is then possible to calculate the underlying coefficient:

Since this coefficient estimate is based on the assumption that

it should be used in a C-R function that maintains this assumption. In effect, it should be
applied to a log-linear C-R function:

Using the formula for the change in the incidence rate and assuming a 10 μg/m3 decline in
PM2.5, it is shown that this results in changes within the bounds suggested by the two
estimates based on using the estimated odds ratios:

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In this instance, it seems that simply using the relative risk to estimate the underlying
coefficient results in a good approximation of the change in incidence. Since it is unclear
which of the two other coefficients (β1 or β2) should be used -- as the published work was
not explicit – the coefficient based on the relative risk and the log-linear functional form
seems like a reasonable approach.

D.6 Cox proportional Hazards Model

Use of a Cox proportional hazards model in an epidemiological study results in a C-R
function that is log-linear in form. It is often used to model survival times, and as a result,
this discussion focuses on mortality impacts.
The Cox proportional hazards model is based on a hazard function, defined as the
probability that an individual dies at time t, conditional on having survived up to time t
(Collet, 1994, p. 10). More formally, the hazard function equals the probability density
function for the risk of dying divided by one minus the cumulative probability density
function:

The proportional hazards model takes the form:

where X is a vector of explanatory variables, β is a vector of coefficients, and h0(t) is the

so-called “baseline hazard” rate. This terminology differs from that used in most of this
discussion: this “baseline hazard” is the risk when all of the covariates (X) are set to zero;
this is not the risk in the baseline scenario.
The Cox proportional hazards model is sometimes termed a “semi-parametric” model,
because the baseline hazard rate is calculated using a non-parametric method, while the

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impact of explanatory variables is parameterized. Collet (1994) details the estimation of

Cox proportional hazards models; in particular, see Collet’s discussion (pp. 95-97) of
nonparametric estimation of the baseline hazard.
Taking the ratio of the hazard functions for the baseline and control scenarios gives the
relative risk:

where it is assumed that the only difference between the baseline and control is the level of
PM pollution.
The relative risk is often presented rather than the coefficient β, so it is necessary to
estimate β in order to develop functional relationship between DPM and Dy, as described
previously for log-linear C-R functions.

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Appendix E: Health Incidence & Prevalence Data

in U.S. Setup
Health impact functions developed from log-linear or logistic models estimate the percent
change in an adverse health effect associated with a given pollutant change. In order to
estimate the absolute change in incidence using these functions, we need the baseline
incidence rate of the adverse health effect. And for certain health effects, such as asthma
exacerbation, we need a prevalence rate, which estimates the percentage of the general
population with a given ailment like asthma. This appendix describes the data used to
estimate baseline incidence and prevalence rates for the health effects considered in this
analysis.

E.1 Mortality
This section describes the development of the year 2000 through 2050 county mortality
rates for use in BenMAP. First, we describe the source of 1996-1998 county-level
mortality rates, and then we describe how we use national-level Census mortality rate
projections to develop 2000-2050 county-level mortality rate projections.

E.1.1 Mortality Rates 1996-1998

Age, cause, and county-specific mortality rates were obtained from the U.S. Centers for
Disease Control (CDC) for the years 1996 through 1998. CDC maintains an online data
repository of health statistics, CDC Wonder, accessible at http://wonder.cdc.gov/. The
mortality rates provided are derived from U.S. death records and U.S. Census Bureau
postcensal population estimates. Mortality rates were averaged across three years (1996
through 1998) to provide more stable estimates. Population-weighted national mortality
rates are presented in Table E-1.

Table E-1. Population-Weighted Mortality Rates (per 100 people per year) for
Selected Conditions, by Age Group

Mortality Category 0-17 18-24 25-29 30-34 35-44 45-54 55-64 65-74 75-84 85+
(ICD codes)
All-Cause 0.045 0.093 0.119 0.119 0.211 0.437 1.056 2.518 5.765 15.160
Non-Accidental (ICD 0.025 0.022 0.057 0.057 0.150 0.383 1.006 2.453 5.637 14.859
<800)
Chronic Lung Disease 0.000 0.001 0.001 0.001 0.002 0.009 0.046 0.166 0.367 0.561
(ICD 490-496)
Cardio-Pulmonary 0.004 0.005 0.013 0.013 0.044 0.143 0.420 1.163 3.179 9.846

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E.1.2 Mortality Rate Projections 2000-2050

To estimate age- and county-specific mortality rates in years 2000 through 2050, we
calculated adjustment factors, based on a series of Census Bureau projected national
mortality rates, to adjust the CDC Wonder age- and county-specific mortality rates in
1996-1998 to corresponding rates for each future year. The procedure we used was as
follows:
 For each age group, we derived an estimate of the national mortality rate in 1997 (the
midpoint year in the period 1996 - 1998) consistent with the series of Census Bureau
projected national mortality rates, which starts in 1999. We did this by regressing
projected mortality rate on year, separately for each age group, using the ten years of
Census Bureau projected rates from 1999 - 2008. The resulting estimated national age-
group-specific mortality rates for 1997 are shown in Table E-2. Note that the Census
Bureau projected mortality rates were derived from crude death rates using the following
formula, given by Chiang (1967, p.2 equation 7): M = Q/(1-(1-A)*Q), where M denotes
projected mortality rate, Q denotes crude death rate, and A denotes the fraction of the
interval (one year) lived by individuals who die in the interval. A=0.1 if age < 1, and
A=0.5 otherwise.
 We then calculated, separately for each age-group, the ratio of Census Bureau national
mortality rate in year Y (Y = 2000, 2001, ..., 2050) to the national mortality rate in 1997,
estimated in the previous step to be consistent with the Census Bureau series of rates
starting in 1999. These ratios are shown for selected years in Table E-3.
 Finally, to estimate mortality rates in year Y (Y = 2000, 2001, ..., 2050) that are both
age-group-specific and county-specific, we multiplied the CDC Wonder county-specific
age-group-specific mortality rates for 1996-1998 by the appropriate ratio calculated in
the previous step. For example, to estimate the projected mortality rate in 2010 among
ages 18-24 in Wayne County, MI, we multiplied the CDC Wonder mortality rate for ages
18-24 in Wayne County in 1996-1998 by the ratio of Census Bureau projected national
mortality rate in 2010 for ages 18-24 to (estimated) Census Bureau national mortality
rate in 1997 for ages 18-24.

Table E-2. All-Cause Mortality Rate (per 100 people per year), by Source, Year, and Age
Group

Source & Year Infant * 1-17 18-24 25-34 35-44 45-54 55-64 65-74 75-84 85+
Census Bureau 2000 0.687 0.030 0.093 0.106 0.192 0.408 0.998 2.454 5.636 13.541
Est. Census Bureau 1997 0.706 0.031 0.095 0.108 0.199 0.421 1.032 2.555 5.787 13.846
CDC Wonder 1996-1998 0.246 0.034 0.093 0.119 0.211 0.437 1.056 2.518 5.765 15.160
Estimated 2000 ** 0.239 0.033 0.091 0.116 0.204 0.424 1.022 2.419 5.615 14.826

* Note that the Census Bureau estimate is for all deaths in the first year of
life. The CDC Wonder estimate if for post-neonatal mortality (deaths after
the first month), because the health impact function (see Appendix F)

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estimates post-neonatal mortality.

** The estimate for 2000 is a population-weighted average of the
county-level forecasts for 2000 that are calculated from the CDC Wonder
county-level estimates and the ratio of the Census Bureau estimates for 2000
and 1997.

Table E-3. Ratio of Future Year All-Cause Mortality Rate to 1997 Estimated All-Cause
Mortality Rate, by Age Group

Year Infant 1-17 18-24 25-34 35-44 45-54 55-64 65-74 75-84 85+

2000 0.97 0.97 0.97 0.98 0.97 0.97 0.97 0.96 0.97 0.98

2005 0.93 0.94 0.93 0.95 0.92 0.92 0.90 0.90 0.93 0.95

2010 0.88 0.88 0.88 0.91 0.87 0.88 0.86 0.84 0.89 0.91

2015 0.83 0.81 0.84 0.88 0.82 0.83 0.82 0.79 0.83 0.89

2020 0.78 0.76 0.79 0.86 0.77 0.78 0.78 0.76 0.77 0.86

2025 0.72 0.71 0.75 0.80 0.73 0.73 0.74 0.72 0.73 0.82

2030 0.66 0.66 0.70 0.75 0.68 0.68 0.69 0.70 0.71 0.77

2035 0.61 0.61 0.66 0.70 0.64 0.64 0.65 0.67 0.68 0.72

2040 0.56 0.56 0.62 0.66 0.60 0.60 0.60 0.63 0.65 0.70

2045 0.51 0.52 0.58 0.62 0.56 0.57 0.57 0.60 0.63 0.69

2050 0.47 0.48 0.55 0.58 0.53 0.53 0.54 0.56 0.59 0.68

E.2 Hospitalizations
Regional hospitalization counts were obtained from the National Center for Health
Statistics’ (NCHS) National Hospital Discharge Survey (NHDS). NHDS is a
sample-based survey of non-Federal, short-stay hospitals (<30 days), and is the principal
source of nationwide hospitalization data. The survey collects data on patient
characteristics, diagnoses, and medical procedures. However, note that the following
hospital types are excluded from the survey: hospitals with an average patient length of
stay of greater than 30 days, federal, military, Department of Veterans Affairs hospitals,
institutional hospitals (e.g. prisons), and hospitals with fewer than six beds.
Public use data files for the year 1999 survey were downloaded (from:
ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHDS/) and processed to estimate
hospitalization counts by region. NCHS groups states into four regions using the
following groupings defined by the U.S. Bureau of the Census:
 Northeast - Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New
York, New Jersey, Pennsylvania
 Midwest - Ohio, Indiana, Illinois, Michigan, Wisconsin, Minnesota, Iowa, Missouri, North
Dakota, South Dakota, Nebraska, Kansas

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 South - Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina,
South Carolina, Georgia, Florida, Kentucky, Tennessee, Alabama, Mississippi, Arkansas,
Louisiana, Oklahoma, Texas
 West - Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada,
Washington, Oregon, California, Alaska, Hawaii
We calculated per capita hospitalization rates, by dividing these counts by the estimated
regional population estimates for 1999 that we derived from the U.S. Bureau of the Census
and the population projections used by NHDS to generate the counts. Note that NHDS
started with hospital admission counts, based on a sample of admissions, and then they
used population estimates to generate population-weighted hospital admission counts that
are representative of each region. This weighting used forecasts of 1999 population data.
Ideally, we would use these same forecasts to generate our admission rates. However,
while NHDS presented counts of hospital admissions with a high degree of age specificity,
it presented regional population data for only four age groups: 0-14, 15-44, 45-64, and 65+.
Using only the NHDS data, we would be limited to calculating regional admission rates for
four groups. Because we are interested in a broader range of age groups, we turned to
2000 Census.
We used the 2000 Census to obtain more age specificity, and then corrected the 2000
Census figures so that the total population equaled the total for 1999 forecasted by NHDS.
That is, we sued the following procedure: (1) we calculated the count of hospital
admissions by region in 1999 for the age groups of interest, (2) we calculated the 2000
regional populations corresponding to these age groups, (3) calculated regional correction
factors, that equal the regional total population in 1999 divided by the regional total
population in 2000 by region, (4) multiplied the 2000 population estimates by these
correction factors, and (5) divided the 1999 regional count of hospital admissions by the
estimated 1999 population.
The endpoints in hospitalization studies are defined using different combinations of ICD
codes. Rather than generating a unique baseline incidence rate for each ICD code
combination, for the purposes of this analysis, we identified a core group of hospitalization
rates from the studies and applied the appropriate combinations of these rates in the health
impact functions:
 all respiratory (ICD-9 460-519)
 chronic lung disease (ICD-9 490-496)
 asthma (ICD-9 493)
 pneumonia (ICD-9 480-487)
 acute bronchitis (ICD-9 466)
 acute laryngitis (ICD-9 464)
 all cardiovascular (ICD-9 390-459)
 ischemic heart disease (ICD-9 410-414)
 dysrhythmia (ICD-9 427)

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 congestive heart failure (ICD-9 428)

For each C-R function, we selected the baseline rate or combination of rates that most
closely matches to the study endpoint definition. For studies that define chronic lung
disease as ICD 490-492, 494-496, we subtracted the incidence rate for asthma (ICD 493)
from the chronic lung disease rate (ICD 490-496). In some cases, the baseline rate will not
match exactly to the endpoint definition in the study. For example, Burnett et al. (2001)
studied the following respiratory conditions in infants <2 years of age: ICD 464.4, 466,
480-486, 493. For this C-R function we apply an aggregate of the following rates: ICD
464, 466, 480-487, 493. Although they do not match exactly, we assume that relationship
observed between the pollutant and study-defined endpoint is applicable for the additional
codes. Table E-4 presents a summary of the national hospitalization rates for 1999 from
NHDS.

Table E-4. Hospitalization Rates (per 100 people per year), by Region and Age
Group

Hospital Admission Category ICD-9 Code 0-18 18-24 25-34 35-44 45-54 55-64 65+

Respiratory all respiratory 460-519 1.066 0.271 0.318 0.446 0.763 1.632 5.200

acute laryngitis 464 0.055 0.002 0.001 0.002 0.008 0.000 0.005

acute bronchitis 466 0.283 0.017 0.014 0.017 0.027 0.040 0.156

pneumonia 480-487 0.308 0.069 0.103 0.155 0.256 0.561 2.355

asthma 493 0.281 0.081 0.110 0.099 0.144 0.161 0.205

chronic lung disease 490-496 0.291 0.089 0.124 0.148 0.301 0.711 1.573

Cardiovascular all cardiovascular 390-429 0.030 0.052 0.146 0.534 1.551 3.385 8.541

ischemic heart disease 410-414 0.004 0.008 0.031 0.231 0.902 2.021 3.708

dysrhythmia 427 0.011 0.017 0.027 0.076 0.158 0.392 1.387

congestive heart 428 0.003 0.005 0.011 0.011 0.160 0.469 2.167
failure

E.3 Emergency Room Visits for Asthma

Regional asthma emergency room visit counts were obtained from the National Hospital
Ambulatory Medical Care Survey (NHAMCS). NHAMCS is a sample-based survey,
conducted by NCHS, designed to collect national data on ambulatory care utilization in
hospital emergency and outpatient departments of non-Federal, short-stay hospitals (<30
days). The target universe of the NHAMCS is in-person visits made in the United States to
emergency and outpatient departments of non-Federal, short-stay hospitals (hospitals with
an average stay of less than 30 days) or those whose specialty is general (medical or
surgical) or children’s general.

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Public use data files for the year 2000 survey were downloaded (from:
ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHAMCS/) and processed to
estimate hospitalization counts by region. We obtained population estimates from the
2000 U.S. Census. The NCHS regional groupings described above were used to estimate
regional emergency room visit rates. Table E-5 presents the estimated asthma emergency
room rates by region.

Table E-5. Emergency Room Visit Rates (per 100 people per year) for Asthma, by
Region and Age Group

ER Category ICD-9 Code Region 0-18 18-64 65+

asthma 493 Northeast 0.761 0.802 0.300
Midwest 1.476 0.877 0.334
South 1.243 0.420 0.192
West 0.381 0.381 0.137

E.4 Nonfatal Heart Attacks

The relationship between short-term particulate matter exposure and heart attacks was
quantified in a case-crossover analysis by Peters et al. (2001). The study population was
selected from heart attack survivors in a medical clinic. Therefore, the applicable
population to apply to the C-R function is all individuals surviving a heart attack in a given
year. Several data sources are available to estimate the number of heart attacks per year.
For example, several cohort studies have reported estimates of heart attack incidence rates
in the specific populations under study. However, these rates depend on the specific
characteristics of the populations under study and may not be the best data to extrapolate
nationally. The American Heart Association reports approximately 540,000 new heart
attacks per year using data from a multi-center study (Haase, 2002, to be published in the
American Heart Association’s 2003 Statistical Handbook). Exclusion of heart attack
deaths reported by CDC Wonder yields approximately 330,000 nonfatal cases per year.
An alternative approach to the estimation of heart attack rates is to use data from the
National Hospital Discharge Survey, assuming that all heart attacks that are not instantly
fatal will result in a hospitalization. According to the National Hospital Discharge Survey,
in 1999 there were approximately 829,000 hospitalizations due to heart attacks (acute
myocardial infarction: ICD-9 410) (Popovic, 2001, Table 8). We used regional
hospitalization rates over estimates extrapolated from cohort studies because the former is
part of a nationally representative survey with a larger sample size, which is intended to
provide reliable national estimates. As additional information is provided regarding the
American Heart Association methodology, we will evaluate the usefulness of this estimate
of heart attack incidence.

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Rosamond et al. (1999) reported that approximately six percent of male and eight percent
of female hospitalized heart attack patients die within 28 days (either in or outside of the
hospital). We, therefore, applied a factor of 0.93 to the count of hospitalizations to
estimate the number of nonfatal heart attacks per year. To estimate the rate of nonfatal
heart attack, we divided the count by the population estimate for 2000 from the U.S.
Census. Table E-6 presents the regional nonfatal heart attack incidence rates.

Table E-6. Nonfatal Heart Attack Rates (per 100 people per year), by Region and
Age Group

Effect Region 0-18 18-64 65+

nonfatal heart attacks (ICD-9 Northeast 0.0000 0.2167 1.6359
410)
Midwest 0.0003 0.1772 1.4898

South 0.0006 0.1620 1.1797

West 0.0000 0.1391 1.1971

* Rates are based on data from the 1999 National Hospital

Discharge Survey (NHDS) and an estimate from Rosamond et al.
that approximately 7% of individuals hospitalized for a heart
attack die within 28 days.

E.5 School Loss Days

Epidemiological studies have examined the relationship between air pollution and a variety
of measures of school absence. These measures include: school loss days for all causes,
illness-related, and respiratory illness-related. We have two sources of information. The
first is the National Center for Education Statistics, which provided an estimate of
all-cause school loss days, and the other is the National Health Interview Survey (Adams et
al., 1999, Table 47), which has data on different categories of acute school loss days.
Table E-7 presents the estimated school loss day rates. Further detail is provided below on
these rates.

Table E-7. School Loss Day Rates (per student per year)

Type Northeast Midwest South West

Respiratory illness-related 1.3 1.7 1.1 2.2
absences
Illness-related absences 2.4 2.6 2.6 3.7
All-cause 9.9 9.9 9.9 9.9
* We based illness-related school loss day rates on data from the

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1996 NHIS and an estimate of 180 school days per year. This
excludes school loss days due to injuries. We based the all-cause
school loss day rate on data from the National Center for
Education Statistics.

All-Cause School Loss Day Rate

Based on data from the U.S. Department of Education (1996, Table 42-1), the National
Center for Education Statistics estimates that for the 1993-1994 school year, 5.5 percent of
students are absent from school on a given day. This estimate is comparable to
study-specific estimates from Chen et al. (2000) and Ransom and Pope (1992), which
ranged from 4.5 to 5.1 percent.

Illness-Related School Loss Day Rate

The National Health Interview Survey (NHIS) has regional estimates of school loss days
due to a variety of acute conditions (Adams et al., 1999). NHIS is a nationwide
sample-based survey of the health of the noninstitutionalized, civilian population,
conducted by NCHS. The survey collects data on acute conditions, prevalence of chronic
conditions, episodes of injury, activity limitations, and self-reported health status.
However, it does not provide an estimate of all-cause school loss days.
In estimating illness-related school loss days, we started with school loss days due to acute
problems (Adams et al., 1999, Table 47) and subtracted lost days due to injuries, in order
to match the definition of the study used in the C-R function to estimate illness-related
school absences (Gilliland et al., 2001). We then divided by 180 school days per to
estimate illness-related school absence rates per school day. Similarly, when estimating
respiratory illness-related school loss days, we use data from Adams et al. (1999, Table
47). Note that we estimated 180 school days in a year to calculate respiratory
illness-related school absence rates per year.

E.6 Other Acute and Chronic Effects

For many of the minor effect studies, baseline rates from a single study are often the only
source of information, and we assume that these rates hold for locations in the U.S. The
use of study-specific estimates are likely to increase the uncertainty around the estimate
because they are often estimated from a single location using a relatively small sample.
These endpoints include: acute bronchitis, chronic bronchitis, upper respiratory symptoms,
lower respiratory symptoms. Table E-8 presents a summary of these baseline rates.

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Table E-8. Selected Acute and Chronic Incidence (Cases / Person-Year)

& Prevalence (Percentage Population)

Endpoint Age Parameter Rate Source

American Lung Association
Acute Bronchitis 8-12 Incidence 0.043
(2002b, Table 11)
Chronic Bronchitis 27+ Incidence 0.00378 Abbey et al (1993, Table 3)
Chronic Bronchitis 18+ Prevalence 4.43%
18-44 3.67% American Lung Association
45-64 5.05% (2002a, Table 4)

65+ 5.87%
Lower Respiratory
7-14 Incidence 0.438 Schwartz et al (1994, Table 2)
Symptoms (LRS)
Minor Restricted Activity Ostro and Rothschild (1989, p.
18-64 Incidence 7.8
Days (MRAD) 243)
Work Loss Day (WLD) 18-64 Incidence 2.172
18-24 1.971 Adams et al (1999, Table )
U.S. Bureau of the Census (1997,
25-44 2.475 No. 22)
45-64 1.796

NOTE: The incidence rate is the number of cases per person per
year. Prevalence refers to the fraction of people that have a
particular illness during a particular time period.

E.6.1 Acute Bronchitis

The annual rate of acute bronchitis for children ages 5 to 17 was obtained from the
American Lung Association (2002b, Table 11). The authors reported an annual incidence
rate per person of 0.043, derived from the 1996 National Health Interview Survey.

E.6.2 Chronic Bronchitis Incidence Rate

The annual incidence rate for chronic bronchitis is estimated from data reported by Abbey
et al. (1993, Table 3). The rate is calculated by taking the number of new cases (234),
dividing by the number of individuals in the sample (3,310), dividing by the ten years
covered in the sample, and then multiplying by one minus the reversal rate (estimated to be
46.6% based on Abbey et al. (1995a, Table 1).
Age-specific incidence rates are not available. Abbey et al. (1995a, Table 1) did report the
incidences by three age groups (25-54, 55-74, and 75+) for “cough type” and “sputum
type” bronchitis. However, they did not report an overall incidence rate for bronchitis by
age-group. Since, the cough and sputum types of bronchitis overlap to an unknown extent,
we did not attempt to generate age-specific incidence rates for the over-all rate of

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bronchitis.

E.6.3 Chronic Bronchitis Prevalence Rate

We obtained the annual prevalence rate for chronic bronchitis from the American Lung
Association (2002a, Table 4). Based on an analysis of 1999 National Health Interview
Survey data, they estimated a rate of 0.0443 for persons 18 and older, they also reported
the following prevalence rates for people in the age groups 18-44, 45-64, and 65+: 0.0367,
0.0505, and 0.0587, respectively.

E.6.4 Lower Respiratory Symptoms

Lower respiratory symptoms (LRS) are defined as two or more of the following: cough,
chest pain, phlegm, wheeze. The proposed yearly incidence rate for 100 people, 43.8, is
based on the percentiles in Schwartz et al. (Schwartz et al., 1994, Table 2). The authors
did not report the mean incidence rate, but rather reported various percentiles from the
incidence rate distribution. The percentiles and associated per person per day values are 10
th = 0 percent, 25th = 0 percent, 50th = 0 percent, 75th = 0.29 percent, and 90th = 0.34

percent. The most conservative estimate consistent with the data are to assume the
incidence per person per day is zero up to the 75th percentile, a constant 0.29 percent
between the 75th and 90th percentiles, and a constant 0.34 percent between the 90th and 100
th percentiles. Alternatively, assuming a linear slope between the 50th and 75th, 75th and 90
th, and 90th to 100th percentiles, the estimated mean incidence rate per person per day is

0.12 percent. (For example, the 62.5th percentile would have an estimated incidence rate
per person per day of 0.145 percent.) We used the latter approach in this analysis.

E.6.5 Minor Restricted Activity Days (MRAD)

Ostro and Rothschild (1989, p. 243) provide an estimate of the annual incidence rate of
MRADs per person of 7.8.

E.6.6 Work Loss Days

The yearly work-loss-day incidence rate per 100 people is based on estimates from the
1996 National Health Interview Survey (Adams et al., 1999, Table 41). They reported a
total annual work loss days of 352 million for individuals ages 18 to 65. The total
population of individuals of this age group in 1996 (162 million) was obtained from (U.S.
Bureau of the Census, 1997, No. 22). The average annual rate of work loss days per
individual is 2.17. Using a similar approach, we calculated work-loss-day rates for ages
18-24, 25-44, and 45-64, respectively.

E.7 Asthma-Related Health Effects

Several studies have examined the impact of air pollution on asthma development or
exacerbation. Many of the baseline incidence rates used in the C-R functions are based on
study-specific estimates. The baseline rates for the various endpoints are described below

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and summarized in TableE-9.

Table E-9. Asthma-Related Health Effects Rates

Endpoint Age Parameter a Rate Source

Asthma Exacerbation, Shortness 8-13 Incidence 13.51

Ostro et al (2001, p. 202)
of Breath, African American 8-13 Prevalence 7.40%

Asthma Exacerbation, Wheeze, 8-13 Incidence 27.74

Ostro et al (2001, p. 202)
African American 8-13 Prevalence 17.30%

Asthma Exacerbation, Cough, 8-13 Incidence 24.46

Ostro et al (2001, p. 202)
African American 8-13 Prevalence 14.50%
Asthma Exacerbation, Cough 6-13 Incidence 31.39 Vedal et al (1998, Table 1)
Upper Respiratory Symptoms 124.79
9-11 Incidence
(URS)

NOTE: The incidence rate is the number of cases per person per
year. Prevalence refers to the fraction of people that have a
particular illness during a particular time period.

E.7.1 Shortness of Breath

To estimate the annual rate of new shortness of breath episodes among African-American
asthmatics, ages 8-13, we used the rate reported by Ostro et al. (2001, p.202). We
estimated the daily prevalence of shortness of breath episodes among African-American
asthmatics, ages 8-13, by taking a weighted average of the reported rates in Ostro et al.
(2001, p.202).

E.7.2 Wheeze
The daily rate of new wheeze episodes among African-American asthmatics, ages 8-13, is
reported by Ostro et al. (2001, p.202) as 0.076. We multiplied this value by 100 and by
365 to get the annual incidence rate per 100 people. The daily rate of prevalent wheeze
episodes (0.173) among African-American asthmatics, ages 8-13, is estimated by taking a
weighted average of the reported rates in Ostro et al. (2001, p.202)

E.7.3 Cough
The daily rate of new cough episodes among African-American asthmatics, ages 8-13, is
reported by Ostro et al. (2001, p.202) as 0.067. We multiplied this value by 100 and by
365 to get the annual incidence rate per 100 people. The daily rate of prevalent cough
episodes (0.145) among African-American asthmatics, ages 8-13, is estimated by taking a
weighted average of the reported rates in Ostro et al. (2001, p.202).

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E.7.4 Upper Respiratory Symptoms

Upper Respiratory Symptoms are defined as one or more of the following: runny or stuffy
nose; wet cough; burning, aching, or red eyes. Using the incidence rates for upper
respiratory symptoms among asthmatics, published in Pope et al. (1991, Table 2), we
calculated a sample size-weighted average incidence rate.

E.7.5 Asthma Population Estimates

In studies examining the association between air pollution and the development or
exacerbation of asthma, often times an estimate of the percent of the population with
asthma is required. Asthma percentages were obtained either directly from the National
Health Interview Survey (NHIS) or an American Lung Association (2002c) report
summarizing data from NHIS. Table E-10 presents asthma prevalence rates used to define
asthmatic populations in the health impact functions.

Table E-10. Asthma Prevalence Rates Used to Estimate Asthmatic Populations

Population Group Prevalence Source

All Ages 3.86%
<18 5.27%
5-17 5.67%
American Lung Association (2002c) *
18-44 3.71%
45-64 3.33%
65+ 2.21%
African-American, 5 to 17 7.26%
American Lung Association (2002c) *
African-American, <18 7.35%
Male, 27+ 2.10% 2000 NHIS public use data files **

* American Lung Association (2002c) is based on the 1999

National Health Interview Survey (Adams et al, 1999).
** See
ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHIS/20
00/

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 Appendix F: Particulate Matter Health Impact Functions in U.S. Setup

Appendix F: Particulate Matter Health Impact

Functions in U.S. Setup
In this Appendix, we present the PM-related health impact functions in BenMAP. Each
sub-section has a table with a brief description of the health impact function and the
underlying parameters. Following each table, we present a brief summary of each of the
studies and any items that are unique to the study.
Note that Appendix D mathematically derives the standard types of health impact functions
encountered in the epidemiological literature, such as, log-linear, logistic and linear, so we
simply note here the type of functional form. And Appendix E presents a description of
the sources for the incidence and prevalence data used in the health impact functions.

F.1 Long-term Mortality

There are two types of exposure to PM that may result in premature mortality. Short-term
exposure may result in excess mortality on the same day or within a few days of exposure.
Long-term exposure over, say, a year or more, may result in mortality in excess of what it
would be if PM levels were generally lower, although the excess mortality that occurs will
not necessarily be associated with any particular episode of elevated air pollution levels. In
other words, long-term exposure may capture a facet of the association between PM and
mortality that is not captured by short-term exposure. Table F-1 lists the long-term
mortality health impact functions.

Table F-1. Health Impact Functions for Particulate Matter and Long-Term
Mortality
Effect Author Year Location Age Metric Beta Std Form Notes
Err

Mortality, All Expert A 2006 30-9 Annual 0.0151 Log-linear

Cause 9 80

Mortality, All Expert B 2006 30-9 Annual 0.0126 Log-linear Range >10 to 30 ug. Unconditional dist. 2% no
Cause 9 20 causality included.

Mortality, All Expert B 2006 30-9 Annual 0.0119 Log-linear Range 4 to 10 ug. Unconditional dist. 2% no
Cause 9 50 causality included.

Mortality, All Expert C 2006 30-9 Annual 0.0119 Log-linear

Cause 9 30

Mortality, All Expert D 2006 30-9 Annual 0.0083 Log-linear Unconditional dist. 5% no causality included.
Cause 9 80

Mortality, All Expert E 2006 30-9 Annual 0.0196 Log-linear Unconditional dist. 1% no causality included.
Cause 9 70

Mortality, All Expert F 2006 30-9 Annual 0.0114 Log-linear Range >7 to 30 ug
Cause 9 40

Mortality, All Expert F 2006 30-9 Annual 0.0093 Log-linear Range 4 to 7 ug

Cause 9 70

Mortality, All Expert G 2006 30-9 Annual 0.0069 Log-linear Unconditional dist. 30% no causality included.
Cause 9 70

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Effect Author Year Location Age Metric Beta Std Form Notes
Err

Mortality, All Expert H 2006 30-9 Annual 0.0087 Log-linear

Cause 9 00

Mortality, All Expert I 2006 30-9 Annual 0.0118 Log-linear Unconditional dist. 5% no causality included.
Cause 9 10

Mortality, All Expert J 2006 30-9 Annual 0.0096 Log-linear

Cause 9 20

Mortality, All Expert K 2006 30-9 Annual 0.0068 Log-linear Range >16 to 30. No threshold. Conditional
Cause 9 90 dist.

Mortality, All Expert K 2006 30-9 Annual 0.0039 Log-linear Range 4 to 16 ug. No threshold. Conditional
Cause 9 40 dist.

Mortality, All Expert K 2006 30-9 Annual 0.0039 Log-linear Range 4 to 16 ug. Threshold 0 to 5 ug.
Cause 9 40 Conditional dist.

Mortality, All Expert K 2006 30-9 Annual 0.0039 Log-linear Range 4 to 16 ug. Threshold 5 to 10 ug.
Cause 9 40 Conditional dist.

Mortality, All Expert L 2006 30-9 Annual 0.0093 Log-linear Range >10 to 30 ug. Unconditional dist. 1% no
Cause 9 40 causality included.

Mortality, All Expert L 2006 30-9 Annual 0.0073 Log-linear Range 4 to 10 ug. Unconditional dist. 25% no
Cause 9 90 causality included.

Mortality, All Laden et al. 2006 25-9 Annual 0.0148 0.0041 Log-linear Adjusted coefficient with 10 ug/m3 threshold.
Cause 6 cities 9 42 70

Mortality, All Laden et al. 2006 25-9 Annual 0.0148 0.0041 Log-linear
Cause 6 cities 9 42 70

Mortality, All Pope et al. 2002 30-9 Annual 0.0065 0.0024 Log-linear Adjusted coefficient with 10 ug/m3 threshold.
Cause 51 cities 9 55 27

Mortality, All Pope et al. 2002 30-9 Annual 0.0072 0.0026 Log-linear Adjusted coefficient with 12 ug/m3 threshold.
Cause 51 cities 9 84 96

Mortality, All Pope et al. 2002 30-9 Annual 0.0087 0.0032 Log-linear Adjusted coefficient with 15 ug/m3 threshold.
Cause 51 cities 9 40 36

Mortality, All Pope et al. 2002 30-9 Annual 0.0058 0.0021 Log-linear Adjusted coefficient with 7.5 ug/m3 threshold.
Cause 51 cities 9 27 57

Mortality, All Pope et al. 2002 30-9 Annual 0.0058 0.0021 Log-linear
Cause 51 cities 9 27 57

Mortality, All Woodruff et 1997 Infan Annual 0.0039 0.0012 Logistic Adjusted coefficient with 10 ug/m3 threshold.
Cause al. 86 cities t 22 21

Mortality, All Woodruff et 1997 Infan Annual 0.0039 0.0012 Logistic

Cause al. 86 cities t 22 21

Mortality, All Woodruff et 2006 204 Infan Annual 0.0067 0.0073 Logistic Adjusted coefficient with 10 ug/m3 threshold.
Cause al. counties t 66 39

Mortality, All Woodruff et 2006 204 Infan Annual 0.0067 0.0073 Logistic
Cause al. counties t 66 39

F.1.1 Expert Functions

In this section, we describe the approach taken to incorporate into BenMAP concentration-
response (C-R) functions that were obtained through expert elicitation for EPA (IEc,
2006).
We have specified expert distributions for the PM2.5 effect either as truncated parametric
distributions or as non-parametric distributions. Therefore they can only be included in

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BenMAP in the form of custom distribution tables containing 15,000 random draws (with
replacement) from an underlying distribution. We first describe the way these custom
distribution tables were created. Then we explain how these custom distribution tables
should be handled in a configuration file to represent the expert-specified distribution as
closely as possible.
Note that the table on page 3-30 of the expert elicitation report (IEc, 2006) refers to the
non-parametric distributions as “custom” distributions. However, BenMAP refers to
distribution tables that are supplied in the form of a simulated draw as “custom distribution
tables”. In order to avoid confusion in terminology, we will call the expert-specified
distributions, which did not have a parametric shape, “non-parametric” expert
distributions.
We divided the experts into two groups – those who specified a parametric distribution and
those who specified a non-parametric distribution. This division was necessary because
the two groups required different methods for generating the custom distribution tables.
We describe the respective algorithms below and then provide an assessment of the results
for each expert.

F.1.1.1 Parametric Distributions

Experts A, C, D, E, G, I, J, and K chose parametric distribution functions to represent their
subjective beliefs about the percent change in risk associated with an increase in PM2.5.
In particular, they specified the following characteristics of the distribution:
 The shape (e.g., Normal, Triangular, Weibull)
 The truncation points (i.e., minimum and/or maximum)
 Two or three percentile points
 The likelihood that the association is causal and whether the function includes that (i.e.,
whether the function is conditional on the association being causal or unconditional).
There were two types of inconsistencies encountered in these specifications:
(1) The experts who chose Normal or Weibull shapes for their distributions also specified
minimum and/or maximum values at which there could be an effect. The Normal
distribution has an unlimited support from -∞ to +∞. The Weibull distribution has support
(l,+∞), where l is a location parameter that can be any value on the real line. The
specification of a minimum or a maximum value for the effect is therefore inconsistent
with specifying these distributions. Therefore, we interpreted these experts’ distributions
as truncated Normal or truncated Weibull distributions. In other words, we assumed that
the shape of the distribution is Normal or Weibull between the truncation points.
(2) Experts A, C, and J indicated that they included the likelihood of causality in their
subjective distributions. However, the continuous parametric distributions specified were
inconsistent with the causality likelihoods provided by these experts. Because there was
no way to reconcile this, we chose to interpret the distributions of these experts as

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unconditional and ignore the additional information on the likelihood of causality. For
example, Expert A specified a truncated Normal distribution with a minimum 0 and a
maximum 4. The expert also indicated that the likelihood of causality is 95 percent and it
is included in the distribution. This implies that the 5th percentile of the truncated Normal
distribution should be zero. The minimum and 5th percentile of the distribution both being
zero imply a density with a large (discrete) mass at zero. This, however, is not consistent
with specifying a continuous Normal density. (In the case of Expert A, in addition, he
specified a 5th percentile value of 0.29, whereas a 5 percent chance of non-causality would
imply a 5th percentile value of 0.)
In order to create a random draw from a parametric distribution it is not sufficient to know
its shape and truncation points. In addition, one needs to know the values of parameters
that distinguish this particular distribution from a class of similarly shaped distributions
with identical truncation points. Experts D and I reported parameter values of their
subjective distributions (see details in Table 1). Therefore, we simply drew 15,000 times
from each of their distributions.
However, the only information, in addition to the shape and truncation points, which the
other experts provided was the percentile points. To derive the parameter values of
interest, we used this information as follows:
Let F(x;θ,min,max) be a truncated continuous parametric (cumulative) distribution
function with (vector of) parameters θ and truncation points min and max. The nth
percentile point is defined as the value xn such that F(xn;θ,min,max)=n/100. Thus, if we
know that the expert distribution’s nth percentile point is xn and mth percentile point is xm
then the following has to hold:

F(xn;θ,min,max)=n/100
F(xm;θ,min,max)=m/100

This is a system of non-linear equations that can be solved for the unknown distribution
parameters θ. We used the Nelder and Mead (1965) numeric optimization algorithm,
available in R, to find the best-fitting estimates of parameters θ for the truncated
distributions specified by the experts. Once estimates of θ were obtained, the distributions
were specified fully and we had enough information to make 15,000 draws from each.

Table F-2 below summarizes the results for each expert who specified a parametric
distribution. In each case, we provide an “input” line that has all the information that was
provided by the expert. We also show the “output” line that contains the inferred
parameters and five percentile points of the distribution from which draws were made.
Highlighted in yellow are the percentiles specified by the expert and used to create the
equation system for the optimization. After finding the best-fitting parameters, we
calculated the associated percentiles and confirmed that they are close to the input values.

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Table F-2. Description of the Parametric Expert Functions

Expert Information Distribution Min P5 P25 P50 P75 P95 Max Parameters

mean=?
input Normal 0 0.290 2.900 4
sd=?
A
mean=1.42
output 0.290 0.929 1.481 2.059 2.900
sd=0.895
mean=?
input Normal 0 1.200 2.000 +∞
sd=?
C
mean=1.196
output 0.423 0.875 1.200 1.528 2.000
sd=0.488
input Triangular 0.100 1.600 mode=0.95
D
output 0.350 0.662 0.897 1.107 1.382
mean=?
input Normal 0 2.000 3.000 +∞
sd=?
E
mean=2
output 1.002 1.590 2.000 2.410 3.000
sd=0.608
mean=?
input Normal -∞ 1.000 1.300 1.500
sd=?
G
mean=1.001
output 0.695 0.875 1.000 1.124 1.300
sd=0.185
mean=1.25
input Normal 0.200 2.300
sd=0.53
I
output 0.473 0.912 1.250 1.588 2.027
shape=?
input Weibull 0 0.150 0.900 2.000 3.000 scale=?
location=?
J
shape=2.21
output 0.150 0.525 0.900 1.331 2.000 scale=1.413
location=-0.326
mean=?
K1 input Normal -∞ 0.100 0.400 0.800
sd=?
4-16
mean=0.404
ug/m3 output 0.100 0.277 0.400 0.521 0.682
sd=0.184
mean=?
K2 input Normal -∞ 0.100 0.700 1.500
sd=?
>16-30
mean=0.707
ug/m3 output 0.100 0.455 0.700 0.942 1.264
sd=0.367

For example, Expert A indicated that the distribution of the effect is Normal, with minimum
0 and maximum 4. Under the assumption that this is actually a truncated Normal
distribution, we looked for the corresponding mean and standard deviation for it. The 5th
and the 95th percentile values (0.29 and 2.90, respectively) were used to specify the
following equations:

N(0.29;mean=?,sd=?,min=0,max=4)=0.05

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N(2.90; mean=?,sd=?,min=0,max=4)=0.95

The solution to this system was a mean of 1.42 and a standard deviation of 0.89. We also
verified that these parameters produced percentile values consistent with the ones supplied
by the expert. We similarly solved for the parameters of the other experts who specified
parametric distributions, with the exception of experts D and I, who specified their
distributions fully.

The experts were asked to describe uncertainty distributions for the percent change in
mortality risk associated with a 1 μg/m3 change in PM2.5. All of the experts assumed
log-linear (or piecewise log-linear) C-R functions. If Z denotes the percent change elicited
from an expert, the relative risk associated with a 1 μg/m3 change in PM2.5 is (1+Z/100),
and the PM2.5 coefficient in the log-linear C-R function is ln(1+(Z/100)). We applied this
transformation to the values drawn from each distribution.

Finally, some experts stated that their distribution does not incorporate the likelihood of
causality – i.e., they specified conditional distributions. We made 15,000 draws from an
expert’s conditional distribution. BenMAP contains a function that is zero. If an expert
specified, for example, a five percent chance that there is not a causal association, BenMAP
will draw from this zero function with five percent probability and draw from the
15,000-draw custom distribution (of positive values) with 95 percent probability. Table F-3
below shows summary statistics for the draws from the parametric distributions that became
BenMAP “custom” distribution tables. Additional details on the form of the distributions
are below and in Belova et al (2007).

Table F-3. Descriptive Statistics of the Random Draws from the Parametric Expert
Distributions
Standard
Expert Mean Min P25 P50 P75 Max
Deviation
A 0.01518 0.00773 0.00000 0.00944 0.01483 0.02051 0.03917
C 0.01193 0.00466 0.00001 0.00870 0.01189 0.01509 0.02848
D (cond) 0.00884 0.00305 0.00105 0.00671 0.00899 0.01108 0.01577
D 0.00838 0.00354 0.00000 0.00623 0.00875 0.01092 0.01577
E (cond) 0.01975 0.00591 0.00026 0.01577 0.01986 0.02376 0.04534
E 0.01967 0.00619 0.00000 0.01575 0.01989 0.02381 0.04534
G (cond) 0.00996 0.00181 0.00256 0.00873 0.00996 0.01123 0.01489
G 0.00697 0.00480 0.00000 0.00000 0.00892 0.01062 0.01489
I (cond) 0.01240 0.00458 0.00200 0.00905 0.01244 0.01575 0.02273
I 0.01181 0.00523 0.00000 0.00845 0.01214 0.01559 0.02273
J 0.00962 0.00567 0.00000 0.00525 0.00902 0.01329 0.02936
K1 (cond) 0.00394 0.00175 -0.00262 0.00278 0.00398 0.00520 0.00797
K1 0.00139 0.00215 -0.00262 0.00000 0.00000 0.00298 0.00796
K2 (cond) 0.00689 0.00350 -0.00766 0.00452 0.00698 0.00937 0.01489
K2 0.00237 0.00382 -0.00402 0.00000 0.00000 0.00489 0.01488

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F.1.1.2 Non-Parametric Distributions

Experts B, F, H, and L chose a non-parametric distribution function to represent their
subjective beliefs about the percent change in risk associated with 1 μg/m3 increase in PM
2.5. They specified the following characteristics of the distribution:

 The truncation points (i.e., minimum and/or maximum)

 Five percentile points
 The likelihood that the association is causal and whether the function includes that (i.e.,
whether the function is conditional on the association being causal or unconditional)

The only information that we had about these distributions was the minimum, the
maximum, and the five percentiles. The shape of the distribution was unknown. Therefore,
we made an assumption that the cumulative distribution function (cdf) is piece-wise linear.
In other words, we assumed that all values between the percentiles are equally likely.
Following this assumption, we used linear interpolation between the percentile points to
derive the cdf for each expert. We then made 15,000 draws from each cdf.

Table F-4 shows the inputs and the outputs of this process for each expert. The inputs are
the minimum, the maximum, and the percentiles. The outputs are the percentiles that we
calculated from the draws from the respective linearly interpolated cdfs.

Table F-4. Description of the Non-Parametric Expert Functions

Expert Information Min P5 P10 P25 P50 P75 P95 Max
B1 0.010 0.100 0.200 1.200 2.100 2.600 2.800
input
4-10
ug/m3 output 0.099 0.203 1.213 2.092 2.599
B2 0.100 0.200 0.500 1.200 2.100 2.600 2.800
input
>10-30
ug/m3 output 0.198 0.501 1.191 2.096 2.597
F1 0.370 0.580 0.730 0.930 1.100 1.400 1.700
input
4-7
ug/m3 output 0.581 0.732 0.928 1.097 1.407
F2 0.290 0.770 0.960 1.100 1.400 1.600 1.800
input
>7-30
ug/m3 output 0.771 0.958 1.100 1.398 1.606

input 0 0 0 0.400 0.700 1.300 2.000 3.000

H
output 0 0 0.407 0.710 1.320 2.010
L1 0 0.200 0.570 1.000 1.400 1.600 2.700
input
4-10
ug/m3 output 0.201 0.570 0.996 1.400 1.619
L2 0.020 0.200 0.570 1.000 1.400 1.600 2.700
input
>10-30
ug/m3 0.018 0.568 1.003 1.396 1.634

Table F-5 below shows summary statistics for the draws from the non-parametric
distributions that became BenMAP “custom” distribution tables. The section below on

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distributional details contains histograms for all the experts’ distributions.

Table F-5. Descriptive Statistics of the Random Draws from the Non-Parametric
Expert Distributions
Standard
Expert Mean Min P25 P50 P75 Max
Deviation
B1 (cond) 0.01217 0.00897 0.00010 0.00200 0.01195 0.02090 0.02761
B1 0.01195 0.00901 0.00000 0.00195 0.01167 0.02075 0.02761
B2 (cond) 0.01290 0.00813 0.00100 0.00489 0.01187 0.02068 0.02761
B2 0.01262 0.00827 0.00000 0.00464 0.01159 0.02042 0.02761
F1 0.00937 0.00268 0.00370 0.00727 0.00924 0.01092 0.01686
F2 0.01144 0.00292 0.00290 0.00951 0.01091 0.01387 0.01784
H 0.00870 0.00662 0.00000 0.00406 0.00702 0.01302 0.02954
L1 (cond) 0.00985 0.00511 0.00001 0.00582 0.00999 0.01391 0.02662
L1 0.00739 0.00613 0.00000 0.00001 0.00727 0.01250 0.02659
L2 (cond)c 0.00953 0.00544 0.00000 0.00567 0.00991 0.01389 0.02661
L2 0.00934 0.00549 0.00000 0.00531 0.00964 0.01371 0.02661

F.1.1.3 Using Expert Functions in BenMAP

When an expert has specified certain functional specifics with certain probabilities, the
resulting “C-R function” becomes a set of possible functions, each with an associated
probability. For example, expert K specified a piecewise log-linear function (i.e., two
different log-linear functions on two different parts of the range of PM2.5); this expert also
specified a threshold within different ranges with different probabilities (and no threshold
with a specified probability). BenMAP incorporates such a set of possible functions
specified by an expert function by assigning appropriate weights to each specification. We
illustrate this using expert K’s specification.

Expert K specified one log-linear function if the baseline PM2.5 value falls within the range
from 4 μg/m3 to 16 μg/m3 and another log-linear function if the baseline value falls within
the range from >16 μg/m3 to 30 μg/m3. BenMAP thus incorporates two sets of functions –
one set for each of these two PM2.5 ranges – and selects from the set appropriate for a given
PM2.5 baseline value. Expert K also specified a 64% probability that there is no causal
relationship; an 18% probability that there is a causal relationship with no threshold, a 4%
probability that there is a causal relationship with a threshold somewhere between 5 μg/m3
to 10 μg/m3, and a 14% probability that there is a causal relationship with a threshold
somewhere between 0 μg/m3 to 5 μg/m3. Thus, the set of log-linear functions in BenMAP
for expert K on the range from 4 μg/m3 to 16 μg/m3 contains:

 a function with PM2.5 coefficient = 0 (no causality), which BenMAP selects with 65%
probability;
 a function with the PM2.5 coefficient expert K specified for the log-linear function on that
range and no threshold, which BenMAP selects with 18% probability;
 a function with the PM2.5 coefficient expert K specified for the log-linear function on that
range and a threshold (with uniform probability) between 0 μg/m3 to 5 μg/m3, which

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BenMAP selects with 14% probability; and

 a function with the PM2.5 coefficient expert K specified for the log-linear function on that
range and a threshold (with uniform probability) between 5 μg/m3 to 10 μg/m3, which
BenMAP selects with 4% probability.

If the PM2.5 baseline value is greater than 16 μg/m3, BenMAP goes through an analogous
procedure to select a function from among the two functions in that set.
F.1.1.4 Distributional Details by Expert
Distributional details on each expert distribution are presented below. The derivation of
the distributions is described above with additional details provided by Belova et al
(2007).

F.1.1.4.1 Expert A

Figure F-1. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert A

Notes:
- Expert A specified a truncated Normal Distribution. We inferred the following values
for the parameters of this distribution: mean=1.42 and standard deviation=0.89.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.2 Expert B

Figure F-2. Characteristics of the Random Draw from the Approximated

Distribution of the PM2.5 Effect Specified by Expert B

(1) Results for the range 4-10 ug/m3

Notes:
- Expert B specified a non-parametric distribution using five percentile points. We
linearly interpolated the cdf between them. Panel (a) shows q-q plot of the expert
percentiles and empirical percentiles for the draw. Panel (b) shows empirical cdf
associated with the draw, the red “X” marks indicate corresponding expert percentiles.
The distribution was conditional on causality. We created a corresponding unconditional
distribution by adding extra 2 percent zeros to the draw. Panels (c) and (d) show the
respective distributions.

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- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

Figure F-2. Characteristics of the Random Draw from the Approximated

Distribution of the PM2.5 Effect Specified by Expert B (continued)

(2) Results for the range >10-30 ug/m3

Notes:
- Expert B specified a non-parametric distribution using five percentile points. We
linearly interpolated the cdf between them. Panel (a) shows q-q plot of the expert
percentiles and empirical percentiles for the draw. Panel (b) shows empirical cdf
associated with the draw, the red “X” marks indicate corresponding expert percentiles.
The distribution was conditional on causality. We created a corresponding unconditional
distribution by adding extra 2 percent zeros to the draw. Panels (c) and (d) show the

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respective distributions.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

F.1.1.4.3 Expert C

Figure F-3. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert C

Notes:
- Expert C specified a truncated Normal Distribution. We inferred the following values
for the parameters of this distribution: mean=1.20 and standard deviation=0.49.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.4 Expert D

Figure F-4. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert D

Notes:
- Expert D specified a Triangular Distribution with minimum=0.1, maximum=1.6, and
mode=0.95. The distribution was conditional on causality. We created a corresponding
unconditional distribution by adding extra 5 percent zeros to the draw.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.5 Expert E

Figure F-5. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert E

Notes:
- Expert E specified a truncated Normal Distribution. We inferred the following
parameters for this distribution: mean=2.00 and standard deviation=0.61. The
distribution was conditional on causality. We created a corresponding unconditional
distribution by adding extra 1 percent zeros to the draw.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.6 Expert F

Figure F-6. Characteristics of the Random Draw from the Approximated

Distribution of the PM2.5 Effect Specified by Expert F

(1) Results for the range 4-7 ug/m3

Notes:
- Expert F specified a non-parametric distribution using five percentile points. We
linearly interpolated the cdf between them. Panel (a) shows q-q plot of the expert
percentiles and empirical percentiles for the draw. Panel (b) shows empirical cdf
associated with the draw, the red “X” marks indicate corresponding expert percentiles.
Panel (c) shows the histogram of the distribution.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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Figure F-6. Characteristics of the Random Draw from the Approximated

Distribution of the PM2.5 Effect Specified by Expert F (continued)
(2) Results for the range >7-30 ug/m3

Notes:
- Expert F specified a non-parametric distribution using five percentile points. We
linearly interpolated the cdf between them. Panel (a) shows q-q plot of the expert
percentiles and empirical percentiles for the draw. Panel (b) shows empirical cdf
associated with the draw, the red “X” marks indicate corresponding expert percentiles.
Panel (c) shows the histogram of the distribution.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.7 Expert G

Figure F-7. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert G

Notes:
- Expert G specified a truncated Normal Distribution. We inferred the following
parameters for this distribution: mean=1.00 and standard deviation=0.19. The
distribution was conditional on causality. We created a corresponding unconditional
distribution by adding extra 30 percent zeros to the draw.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.8 Expert H

Figure F-8. Characteristics of the Random Draw from the Approximated

Distribution of the PM2.5 Effect Specified by Expert H

Notes:
- Expert H specified a non-parametric distribution using six percentile points. We linearly
interpolated the cdf between them. Panel (a) shows q-q plot of the expert percentiles and
empirical percentiles for the draw. Panel (b) shows empirical cdf associated with the
draw, the red “X” marks indicate corresponding expert percentiles. Panel (c) shows the
histogram of the distribution.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.9 Expert I

Figure F-9. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert I

Notes:
- Expert I specified a truncated Normal Distribution with mean=1.25 and standard
deviation=0.53. The distribution was conditional on causality. We created a
corresponding unconditional distribution by adding extra 5 percent zeros to the draw.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.10 Expert J

Figure F-10. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert J

Notes:
- Expert J specified a truncated Weibull Distribution. We inferred the following values
for the parameters of this distribution: shape=2.21, scale=1.41, and location=-0.33.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.11 Expert K

Figure F-11. Histogram of the Random Draw from the Distribution of the PM2.5
Effect Specified by Expert K

Notes:
- Expert K specified a truncated Normal Distribution two ranges (4-16 ug/m3 and >16-30
ug/m3). We inferred the following parameters for this distribution: mean=0.40 and
standard deviation=0.18 in the lower range and mean=0.71 and standard deviation=0.37
in the upper range. The distribution was conditional on causality. We created a
corresponding unconditional distribution by adding extra 65 percent zeros to the draws in
each range.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

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F.1.1.4.12 Expert L

Figure F-12. Characteristics of the Random Draw from the Approximated

Distribution of the PM2.5 Effect Specified by Expert L

(1) Results for the range 4-10 ug/m3

Notes:
- Expert L specified a non-parametric distribution using five percentile points. We
linearly interpolated the cdf between them. Panel (a) shows q-q plot of the expert
percentiles and empirical percentiles for the draw. Panel (b) shows empirical cdf
associated with the draw, the red “X” marks indicate corresponding expert percentiles.
The distribution was conditional on causality. We created a corresponding unconditional
distribution by adding extra 25 percent zeros to the draw. Panels (c) and (d) show the
respective distributions.
- The experts specified distributions for the percent changes in the relative risk. The
distribution of the corresponding PM2.5 effects was the following transformation of the

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percent change in relative risk Z – log(1+(Z/100)).

Figure F-12. Characteristics of the Random Draw from the Approximated

Distribution of the PM2.5 Effect Specified by Expert L (continued)

(2) Results for the range >10-30 ug/m3

Notes:
- Expert L specified a non-parametric distribution using five percentile points. We
linearly interpolated the cdf between them. Panel (a) shows q-q plot of the expert
percentiles and empirical percentiles for the draw. Panel (b) shows empirical cdf
associated with the draw, the red “X” marks indicate corresponding expert percentiles.
The distribution was conditional on causality. We created a corresponding unconditional
distribution by adding extra 1 percent zeros to the draw. Panels (c) and (d) show the
respective distributions.
- The experts specified distributions for the percent changes in the relative risk. The

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distribution of the corresponding PM2.5 effects was the following transformation of the
percent change in relative risk Z – log(1+(Z/100)).

F.1.2 Laden et al (2006)

A large body of epidemiologic literature has found an association of increased fine
particulate air pollution (PM2.5) with acute and chronic mortality. The effect of
improvements in particle exposure is less clear. Earlier analysis of the Harvard Six Cities
adult cohort study showed an association between long-term ambient PM2.5 and mortality
between enrollment in the mid-1970's and follow-up until 1990. The authors extended
mortality follow-up for eight years in a period of reduced air pollution concentrations.
Annual city-specific PM2.5 concentrations were measured between 1979-1988, and
estimated for later years from publicly available data. E xposure was defined as (1)
city-specific mean PM2.5 during the two follow-up periods, (2) mean PM2.5 in the first
period and change between these periods, (3) overall mean PM2.5 across the entire
follow-up, and (4) year-specific mean PM2.5. Mortality rate ratios were estimated with
Cox proportional hazards regression controlling for individual risk factors. The authors
found an increase in overall mortality associated with each 10 ug/m3 increase in PM2.5
modeled either as the overall mean (RR=1.16, 95%CI=1.07-1.26) or as exposure in the
year of death (RR=1.14, 95%CI=1.06-1.22). PM2.5 exposure was associated with lung
cancer (RR=1.27, 95%CI=0.96-1.69) and cardiovascular deaths (RR=1.28,
95%CI=1.13-1.44). Improved overall mortality was associated with decreased mean
PM2.5 (10 microg/m(3)) between periods (RR=0.73, 95% CI=0.57-0.95). Total,
cardiovascular, and lung cancer mortality were each positively associated with ambient
PM2.5 concentrations. Reduced PM2.5 concentrations were associated with reduced
mortality risk.

All-Cause Mortality
The coefficient and standard error for PM2.5 are estimated from the relative risk (1.16) and
95% confidence interval (1.07-1.26) associated with a change in annual mean exposure of
10.0 µg/m3 (Laden et al, 2006, p. 667).

F.1.3 Pope et al (2002)

The Pope et al. (2002) analysis is a longitudinal cohort tracking study that uses the same
American Cancer Society (ACS) cohort as the original Pope et al. (1995) study, and the
Krewski et al. (2000) reanalysis. Pope et al. (2002) analyzed survival data for the cohort
from 1982 through 1998, 9 years longer than the original Pope study. Pope et al. (2002)
also obtained PM2.5 data in 116 metropolitan areas collected in 1999, and the first three
quarters of 2000. This is more metropolitan areas with PM2.5 data than was available in
the Krewski reanalysis (61 areas), or the original Pope study (50 areas), providing a larger
size cohort.
They used a Cox proportional hazard model to estimate the impact of long-term PM

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exposure using three alternative measures of PM2.5 exposure; metropolitan area-wide

annual mean PM levels from the beginning of tracking period (’79-’83 PM data, conducted
for 61 metropolitan areas with 359,000 individuals), annual mean PM from the end of the
tracking period (’99-’00, for 116 areas with 500,000 individuals), and the average annual
mean PM levels of the two periods (for 51 metropolitan areas, with 319,000 individuals).
PM levels were lower in ’99-00 than in ’79 - ’83 in most cities, with the largest
improvements occurring in cities with the highest original levels.
Pope et al. (2002) followed Krewski et al. (2000) and Pope et al. (1995, Table 2) and
reported results for all-cause deaths, lung cancer (ICD-9 code: 162), cardiopulmonary
deaths (ICD-9 codes: 401-440 and 460-519), and “all other” deaths. All-cause mortality
includes accidents, suicides, homicides and legal interventions. The category “all other”
deaths is all-cause mortality less lung cancer and cardiopulmonary deaths. Like the earlier
studies, Pope et al. (2002) found that mean PM2.5 is significantly related to all-cause and
cardiopulmonary mortality. In addition, Pope et al. (2002) found a significant relationship
with lung cancer mortality, which was not found in the earlier studies. None of the three
studies found a significant relationship with “all other” deaths.
Pope et al. (2002) obtained ambient data on gaseous pollutants routinely monitored by
EPA during the 1982-1998 observation period, including SO2, NO2, CO, and ozone. They
did not find significant relationships between NO2, CO, and ozone and premature
mortality, but there were significant relationships between SO4 (as well as SO2), and
all-cause, cardiopulmonary, lung cancer and “all other” mortality.

All-Cause Mortality, ’79-’83 Exposure

The coefficient and standard error for PM2.5 using the ’79-’83 PM data are estimated from
the relative risk (1.04) and 95% confidence interval (1.01-1.08) associated with a change
in annual mean exposure of 10.0 µg/m3 (Pope et al, 2002, Table 2).

All-Cause Mortality, Average of ’79-’83 and ’99-’00 Exposure

The coefficient and standard error for PM2.5 using the average of ’79-’83 and ’99-’00 PM
data are estimated from the relative risk (1.06) and 95% confidence interval (1.02-1.11)
associated with a change in annual mean exposure of 10.0 µg/m3 (Pope et al, 2002, Table
2).

F.1.4 Woodruff et al (1997)

In a study of four million infants in 86 U.S. metropolitan areas conducted from 1989 to
1991, Woodruff et al. (1997) found a significant link between PM10 exposure in the first
two months of an infant’s life with the probability of dying between the ages of 28 days
and 364 days. PM10 exposure was significant for all-cause mortality. PM10 was also

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significant for respiratory mortality in average birth-weight infants, but not low
birth-weight infants.

Post-Neonatal Mortality
The coefficient and standard error are based on the odds ratio (1.04) and 95% confidence
interval (1.02-1.07) associated with a 10 µg/m3 change in PM10 (Woodruff et al., 1997,
Table 3).

F.1.5 Woodruff et al (2006)

Studies suggest that airborne particulate matter (PM) may be associated with postneonatal
infant mortality, particularly with respiratory causes and sudden infant death syndrome
(SIDS). To further explore this issue, the authors examined the relationship between
long-term exposure to fine PM air pollution and postneonatal infant mortality in
California. They linked monitoring data for PM2.5 to infants born in California in 1999
and 2000 using maternal addresses for mothers who lived within 5 miles of a PM2.5
monitor. They matched each postneonatal infant death to four infants surviving to 1 year of
age, by birth weight category and date of birth (within 2 weeks). For each matched set, they
calculated exposure as the average PM2.5 concentration over the period of life for the
infant who died. They used conditional logistic regression to estimate the odds of
postneonatal all-cause, respiratory-related, SIDS, and external-cause (a control category)
mortality by exposure to PM2.5, controlling for the matched sets and maternal
demographic factors. They matched 788 postneonatal infant deaths to 3,089 infant
survivors, with 51 and 120 postneonatal deaths due to respiratory causes and SIDS,
respectively. They found an adjusted odds ratio for a 10-microg/m3 increase in PM2.5 of
1.07 [95% confidence interval (CI), 0.93-1.24] for overall postneonatal mortality, 2.13
(95% CI, 1.12-4.05) for respiratory-related postneonatal mortality, 0.82 (95% CI,
0.55-1.23) for SIDS, and 0.83 (95% CI, 0.50-1.39) for external causes.

Post-Neonatal Mortality
The coefficient and standard error for PM2.5 are estimated from the relative risk (1.07) and
95% confidence interval (0.93-1.24) associated with a change in annual mean exposure of
10.0 µg/m3 (Woodruff et al., 2006, p. 786).

F.2 Chronic / Severe Illness

Table F-6 summarizes the health impacts functions used to estimate the relationship
between PM2.5 and chronic / severe health effects. Below, we present a brief summary of
each of the studies and any items that are unique to the study.

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Table F-6. Health Impact Functions for Particulate Matter and Chronic Illness
Effect Author Year Lcoation Age Co-P Metric Beta Std Err Form Notes
oll

Chronic Bronchitis Abbey et 1995 SF, SD, South 27-99 Annual 0.013185 0.006796 Logistic Adjusted coefficient
al. Coast Air Basin with 10 ug/m3
threshold.

Chronic Bronchitis Abbey et 1995 SF, SD, South 27-99 Annual 0.013185 0.006796 Logistic
al. Coast Air Basin

Acute Myocardial Peters et 2001 Boston, MA 18-99 D24HourMe 0.033230 0.012791 Logistic Adjusted coefficient
Infarction, Nonfatal al. an with 10 ug/m3
threshold.

Acute Myocardial Peters et 2001 Boston, MA 18-99 D24HourMe 0.024121 0.009285 Logistic
Infarction, Nonfatal al. an

F.2.1 Abbey et al (1995b)

Abbey et al. (1995b) examined the relationship between estimated PM2.5 (annual mean
from 1966 to 1977), PM10 (annual mean from 1973 to 1977) and TSP (annual mean from
1973 to 1977) and the same chronic respiratory symptoms in a sample population of 1,868
Californian Seventh Day Adventists. The initial survey was conducted in 1977 and the
final survey in 1987. To ensure a better estimate of exposure, the study participants had to
have been living in the same area for an extended period of time. In single-pollutant
models, there was a statistically significant PM2.5 relationship with development of chronic
bronchitis, but not for AOD or asthma; PM10 was significantly associated with chronic
bronchitis and AOD; and TSP was significantly associated with all cases of all three
chronic symptoms. Other pollutants were not examined.

Chronic Bronchitis
The estimated coefficient (0.0137) is presented for a one µg/m3 change in PM2.5 (Abbey et
al., 1995b, Table 2). The standard error is calculated from the reported relative risk (1.81)
and 95% confidence interval (0.98-3.25) for a 45 µg/m3 change in PM2.5.

Incidence Rate: annual bronchitis incidence rate per person (Abbey et al., 1993, Table 3) =
0.00378
Population: population of ages 27 and older without chronic bronchitis = 95.57% of population
27+. Using the same data set, Abbey et al. (1995a, p. 140) reported that the respondents in 1977
ranged in age from 27 to 95. The American Lung Association (2002b, Table 4) reports a chronic
bronchitis prevalence rate for ages 18 and over of 4.43%.

F.2.2 Peters et al (2001)

Peters et al. (2001) studied the relationship between increased particulate air pollution and

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onset of heart attacks in the Boston area from 1995 to 1996. The authors used air quality
data for PM10, PM10-2.5, PM2.5,“black carbon”, O3, CO, NO2, and SO2 in a case-crossover
analysis. For each subject, the case period was matched to three control periods, each 24
hours apart. In univariate analyses, the authors observed a positive association between
heart attack occurrence and PM2.5 levels hours before and days before onset. The authors
estimated multivariate conditional logistic models including two-hour and twenty-four
hour pollutant concentrations for each pollutant. They found significant and independent
associations between heart attack occurrence and both two-hour and twenty-four hour PM
2.5 concentrations before onset. Significant associations were observed for PM10 as well.
None of the other particle measures or gaseous pollutants were significantly associated
with acute myocardial infarction for the two hour or twenty-four hour period before onset.
The patient population for this study was selected from health centers across the United
States. The mean age of participants was 62 years old, with 21% of the study population
under the age of 50. In order to capture the full magnitude of heart attack occurrence
potentially associated with air pollution and because age was not listed as an inclusion
criteria for sample selection, we apply an age range of 18 and over in the C-R function.
According to the National Hospital Discharge Survey, there were no hospitalizations for
heart attacks among children <15 years of age in 1999 and only 5.5% of all hospitalizations
occurred in 15-44 year olds (Popovic, 2001, Table 10).

Acute Myocardial Infarction, Nonfatal

The coefficient and standard error are calculated from an odds ratio of 1.62 (95% CI
1.13-2.34) for a 20 µg/m3 increase in twenty-four hour average PM2.5 (Peters et al., 2001,
Table 4, p. 2813).
Incidence Rate: region-specific daily nonfatal heart attack rate per person 18+ = 93% of
region-specific daily heart attack hospitalization rate (ICD code 410). This estimate assumes
that all heart attacks that are not instantly fatal will result in a hospitalization. In addition,
Rosamond et al. (1999) report that approximately six percent of male and eight percent of
female hospitalized heart attack patients die within 28 days (either in or outside of the
hospital). We applied a factor of 0.93 to the number of hospitalizations to estimate the
number of nonfatal heart attacks per year.
Population: population of ages 18 and older

F.3 Hospitalizations
Table F-7 summarizes the health impacts functions used to estimate the relationship
between PM2.5 and hospital admissions. Below, we present a brief summary of each of the
studies and any items that are unique to the study.

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Table F-7. Health Impact Functions for Particulate Matter and Hospital Admissions
Effect Author Year Lcoation Age Co-Pol Metric Beta Std Err Form Notes
l

Congestive Heart Failure Ito 2003 Detroit, MI 65-99 D24HourMe 0.00345 0.00145 Log-linear Adjusted coefficient
an 8 3 with 10 ug/m3
threshold.

Congestive Heart Failure Ito 2003 Detroit, MI 65-99 D24HourMe 0.00307 0.00129 Log-linear
an 4 2

HA, Dysrhythmia Ito 2003 Detroit, MI 65-99 D24HourMe 0.00140 0.00228 Log-linear Adjusted coefficient
an 5 7 with 10 ug/m3
threshold.

Dysrhythmia Ito 2003 Detroit, MI 65-99 D24HourMe 0.00124 0.00203 Log-linear

an 9 3

Ischemic Heart (less Ito 2003 Detroit, MI 65-99 D24HourMe 0.00161 0.00130 Log-linear Adjusted coefficient
Myocardial Infarctions) an 4 0 with 10 ug/m3
threshold.

Ischemic Heart (less Ito 2003 Detroit, MI 65-99 D24HourMe 0.00143 0.00115 Log-linear
Myocardial Infarctions) an 5 6

Chronic Lung Ito 2003 Detroit, MI 65-99 D24HourMe 0.00131 0.00232 Log-linear Adjusted coefficient
an 6 2 with 10 ug/m3
threshold.

Chronic Lung Ito 2003 Detroit, MI 65-99 D24HourMe 0.00116 0.00206 Log-linear
an 9 4

Pneumonia Ito 2003 Detroit, MI 65-99 D24HourMe 0.00447 0.00186 Log-linear Adjusted coefficient
an 6 7 with 10 ug/m3
threshold.

Pneumonia Ito 2003 Detroit, MI 65-99 D24HourMe 0.00397 0.00165 Log-linear

an 9 9

All Cardiovascular (less Moolgavka 2000 Los 18-64 D24HourMe 0.00151 0.00036 Log-linear Adjusted coefficient
Myocardial Infarctions) r Angeles, an 1 8 with 10 ug/m3
CA threshold.

All Cardiovascular (less Moolgavka 2000 Los 18-64 D24HourMe 0.00140 0.00034 Log-linear
Myocardial Infarctions) r Angeles, an 0 1
CA

Chronic Lung (less Moolgavka 2000 Los 18-64 D24HourMe 0.00237 0.00079 Log-linear Adjusted coefficient
Asthma) r Angeles, an 4 1 with 10 ug/m3
CA threshold.

Chronic Lung (less Moolgavka 2000 Los 18-64 D24HourMe 0.00220 0.00073 Log-linear
Asthma) r Angeles, an 0 3
CA

All Cardiovascular (less Moolgavka 2003 Los 65-99 D24HourMe 0.00170 0.00037 Log-linear Adjusted coefficient
Myocardial Infarctions) r Angeles, an 5 1 with 10 ug/m3
CA threshold.

All Cardiovascular (less Moolgavka 2003 Los 65-99 D24HourMe 0.00158 0.00034 Log-linear
Myocardial Infarctions) r Angeles, an 0 4
CA

Chronic Lung Moolgavka 2003 Los 65-99 D24HourMe 0.00199 0.00056 Log-linear Adjusted coefficient
r Angeles, an 6 5 with 10 ug/m3
CA threshold.

Chronic Lung Moolgavka 2003 Los 65-99 D24HourMe 0.00185 0.00052 Log-linear
r Angeles, an 0 4
CA

Asthma Sheppard 2003 Seattle, 0-64 D24HourMe 0.00392 0.00123 Log-linear Adjusted coefficient
WA an 8 5 with 10 ug/m3
threshold.

HA, Asthma Sheppard 2003 Seattle, 0-64 D24HourMe 0.00332 0.00104 Log-linear
WA an 4 5

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F.3.1 Ito (2003)

Lippmann et al. (2000) studied the association between particulate matter and daily
mortality and hospitalizations among the elderly in Detroit, MI. Data were analyzed for
two separate study periods, 1985-1990 and 1992-1994. The 1992-1994 study period had a
greater variety of data on PM size and was the main focus of the report. The authors
collected hospitalization data for a variety of cardiovascular and respiratory endpoints.
They used daily air quality data for PM10, PM2.5, and PM10-2.5 in a Poisson regression
model with generalized additive models (GAM) to adjust for nonlinear relationships and
temporal trends. In single pollutant models, all PM metrics were statistically significant
for pneumonia (ICD codes 480-486), PM10-2.5 and PM10 were significant for ischemic heart
disease (ICD code 410-414), and PM2.5 and PM10 were significant for heart failure (ICD
code 428). There were positive, but not statistically significant associations, between the
PM metrics and COPD (ICD codes 490-496) and dysrhythmia (ICD code 427). In separate
co-pollutant models with PM and either ozone, SO2, NO2, or CO, the results were
generally comparable.
In response to concerns with the Splus issue, Ito (2003) reanalyzed the study by Lippmann
et al. (2000). The reanalysis by Ito reported that more generalized additive models with
stringent convergence criteria and generalized linear models resulted in smaller relative
risk estimates.

Chronic Lung Disease (ICD-9 codes 490-496)

The coefficient and standard error are based on the relative risk (1.043) and 95%
confidence interval (0.902-1.207) for a 36 µg/m3 increase in PM2.5 in the 3-day lag GAM
stringent model (Ito, 2003, Table 8).

Pneumonia (ICD-9 codes 480-487)

The estimated PM2.5 coefficient and standard error are based on a relative risk of 1.154
(95% CI -1.027, 1.298) due to a PM2.5 change of 36 µg/m3 in the 1-day lag GAM stringent
model (Ito, 2003, Table 7).

Disrhythmia (ICD-9 code 429)

The co-pollutant coefficient and standard error are calculated from a relative risk of 1.046
(95% CI 0.906-1.207) for a 36 µg/m3 increase in PM2.5 in the 1-day lag GAM stringent
model (Ito, 2003, Table 10).

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Congestive Heart Failure (ICD-9 code 428)

The co-pollutant coefficient and standard error are calculated from a relative risk of 1.117
(95% CI 1.020-1.224) for a 36 µg/m3 increase in PM2.5 in the 1-day lag GAM stringent
model (Ito, 2003, Table 11).

Ischemic Heart Disease (ICD-9 codes 411-414)

The co-pollutant coefficient and standard error are calculated from a relative risk of 1.053
(95% CI 0.971-1.143) for a 36 µg/m3 increase in PM2.5 in the 1-day lag GAM stringent
model (Ito, 2003, Table 9)
Note that Lippmann et al. (2000) report results for ICD codes 410-414. In the benefit
analysis, avoided nonfatal heart attacks are estimated using the results reported by Peters et
al. (2001). The baseline rate in the Peters et al. function is a modified heart attack
hospitalization rate (ICD code 410), since most, if not all, nonfatal heart attacks will
require hospitalization. In order to avoid double counting heart attack hospitalizations, we
have excluded ICD code 410 from the baseline incidence rate used in this function.

F.3.2 Moolgavkar (2000a), Chronic Lung

Moolgavkar (2000a) examined the association between air pollution and COPD hospital
admissions (ICD 490-496) in the Chicago, Los Angeles, and Phoenix metropolitan areas.
He collected daily air pollution data for ozone, SO2, NO2, CO, and PM10 in all three areas.
PM2.5 data was available only in Los Angeles. The data were analyzed using a Poisson
regression model with generalized additive models to adjust for temporal trends. Separate
models were run for 0 to 5 day lags in each location. Among the 65+ age group in Chicago
and Phoenix, weak associations were observed between the gaseous pollutants and
admissions. No consistent associations were observed for PM10. In Los Angeles,
marginally significant associations were observed for PM2.5, which were generally lower
than for the gases. In co-pollutant models with CO, the PM2.5 effect was reduced. Similar
results were observed in the 0-19 and 20-64 year old age groups.
The PM2.5 C-R functions are based on the single and co-pollutant models (PM2.5 and CO)
reported for the 20-64 and 65+ age groups. Since the true PM effect is most likely best
represented by a distributed lag model, then any single lag model should underestimate the
total PM effect. As a result, we selected the lag models with the greatest effect estimates
for use in the C-R functions.

Hospital Admissions, Chronic Lung Disease Less Asthma (ICD-9 codes 490-492,
494-496)

In a model with CO, the coefficient and standard error are calculated from an estimated

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percent change of 2.0 and t-statistic of 2.2 for a 10 µg/m3 increase in PM2.5 in the two-day
lag model (Moolgavkar, 2000a, Table 4, p. 81). In a log-linear model, the percent change is
equal to (RR - 1) * 100.
In this study, Moolgavkar defines and reports the “estimated” percent change as (log RR *
100). Because the relative risk is close to 1, RR-1 and log RR are essentially the same.
For example, a true percent change of 2.0 would result in a relative risk of 1.020 and
coefficient of 0.001980. The “estimated” percent change, as reported by Moolgavkar, of
2.0 results in a relative risk of 1.020201 and coefficient of 0.002.
Note that although Moolgavkar (2000a) reports results for the 20-64 year old age range, for
comparability to other studies, we apply the results to the population of ages 18 to 64.
Note also that in order to avoid double counting non-elderly asthma hospitalizations (ICD
code 493), which are typically estimated separately in EPA benefit analyses, we have
excluded ICD code 493 from the baseline incidence rate used in this function.

F.3.3 Moolgavkar (2000b), Cardiovascular

Moolgavkar (2000b) examined the association between air pollution and cardiovascular
hospital admissions (ICD 390-448) in the Chicago, Los Angeles, and Phoenix metropolitan
areas. He collected daily air pollution data for ozone, SO2, NO2, CO, and PM10 in all three
areas. PM2.5 data was available only in Los Angeles. The data were analyzed using a
Poisson regression model with generalized additive models to adjust for temporal trends.
Separate models were run for 0 to 5 day lags in each location. Among the 65+ age group,
the gaseous pollutants generally exhibited stronger effects than PM10 or PM2.5. The
strongest overall effects were observed for SO2 and CO. In a single pollutant model, PM2.5
was statistically significant for lag 0 and lag 1. In co-pollutant models with CO, the PM2.5
effect dropped out and CO remained significant. For ages 20-64, SO2 and CO exhibited
the strongest effect and any PM2.5 effect dropped out in co-pollutant models with CO.

Hospital Admissions, All Cardiovascular (ICD codes 390-409, 411-459)

The single pollutant coefficient and standard error are calculated from an estimated percent
change of 1.4 and t-statistic of 4.1 for a 10 µg/m3 increase in PM2.5 in the zero lag model
(Moolgavkar, 2000b, Table 4, p. 1203).
Note that (Moolgavkar (2000b) report results that include ICD code 410 (heart attack). In a
benefit analysis, avoided nonfatal heart attacks are typically estimated separately. The
baseline rate in the Peters et al. function is a modified heart attack hospitalization rate (ICD
code 410), since most, if not all, nonfatal heart attacks will require hospitalization. In
order to avoid double counting heart attack hospitalizations, we have excluded ICD code
410 from the baseline incidence rate used in this function.

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F.3.4 Moolgavkar (2003)

Moolgavkar (2000a) examined the association between air pollution and COPD hospital
admissions (ICD 490-496) in the Chicago, Los Angeles, and Phoenix metropolitan areas.
In response to concerns with Splus issue, Moolgavkar (2003) reanalyzed his earlier studies.
In the reanalysis, he reported that more generalized additive models with stringent
convergence criteria and generalized linear models resulted in smaller relative risk
estimates.

Hospital Admissions, Chronic Lung (ICD-9 codes 490-496)

The coefficient and standard error are calculated from an estimated percentage change of
1.85 and t-statistic of 3.53 for a 10 µg/m3 increase in PM2.5 in the 2-day lag GAM-30df
stringent (10-8) model (Moolgavkar, 2003, Table 17). In a log-linear model, the percent
change is equal to (RR - 1) * 100.
The PM2.5 C-R functions for the 65+ age group are based on the reanalysis in Moolgavkar
(2003) of the single and co-pollutant models (PM2.5 and CO). The true PM effect is most
likely best represented by a distributed lag model, then any single lag model should
underestimate the total PM effect. As a result, we selected the lag models with the greatest
effect estimates for use in the C-R functions.

Hospital Admissions, All Cardiovascular (ICD-9 codes 390-429)

The single pollutant coefficient and standard error are calculated from an estimated percent
change of 1.58 and t-statistic of 4.59 for a 10 µg/m3 increase in PM2.5 in the 0-day lag
GAM-30df stringent (10-8) model (Moolgavkar, 2003, Table 12). In a log-linear model,
the percent change is equal to (RR - 1) * 100.

F.3.5 Sheppard (2003)

Sheppard et al. (1999) studied the relation between air pollution in Seattle and nonelderly
(<65) hospital admissions for asthma from 1987 to 1994. They used air quality data for
PM10, PM2.5, coarse PM10-2.5, SO2, ozone, and CO in a Poisson regression model with
control for time trends, seasonal variations, and temperature-related weather effects.
PM2.5 levels were estimated from light scattering data. They found asthma hospital
admissions associated with PM10, PM2.5, PM10-2.5, CO, and ozone. They did not observe
an association for SO2. They found PM and CO to be jointly associated with asthma
admissions. The best fitting co-pollutant models were found using ozone. However,
ozone data was only available April through October, so they did not consider ozone
further. For the remaining pollutants, the best fitting models included PM2.5 and CO.
Results for other co-pollutant models were not reported.
In response to concerns that the work by Sheppard et al. (1999) may be biased because of

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the Splus issue, Sheppard (2003) reanalyzed some of this work, in particular Sheppard
reanalyzed the original study’s PM2.5 single pollutant model.

Hospital Admissions, Asthma (ICD-9 code 493)

The coefficient and standard error are based on the relative risk (1.04) and 95% confidence
interval (1.01-1.06) for a 11.8 µg/m3 increase in PM2.5 in the 1-day lag GAM stringent
model (Sheppard, 2003, pp. 228-229).

F.4 Emergency Room Visits

Table F-8 summarizes the health impacts functions used to estimate the relationship
between PM2.5 and emergency room visits. Below, we present a brief summary of each of
the studies and any items that are unique to the study.

Table F-8. Health Impact Functions for Particulate Matter and Emergency Room
Visits
Effect Author Year Lcoation Age Co-Poll Metric Beta Std Err Form Notes

NO2, 0.01854 Adjusted coefficient with

Asthma Norris et al. 1999 Seattle, WA 0-17 SO2 D24HourMean 2 0.004644 Log-linear 10 ug/m3 threshold.

NO2, 0.01652
Asthma Norris et al. 1999 Seattle, WA 0-17 SO2 D24HourMean 7 0.004139 Log-linear

F.4.1 Norris et al (1999)

Norris et al. (1999) examined the relation between air pollution in Seattle and childhood
(<18) hospital admissions for asthma from 1995 to 1996. The authors used air quality data
for PM10, light scattering (used to estimate fine PM), CO, SO2, NO2, and O3 in a Poisson
regression model with adjustments for day of the week, time trends, temperature, and dew
point. They found significant associations between asthma ER visits and light scattering
(converted to PM2.5), PM10, and CO. No association was found between O3, NO2, or SO2
and asthma ER visits, although O3 had a significant amount of missing data. In
multipollutant models with either PM metric (light scattering or PM10) and NO2 and SO2,
the PM coefficients remained significant while the gaseous pollutants were not associated
with increased asthma ER visits. The PM C-R functions are based on results of the single
and multipollutant models reported.

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Emergency Room Visits, Asthma

In a model with NO2 and SO2, the PM2.5 coefficient and standard error are calculated from
a relative risk of 1.17 (95% CI 1.08-1.26) for a 9.5 µg/m3 increase in PM2.5 (Norris et al.,
1999, p. 491).

F.5 Minor Effects

Table F-9 summarizes the health impacts functions used to estimate the relationship
between PM2.5 and minor effects. Below, we present a brief summary of each of the
studies and any items that are unique to the study.

Table F-9. Health Impact Functions for Particulate Matter and Minor Effects
Effect Author Year Lcoation Age Co-Poll Metric Beta Std Err Form Notes

Acute Bronchitis Dockery et al. 1996 24 8-12 Annual 0.037894 0.023806 Logistic Adjusted coefficient
communitie with 10 ug/m3
s threshold.

Acute Bronchitis Dockery et al. 1996 24 8-12 Annual 0.027212 0.017096 Logistic
communitie
s

Work Loss Days Ostro 1987 Nationwide 18-64 D24HourMea 0.004600 0.000360 Log-linea Adjusted coefficient
n r with 10 ug/m3
threshold.

Work Loss Days Ostro 1987 Nationwide 18-64 D24HourMea 0.004600 0.000360 Log-linea
n r

Minor Restricted Ostro and 1989 Nationwide 18-64 Ozone D24HourMea 0.007410 0.000700 Log-linea Adjusted coefficient
Activity Days Rothschild n r with 10 ug/m3
threshold.

Minor Restricted Ostro and 1989 Nationwide 18-64 Ozone D24HourMea 0.007410 0.000700 Log-linea
Activity Days Rothschild n r

Lower Schwartz and 2000 6 U.S. 7-14 D24HourMea 0.019712 0.006226 Logistic Adjusted coefficient
Respiratory Neas cities n with 10 ug/m3
Symptoms threshold.

Lower Schwartz and 2000 6 U.S. 7-14 D24HourMea 0.019012 0.006005 Logistic
Respiratory Neas cities n
Symptoms

F.5.1 Dockery et al (1996)

Dockery et al. (1996) examined the relationship between PM and other pollutants on the
reported rates of asthma, persistent wheeze, chronic cough, and bronchitis, in a study of
13,369 children ages 8-12 living in 24 communities in U.S. and Canada. Health data were
collected in 1988-1991, and single-pollutant models were used in the analysis to test a
number of measures of particulate air pollution. Dockery et al. found that annual level of

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sulfates and particle acidity were significantly related to bronchitis, and PM2.1 and PM10
were marginally significantly related to bronchitis. The original study measured PM2.1,
however when using the study's results we use PM2.5. This makes only a negligible
difference, assuming that the adverse effects of PM2.1 and PM2.5 are comparable. They
also found nitrates were linked to asthma, and sulfates linked to chronic phlegm. It is
important to note that the study examined annual pollution exposures, and the authors did
not rule out that acute (daily) exposures could be related to asthma attacks and other acute
episodes. Earlier work, by Dockery et al. (1989), based on six U.S. cities, found acute
bronchitis and chronic cough significantly related to PM15. Because it is based on a larger
sample, the Dockery et al. (1996) study is the better study to develop a C-R function
linking PM2.5 with bronchitis.

Bronchitis was counted in the study only if there were “reports of symptoms in the past 12
months” (Dockery et al., 1996, p. 501). It is unclear, however, if the cases of bronchitis
are acute and temporary, or if the bronchitis is a chronic condition. Dockery et al. found
no relationship between PM and chronic cough and chronic phlegm, which are important
indicators of chronic bronchitis. For this analysis, we assumed that the C-R function based
on Dockery et al. is measuring acute bronchitis. The C-R function is based on results of
the single pollutant model reported in Table 1.

Acute Bronchitis
The estimated logistic coefficient and standard error are based on the odds ratio (1.50) and
95% confidence interval (0.91-2.47) associated with being in the most polluted city (PM2.1
= 20.7 µg/m3) versus the least polluted city (PM2.1 = 5.8 µg/m3) (Dockery et al., 1996,
Tables 1 and 4). The original study used PM2.1, however, we use the PM2.1 coefficient and
apply it to PM2.5 data.

Incidence Rate: annual bronchitis incidence rate per person = 0.043 (American Lung Association,
2002a, Table 11)
Population: population of ages 8-12.

F.5.2 Ostro (1987)

Ostro (1987) estimated the impact of PM2.5 on the incidence of work-loss days (WLDs),
restricted activity days (RADs), and respiratory-related RADs (RRADs) in a national
sample of the adult working population, ages 18 to 65, living in metropolitan areas. The
study population is based on the Health Interview Survey (HIS), conducted by the National
Center for Health Statistics. The annual national survey results used in this analysis were
conducted in 1976-1981. Ostro reported that two-week average PM2.5 levels were
significantly linked to work-loss days, RADs, and RRADs, however there was some
year-to-year variability in the results. Separate coefficients were developed for each year

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in the analysis (1976-1981); these coefficients were pooled. The coefficient used in the
concentration-response function presented here is a weighted average of the coefficients in
Ostro (1987, Table III) using the inverse of the variance as the weight.

Work Loss Days

The coefficient used in the C-R function is a weighted average of the coefficients in Ostro
(1987, Table III) using the inverse of the variance as the weight:

The standard error of the coefficient is calculated as follows, assuming that the estimated
year-specific coefficients are independent:

This eventually reduces down to:

Incidence Rate: daily work-loss-day incidence rate per person ages 18 to 64 = 0.00595 (U.S.
Bureau of the Census, 1997, No. 22; Adams et al., 1999, Table 41)
Population: adult population ages 18 to 64

F.5.3 Ostro and Rothschild (1989)

Ostro and Rothschild (1989) estimated the impact of PM2.5 and ozone on the incidence of
minor restricted activity days (MRADs) and respiratory-related restricted activity days
(RRADs) in a national sample of the adult working population, ages 18 to 65, living in
metropolitan areas. The study population is based on the Health Interview Survey (HIS),

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conducted by the National Center for Health Statistics. In publications from this ongoing
survey, non-elderly adult populations are generally reported as ages 18-64. From the study,
it is not clear if the age range stops at 65 or includes 65 year olds. We apply the C-R
function to individuals ages 18-64 for consistency with other studies estimating impacts to
non-elderly adult populations. The annual national survey results used in this analysis
were conducted in 1976-1981. Controlling for PM2.5, two-week average ozone has highly
variable association with RRADs and MRADs. Controlling for ozone, two-week average
PM2.5 was significantly linked to both health endpoints in most years.

Minor Restricted Activity Days

Using the results of the two-pollutant model, we developed separate coefficients for each
year in the analysis, which were then combined for use in this analysis. The coefficient is a
weighted average of the coefficients in Ostro and Rothschild (1989, Table 4) using the
inverse of the variance as the weight:

The standard error of the coefficient is calculated as follows, assuming that the estimated
year-specific coefficients are independent:

This reduces down to:

Incidence Rate: daily incidence rate for minor restricted activity days (MRAD) = 0.02137 (Ostro
and Rothschild, 1989, p. 243)
Population: adult population ages 18 to 64

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F.5.4 Schwartz and Neas (2000)

Schwartz et al. (2000) replicated a previous analysis (Schwartz et al., 1994) linking PM
levels to lower respiratory symptoms in children in six cities in the U.S. The original study
enrolled 1,844 children into a year-long study that was conducted in different years (1984
to 1988) in six cities. The students were in grades two through five at the time of
enrollment in 1984. By the completion of the final study, the cohort would then be in the
eighth grade (ages 13-14); this suggests an age range of 7 to 14. The previous study
focused on PM10, acid aerosols, and gaseous pollutants, although single-pollutant PM2.5
results were reported. Schwartz et al. (2000) focused more on the associations between
PM2.5 and PM10-2.5 and lower respiratory symptoms. In single and co-pollutant models,
PM2.5 was significantly associated with lower respiratory symptoms, while PM10-2.5 was
not. PM10-2.5 exhibited a stronger association with cough than did PM2.5. The PM2.5 C-R
functions for lower respiratory symptoms are based on the results of the reported single
pollutant and co-pollutant model (PM2.5 and PM10-2.5).

Lower Respiratory Symptoms

The coefficient and standard error are calculated from the reported odds ratio (1.33) and
95% confidence interval (1.11-1.58) associated with a 15 µg/m3 change in PM2.5 (Schwartz
and Neas, 2000, Table 2).
Incidence Rate: daily lower respiratory symptom incidence rate per person = 0.0012 (Schwartz et
al., 1994, Table 2)
Population: population of ages 7 to 14

F.6 Asthma-Related Effects

Table F-10 summarizes the health impacts functions used to estimate the relationship
between PM2.5 and asthma exacerbation. Below, we present a brief summary of each of
the studies and any items that are unique to the study.

Table F-10. Health Impact Functions for Particulate Matter and Asthma-Related
Effects
Effect Author Year Lcoation Age Co-Pol Metric Beta Std Err Form Notes
l

Cough Ostro et al. 2001 Los Angeles, 6-18 D24HourMean 0.001013 0.000768 Logistic Adjusted coefficient
CA with 10 ug/m3
threshold.

Cough Ostro et al. 2001 Los Angeles, 6-18 D24HourMean 0.000985 0.000747 Logistic
CA

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Effect Author Year Lcoation Age Co-Pol Metric Beta Std Err Form Notes
l

Shortness Ostro et al. 2001 Los Angeles, 6-18 D24HourMean 0.002636 0.001372 Logistic Adjusted coefficient
of Breath CA with 10 ug/m3
threshold.

Shortness Ostro et al. 2001 Los Angeles, 6-18 D24HourMean 0.002565 0.001335 Logistic
of Breath CA

Wheeze Ostro et al. 2001 Los Angeles, 6-18 D24HourMean 0.001996 0.000825 Logistic Adjusted coefficient
CA with 10 ug/m3
threshold.

Wheeze Ostro et al. 2001 Los Angeles, 6-18 D24HourMean 0.001942 0.000803 Logistic
CA

Upper Pope et al. 1991 Utah Valley 9-11 D24HourMean 0.003600 0.001500 Logistic Adjusted coefficient
Respiratory with 10 ug/m3
Symptoms threshold.

Upper Pope et al. 1991 Utah Valley 9-11 D24HourMean 0.003600 0.001500 Logistic
Respiratory
Symptoms

Cough Vedal et al. 1998 Vancouver, 6-18 D24HourMean 0.008376 0.004273 Logistic Adjusted coefficient
CAN with 10 ug/m3
threshold.

Cough Vedal et al. 1998 Vancouver, 6-18 D24HourMean 0.008000 0.004082 Logistic
CAN

F.6.1 Ostro et al (2001)

Ostro et al. (2001) studied the relation between air pollution in Los Angeles and asthma
exacerbation in African-American children (8 to 13 years old) from August to November
1993. They used air quality data for PM10, PM2.5, NO2, and O3 in a logistic regression
model with control for age, income, time trends, and temperature-related weather effects.
The authors note that there were 26 days in which PM2.5 concentrations were reported
higher than PM10 concentrations. The majority of results the authors reported were based
on the full dataset. These results were used for the basis for the C-R functions. Asthma
symptom endpoints were defined in two ways: “probability of a day with symptoms” and
“onset of symptom episodes”. New onset of a symptom episode was defined as a day with
symptoms followed by a symptom-free day.
The authors found cough prevalence associated with PM10 and PM2.5 and cough incidence
associated with PM2.5, PM10, and NO2. Ozone was not significantly associated with cough
among asthmatics. The authors found that both the prevalent and incident episodes of
shortness of breath were associated with PM2.5 and PM10. Neither ozone nor NO2 were
significantly associated with shortness of breath among asthmatics. The authors found both
the prevalence and incidence of wheeze associated with PM2.5, PM10, and NO2. Ozone
was not significantly associated with wheeze among asthmatics.
The derived health impact functions are based on the results of single pollutant models
looking at the probability of symptoms.

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Asthma Exacerbation, Cough

The coefficient and standard error are based on an odds ratio of 1.03 (95% CI 0.98-1.07)
for a 30 µg/m3 increase in 12-hour average PM2.5 concentration (Ostro et al., 2001, Table
4, p.204).
Incidence Rate: daily cough rate per person (Ostro et al., 2001, p.202) = 0.145
Population: asthmatic African-American population ages 8 to 13 = 7.26% of African-American
population ages 8 to 13. The American Lung Association (2002a, Table 9) estimates asthma
prevalence for African-American children ages 5 to 17 at 7.26% (based on data from the
1999 National Health Interview Survey).

Asthma Exacerbation, Shortness of Breath

The coefficient and standard error are based on an odds ratio of 1.08 (95% CI 1.00-1.17)
for a 30 µg/m3 increase in 12-hour average PM2.5 concentration (Ostro et al., 2001, Table
4, p.204).
Incidence Rate: daily shortness of breath rate per person (Ostro et al., 2001, p.202) = 0.074
Population: asthmatic African-American population ages 8 to 13 = 7.26% of African-American
population ages 8 to 13. (Described above.)

Asthma Exacerbation, Wheeze

The coefficient and standard error are based on an odds ratio of 1.06 (95% CI 1.01-1.11)
for a 30 µg/m3 increase in 12-hour average PM2.5 concentration (Ostro et al., 2001, Table
4, p.204).
Incidence Rate: daily wheeze rate per person (Ostro et al., 2001, p.202) = 0.173
Population: asthmatic African-American population ages 8 to 13 = 7.26% of African-American
population ages 8 to 13. (Described above.)

F.6.2 Pope et al (1991)

Using logistic regression, Pope et al. (1991) estimated the impact of PM10 on the incidence
of a variety of minor symptoms in 55 subjects (34 “school-based” and 21 “patient-based”)
living in the Utah Valley from December 1989 through March 1990. The children in the
Pope et al. study were asked to record respiratory symptoms in a daily diary. With this
information, the daily occurrences of upper respiratory symptoms (URS) and lower
respiratory symptoms (LRS) were related to daily PM10 concentrations. Pope et al.
describe URS as consisting of one or more of the following symptoms: runny or stuffy
nose; wet cough; and burning, aching, or red eyes. Levels of ozone, NO2, and SO2 were
reported low during this period, and were not included in the analysis. The sample in this
study is relatively small and is most representative of the asthmatic population, rather than
the general population. The school-based subjects (ranging in age from 9 to 11) were

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chosen based on “a positive response to one or more of three questions: ever wheezed
without a cold, wheezed for 3 days or more out of the week for a month or longer, and/or
had a doctor say the ‘child has asthma’ (Pope et al., 1991, p. 669).” The patient-based
subjects (ranging in age from 8 to 72) were receiving treatment for asthma and were
referred by local physicians. Regression results for the school-based sample (Pope et al.,
1991, Table 5) show PM10 significantly associated with both upper and lower respiratory
symptoms. The patient-based sample did not find a significant PM10 effect. The results
from the school-based sample are used here.

Upper Respiratory Symptoms

The coefficient and standard error for a one µg/m3 change in PM10 is reported in Table 5.

Incidence Rate: daily upper respiratory symptom incidence rate per person = 0.3419 (Pope et al.,
1991, Table 2)
Population: asthmatic population ages 9 to 11 = 5.67% of population ages 9 to 11. (The
American Lung Association (2002a, Table 7) estimates asthma prevalence for children
ages 5 to 17 at 5.67%, based on data from the 1999 National Health Interview Survey.)

F.6.3 Vedal et al (1998)

Vedal et al. (1998) studied the relationship between air pollution and respiratory symptoms
among asthmatics and non-asthmatic children (ages 6 to 13) in Port Alberni, British
Columbia, Canada. Four groups of elementary school children were sampled from a prior
cross-sectional study: (1) all children with current asthma, (2) children without doctor
diagnosed asthma who experienced a drop in FEV after exercise, (3) children not in groups
1 or 2 who had evidence of airway obstruction, and (4) a control group of children with
matched by classroom. The authors used logistic regression and generalized estimating
equations to examine the association between daily PM10 levels and daily increases in
various respiratory symptoms among these groups. In the entire sample of children, PM10
was significantly associated with cough, phlegm, nose symptoms, and throat soreness.
Among children with diagnosed asthma, the authors report a significant association
between PM10 and cough symptoms, while no consistent effects were observed in the other
groups. Since the study population has an over-representation of asthmatics, due to the
sampling strategy, the results from the full sample of children are not generalizeable to the
entire population. The C-R function presented below is based on results among asthmatics
only.

Asthma Exacerbation, Cough

The PM10 coefficient and standard error are based on an increase in odds of 8% (95% CI
0-16%) reported in the abstract for a 10 µg/m3 increase in daily average PM10.

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Incidence Rate: daily cough rate per person (Vedal et al., 1998, Table 1, p. 1038) = 0.086
Population: asthmatic population ages 6 to 13 = 5.67% of population ages 6 to 13. (The
American Lung Association (2002a, Table 7) estimates asthma prevalence for children 5-
17 at 5.67% (based on data from the 1999 National Health Interview Survey).)

F.7 Calculating Threshold-Adjusted Functions

Following the approach taken in OAQPS’ June 2005 particulate matter (PM) risk
assessment, we used a 10 ug/m3 cutpoint for short-term (daily) C-R functions and a 7.5 ug/
m3 cutpoint for long-term (annual metric) C-R functions from which PM2.5 health impact
functions have been derived. The risk assessment noted that while there are likely
biological thresholds in individuals for specific health responses, the available
epidemiological studies do not support or refute the existence of thresholds at the
population level for either long-term or short-term PM2.5 exposures within the range of air
quality observed in the studies. It may therefore be appropriate to consider health risks
estimated not only with the reported log-linear or logistic C-R functions, but also with
modified functions that approximate non-linear, sigmoidal-shaped functions that would
better reflect possible population thresholds.
However, following the approach currently being taken in OAQPS’ ongoing O3 risk
assessment, we did not derive threshold models for O3 concentration-response functions.
After debating the merits of considering possible thresholds for O3 for hospital admissions
and mortality C-R functions, OAQPS staff concluded that, because the studies report a
relationship down to very low ambient levels, at or below the estimated policy relevant
background (PRB) concentrations (roughly around 0.03 ppm), consideration of threshold
models for O3 is not warranted. In addition, some of the O3 studies reported effects for
mortality and hospital admissions in Canadian cities where the levels never exceeded the
current 0.08 ppm standard.
We approximated hypothetical sigmoidal PM2.5 C-R functions by “hockeystick” functions
based on the reported log-linear or logistic functions. This approximation consisted of (1)
imposing a cutpoint (i.e., an assumed threshold) on the original C-R function, that is
intended to reflect an inflection point in a typical sigmoidal shaped function, below which
there is little or no population response, and (2) adjusting the slope of the original C-R
function above the cutpoint.
If the researchers in the original study fit a log-linear, linear, or logistic model through data
that actually better support a sigmoidal or “hockeystick” form, the slope of the fitted curve
would be smaller than the slope of the upward-sloping portion of the “true” hockeystick
relationship, as shown in Exhibit 3. The horizontal portion of the data below the cutpoint
would essentially cause the estimated slope to be biased downward relative to the “true”
slope of the upward-sloping portion of the hockeystick. The slope of the upward-sloping
portion of the hockeystick model should therefore be adjusted upward (from the slope of
the reported C-R function), as shown in Figure F-13. If the data used in a study do not
extend down below the cutpoint or extend only slightly below it, then the extent of the
downward bias of the reported PM2.5 coefficient will be minimal, as illustrated in Figure

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F-14.

Figure F-13. Relationship Between Estimated Log-Linear Concentration-Response

Function and Hockeystick Model With Threshold C -- General Case

Figure F-14. Relationship Between Estimated Log-Linear Concentration-Response

Function and Hockeystick Model With Threshold C -- Lowest Measured Level

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(LML) Close to Hypothetical Threshold

We used a simple slope adjustment method based on the idea discussed above – that, if the data in
the study were best described by a hockeystick model with a cutpoint at c, then the slope estimated
in the study using a log-linear or logistic model would be approximately a weighted average of the
two slopes of the hockeystick – namely, zero and the slope of the upward-sloping portion of the
hockeystick. If we let:

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That is, the “true” slope of the upward-sloping portion of the hockeystick would be the
slope estimated in the study (using a log-linear or logistic model rather than a hockeystick
model) adjusted by the inverse of the proportion of the range of PM levels observed in the
study that was above the cutpoint. Note that if the LML was below the estimated PRB (or
if it was not available for the study), the estimated PRB was substituted for LML in the
above equation.
Table F-11 presents the threshold adjustments that were used to multiply with both the
mean coefficient estimate and its standard error.

Table F-11. Threshold Adjustment Factors Based on Assumed Threshold of 10 ug/

m3
Thresh Threshold
Author Year Study Location Min Max old Adj Notes
SF, SD, South Coast
Abbey et al. 1995 Air Basin 10 1.000

Dockery et al. 1996 24 communities 5.8 20.7 10 1.393

Ito 2003 Detroit, MI 6 42 10 1.125 Min and max based on 5% and 95%.

Laden et al. 2006 6 cities 10.8 25.5 10 1.000

Moolgavkar 2003 Los Angeles, CA 4 86 10 1.079

Norris et al. 1999 Seattle, WA 9 18.2 10 1.122

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Study did not provide a mean, SD, or

Ostro 1987 Nationwide 10 1.000 pollutant range.
Ostro and Study gave mean and std dev. We
Rothschild 1989 Nationwide 10 1.000 estimate min is above threshold of 10.

Ostro et al. 2001 Los Angeles, CA 4.5 208.7 10 1.028

Peters et al. 2001 Boston, MA 4.6 24.3 10 1.378 Min and max based on 5% and 95%.

Pope et al. 1991 Utah Valley 11 195 10 1.000

Mean: 17.7 & SD: 3.7. PM risk
assessment assumed min = 7.5 and max
Pope et al. 2002 51 cities 7.5 30 7.5 1.000 = 30

Pope et al. 2002 51 cities 7.5 30 10 1.125

Pope et al. 2002 51 cities 7.5 30 12 1.250

Pope et al. 2002 51 cities 7.5 30 15 1.500

Schwartz and
Neas 2000 6 U.S. cities 7.2 86 10 1.037

Sheppard 2003 Seattle, WA 6 32 10 1.182 Min and max based on 5% and 95%.
Min = policy-relevant background.
Actual min was 0.2 in North and 0.5 in
Vedal et al. 1998 Vancouver, CAN 3 159 10 1.047 South.

Woodruff et al. 1997 86 cities 11.9 68.8 10 1.000

Only presented interquartile PM2.5
Woodruff et al. 2006 204 counties 10 1.000 range

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Appendix G: Ozone Health Impact Functions in

U.S. Setup
In this Appendix, we present the health impact functions used to estimate ozone-related
adverse health effects. Each sub-section has a table with a brief description of each health
impact function and the underlying parameters. Following each table, we present a brief
summary of each of the studies and any items that are unique to the study.
Note that Appendix D mathematically derives the standard types of health impact functions
encountered in the epidemiological literature, such as, log-linear, logistic and linear, so we
simply note here the type of functional form. And Appendix E presents a description of
the sources for the incidence and prevalence data used in the health impact functions.

G.1 Short-term Mortality

Table G-1 summarizes the health impacts functions used to estimate the relationship
between ozone and short-term mortality. Below, we present a brief summary of each of
the studies and any items that are unique to the study.

Table G-1. Health Impact Functions for Ozone and Short-Term Mortality
Effect Author Year Lcoation Age Co-Poll Metric Beta Std Err Form Notes

Non-Accidental Bell et al. 2004 95 US cities 0-99 D24HourMea 0.000390 0.000133 Log-linea Warm season.
n r

Non-Accidental Bell et al. 2004 95 US cities 0-99 D24HourMea 0.000520 0.000128 Log-linea All year.
n r

Non-Accidental Bell et al. 2004 95 US cities 0-99 D8HourMax 0.000261 0.000089 Log-linea Warm season.
r 8-hour max from
24-hour mean.

All Cause Bell et al. 2005 US & non-US 0-99 D24HourMea 0.001500 0.000401 Log-linea Warm season.
n r

All Cause Bell et al. 2005 US & non-US 0-99 D8HourMax 0.000795 0.000212 Log-linea Warm season.
r 8-hour max from
24-hour mean.

Cardiopulmonar Huang et al. 2005 19 US cities 0-99 D24HourMea 0.001250 0.000398 Log-linea Warm season.
y n r

Cardiopulmonar Huang et al. 2005 19 US cities 0-99 D8HourMax 0.000813 0.000259 Log-linea Warm season.
y r 8-hour max from
24-hour mean.

Non-Accidental Ito and 1996 Chicago, IL 18-99 PM10 D1HourMax 0.000634 0.000251 Log-linea
Thurston r

Non-Accidental Ito et al. 2005 0-99 D1HourMax 0.000400 0.000066 Log-linea 1-hour max.
r

Non-Accidental Ito et al. 2005 0-99 D24HourMea 0.001750 0.000357 Log-linea Warm season.
n r 24-hour mean.

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Non-Accidental Ito et al. 2005 0-99 D8HourMax 0.001173 0.000239 Log-linea Warm season.
r 8-hour max from
24-hour mean.

Non-Accidental Ito et al. 2005 0-99 D8HourMax 0.000532 0.000088 Log-linea 8-hour max from
r 1-hour max.

All Cause Levy et al. 2005 US and 0-99 D1HourMax 0.000841 0.000134 Log-linea Warm season.
non-US r

All Cause Levy et al. 2005 US and 0-99 D8HourMax 0.001119 0.000179 Log-linea Warm season.
non-US r 8-hour max from
1-hour max.

Non-Accidental Moolgavkar et 1995 Philadelphia, 0-99 D24HourMea 0.001398 0.000266 Log-linea Warm season.
al. PA n r

Non-Accidental Moolgavkar et 1995 Philadelphia, 0-99 TSP, D24HourMea 0.001389 0.000373 Log-linea Warm season.
al. PA SO2 n r

Non-Accidental Moolgavkar et 1995 Philadelphia, 18-99 TSP, D24HourMea 0.000611 0.000216 Log-linea
al. PA SO2 n r

Non-Accidental Samet et al. 1997 Philadelphia, 18-99 CO, D24HourMea 0.000936 0.000312 Log-linea
PA NO2, n r
SO2,
TSP

Non-Accidental Schwartz 2005 14 US cities 0-99 D1HourMax 0.000370 0.000130 Logistic Warm season.

Non-Accidental Schwartz 2005 14 US cities 0-99 D8HourMax 0.000426 0.000150 Logistic Warm season.
8-hour max from
1-hour max.

G.1.1 Bell et al (2004)

Ozone has been associated with various adverse health effects, including increased rates of
hospital admissions and exacerbation of respiratory illnesses. Although numerous
time-series studies have estimated associations between day-to-day variation in ozone
levels and mortality counts, results have been inconclusive. The authors investigated
whether short-term (daily and weekly) exposure to ambient ozone is associated with
mortality in the United States. Using analytical methods and databases developed for the
National Morbidity, Mortality, and Air Pollution Study, they estimated a national average
relative rate of mortality associated with short-term exposure to ambient ozone for 95 large
US urban communities from 1987-2000. The authors used distributed-lag models for
estimating community-specific relative rates of mortality adjusted for time-varying
confounders (particulate matter, weather, seasonality, and long-term trends) and
hierarchical models for combining relative rates across communities to estimate a national
average relative rate, taking into account spatial heterogeneity. A 10-ppb increase in the
previous week's ozone was associated with a 0.52% increase in daily mortality (95%
posterior interval [PI], 0.27%-0.77%) and a 0.64% increase in cardiovascular and
respiratory mortality (95% PI, 0.31%-0.98%). Effect estimates for aggregate ozone during
the previous week were larger than for models considering only a single day's exposure.
Results were robust to adjustment for particulate matter, weather, seasonality, and
long-term trends. These results indicate a statistically significant association between
short-term changes in ozone and mortality on average for 95 large US urban communities,
which include about 40% of the total US population.

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Non-Accidental Mortality
The coefficient and standard error are based on the relative risk (1.003908) and 95%
confidence interval (1.0013-1.0065) associated with a 10 ppb increase in daily average
ozone (Bell et al., 2004, p. 2376).

G.1.2 Bell et al (2005)

Although many time-series studies of ozone and mortality have identified positive
associations, others have yielded null or inconclusive results, making the results of these
studies difficult to interpret. The authors performed a meta-analysis of 144 effect estimates
from 39 time-series studies, and estimated pooled effects by lags, age groups,
cause-specific mortality, and concentration metrics. They compared results with pooled
estimates from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS), a
time-series study of 95 large U.S. urban centers from 1987 to 2000. Both meta-analysis
and NMMAPS results provided strong evidence of a short-term association between ozone
and mortality, with larger effects for cardiovascular and respiratory mortality, the elderly,
and current-day ozone exposure. In both analyses, results were insensitive to adjustment
for particulate matter and model specifications. In the meta-analysis, a 10-ppb increase in
daily ozone at single-day or 2-day average of lags 0, 1, or 2 days was associated with an
0.87% increase in total mortality (95% posterior interval = 0.55% to 1.18%), whereas the
lag 0 NMMAPS estimate is 0.25% (0.12% to 0.39%). Several findings indicate possible
publication bias: meta-analysis results were consistently larger than those from NMMAPS;
meta-analysis pooled estimates at lags 0 or 1 were larger when only a single lag was
reported than when estimates for multiple lags were reported; and heterogeneity of
city-specific estimates in the meta-analysis were larger than with NMMAPS.

All-Cause Mortality
The coefficient and standard error are based on the relative risk (1.008738) and 95%
confidence interval (1.0055-1.0119) associated with a 10 ppb increase in daily average
ozone (Bell et al., 2005, Table 6).

G.1.3 Huang et al (2005)

The authors developed Bayesian hierarchical distributed lag models for estimating
associations between daily variations in summer ozone levels and daily variations in
cardiovascular and respiratory (CVDRESP) mortality counts for 19 large U.S. cities
included in the National Morbidity, Mortality and Air Pollution Study (NMMAPS) for the
summers of 1987–1994. In the first stage, they defined a semi-parametric distributed lag
Poisson regression model to estimate city-specific relative rates of CVDRESP mortality
associated with short-term exposure to summer ozone. In the second stage, they specified a
class of distributions for the true city-specific relative rates to estimate an overall effect by
taking into account the variability within and across cities. They performed the
calculations with respect to several random effects distributions (normal, t-student, and

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mixture of normal), thus relaxing the common assumption of a two-stage normal–normal

hierarchical model. They assessed the sensitivity of the results to: (i) lag structure for
ozone exposure; (ii) degree of adjustment for long-term trends; (iii) inclusion of other
pollutants in the model; (iv) heat waves; (v) random effects distributions; and (vi) prior
hyperparameters. On average across cities, the authors found that a 10 ppb increase in
summer ozone level over the previous week is associated with a 1.25 per cent increase in
CVDRESP mortality (95 per cent posterior regions: 0.47, 2.03). The relative rate estimates
are also positive and statistically significant at lags 0, 1 and 2. They found that associations
between summer ozone and CVDRESP mortality are sensitive to the confounding
adjustment for PM10, but are robust to: (i) the adjustment for long-term trends, other
gaseous pollutants (NO2, SO2 and CO); (ii) the distributional assumptions at the second
stage of the hierarchical model; and (iii) the prior distributions on all unknown parameters.

Cardiopulmonary Mortality
Assuming a 10 ppb change in ozone, Huang et al (2005, Table 1) reported a 1.25% change
in CVDRESP mortality with a 95% confidence interval of 0.47% to 2.03%.
Note that Huang et al (2005, p. 549) define CVDRESP as including ICD-9 codes: 390-448,
480-487, 490-496, and 507. This differs somewhat from the the definition of
"cardiopulmonary" mortality in BenMAP -- defined as ICD-9 codes 401-440 and 460-519.

G.1.4 Levy et al, 2005

The authors conducted an empiric Bayes metaregression to estimate the ozone effect on
mortality, and to assess whether this effect varies as a function of hypothesized
confounders or effect modifiers. They gathered 71 time-series studies relating ozone to
all-cause mortality, and tjey selected 48 estimates from 28 studies for the metaregression.
Metaregression covariates included the relationship between ozone concentrations and
concentrations of other air pollutants, proxies for personal exposure-ambient concentration
relationships, and the statistical methods used in the studies. For the metaregression, they
applied a hierarchical linear model with known level-1 variances. The authors estimated a
grand mean of a 0.21% increase (95% confidence interval = 0.16-0.26%) in mortality per
10-microg/m increase of 1-hour maximum ozone (0.41% increase per 10 ppb) without
controlling for other air pollutants. In the metaregression, air-conditioning prevalence and
lag time were the strongest predictors of between-study variability. Air pollution
covariates yielded inconsistent findings in regression models, although correlation analyses
indicated a potential influence of summertime PM2.5.

All-Cause Mortality
Levy et al (2005, Table 1) reported a 0.43% change in all-cause mortality with a 95%
confidence interval of 0.29% to 0.56% associated with a 10 ug/m3 change in ozone. We
converted ug/m3 to ppb with an assumed relationship of 1.96 ug/m3 per 1.0 ppb.

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G.1.5 Ito and Thurston (1996)

In this study, race, gender, and cause-specific counts of daily mortality in Cook County,
Illinois (which encompasses the city of Chicago) during 1985-1990 were analyzed to
determine if there was any heterogeneity in air pollution/weather/mortality associations
across these various population subcategories. Seasonal cross-correlations between
mortality and environmental variables first were examined to identify appropriate lag
structures. Of the pollution variables considered -- PM10, ozone, CO, SO2, and visual
range-derived extinction coefficient -- both PM10 and ozone showed significant
associations with same-day and next-day mortality. The Poisson regression models
employed included seasonal cycles (sine/cosine series), square and linear terms of lagged
temperature, trend line, day-of-week dummy variables, and the average of the same day's
and previous day's PM10 or ozone.
The authors reported a significant relationship for ozone and PM10 with both pollutants in
the model; no significant effects were found for SO2 and CO. In single pollutant models
the effects were slightly larger. The health impact function for ozone is based on results
from the co-pollutant models.

Non-Accidental Mortality
For a co-pollutant model with PM10, the ozone coefficient (0.000634) and standard error
(0.000251) were obtained directly from the author because the published paper reported
incorrect information.

G.1.6 Ito et al (2005)

The authors conducted a review and meta-analysis of short-term ozone mortality studies,
identified unresolved issues, and conducted an additional time-series analysis for 7 U.S.
cities (Chicago, Detroit, Houston, Minneapolis-St. Paul, New York City, Philadelphia, and
St. Louis). They found a combined estimate of 0.39% (95% confidence interval =
0.26-0.51%) per 10-ppb increase in 1-hour daily maximum ozone for the all-age
nonaccidental cause/single pollutant model (43 studies). Adjusting for the funnel plot
asymmetry resulted in a slightly reduced estimate (0.35%; 0.23-0.47%). In a subset for
which particulate matter (PM) data were available (15 studies), the corresponding
estimates were 0.40% (0.27-0.53%) for ozone alone and 0.37% (0.20-0.54%) with PM in
model. The estimates for warm seasons were generally larger than those for cold seasons.
The additional time-series analysis found that including PM in the model did not
substantially reduce the ozone risk estimates. However, the difference in the weather
adjustment model could result in a 2-fold difference in risk estimates (eg, 0.24% to 0.49%
in multicity combined estimates across alternative weather models for the ozone-only
all-year case). The authors concluded that the results suggest short-term associations
between ozone and daily mortality in the majority of the cities, although the estimates

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appear to be heterogeneous across cities.

Non-Accidental Mortality
Ito et al (2005) reported results for functions with both 1-hour daily maximum and 24-hour
daily average metrics. We present both below.

One-hour Max Function

Assuming a 10 ppb change in the daily 1-hour maximum, Ito et al (2005, p. 446) reported a
0.40% change in non-accidental mortality with a 95% confidence interval of 0.27% to
0.53%.

Daily Average Function

Assuming a 20 ppb change in the daily 24-hour average, Ito et al (2005, p. 448) reported a
3.5% change in non-accidental mortality with a 95% confidence interval of 2.1% to 4.9%.

G.1.7 Moolgavkar et al (1995)

Moolgavkar et al. (1995) examined the relationship between daily non-accidental mortality
and air pollution levels in Philadelphia, Pennsylvania from 1973 to 1988. They examined
ozone, TSP, and SO2 in a three-pollutant model, and found a significant relationship for
ozone and SO2; TSP was not significant. In season-specific models, ozone was
significantly associated with mortality only in the summer months.

Mortality, Non-Accidental
The health impact function for ozone is based on the full-year three-pollutant model
reported in Table 5 (Moolgavkar et al., 1995, p. 482). The coefficient and standard error
are based on the relative risk (1.063) and 95% confidence interval (1.018-1.108) associated
with a 100 ppb increase in daily average ozone.

G.1.8 Samet et al (1997)

Samet et al. (1997) examined the relationship between daily non-accidental mortality and
air pollution levels in Philadelphia, Pennsylvania from 1974 to 1988. They examined
ozone, TSP, SO2, NO2, and CO in a Poisson regression model. In single pollutant models,
ozone, SO2, TSP, and CO were significantly associated with mortality. In a five-pollutant
model, they found a positive statistically significant relationship for each pollutant except

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NO2.

Mortality, Non-Accidental
The health impact function for ozone is based on the five-pollutant model (ozone, CO, NO
2, SO2, and TSP) reported in Table 9 (Samet et al., 1997, p. 20). The ozone coefficient and
standard error are based on the percent increase (1.91) and t-statistic (3) associated with a
20.219 ppb increase in two-day average ozone.

G.1.9 Schwartz (2005)

The author used the case-crossover approach, where the control for each person is the same
person on a day near in time, when he or she did not die. This method controls for season
and individual risk factors by matching. One can also choose the control day to have the
same temperature as the event day. The author applied this approach to a study of more
than 1 million deaths in 14 U.S. cities. He found that, with matching on temperature, a
10-ppb increase in maximum hourly ozone concentrations was associated with a 0.23%
(95% confidence interval [CI] 0.01%, 0.44%) increase in the risk of dying. This finding
was indistinguishable from the risk when only matching on season and controlling for
temperature with regression splines (0.19%; 95% CI 03%, 0.35%). Control for suspended
particulate matter with an aerodynamic diameter of 10 mum or less (PM(10)) did not
change this risk. However, the association was restricted to the warm months (0.37%
increase; 95% CI 0.11%, 0.62%), with no effect in the cold months. The author concluded
that the association between ozone and mortality risk is unlikely to be caused by
confounding by temperature.

Non-Accidental Mortality
Assuming a 10 ppb change in the daily 1-hour maximum, Schwartz (2005, Table 2)
reported a 0.37% change in non-accidental mortality with a 95% confidence interval of
0.11% to 0.62%.

G.2 Hospital Admissions

Table G-2 summarizes the health impacts functions used to estimate the relationship
between ozone and hospital admissions. Below, we present a brief summary of each of the
studies and any items that are unique to the study.

Table G-2. Health Impact Functions for Ozone and Hospital Admissions
Effect Author Year Lcoation Age Co-Poll Metric Beta Std Err Form Notes

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All Burnett et al. 2001 Toronto, 0-1 PM2.5 D1HourMax 0.00730 0.002122 Log-linear Warm season.
Respiratory CAN 1

All Burnett et al. 2001 Toronto, 0-1 PM2.5 D8HourMax 0.00817 0.002377 Log-linear Warm season. 8-hour
Respiratory CAN 7 max from 1-hour
max.

Chronic Lung Moolgavkar et 1997 Minneapolis 65-99 PM10, D24HourMea 0.00280 0.001769 Log-linear
al. , MN CO n 0

Chronic Lung Moolgavkar et 1997 Minneapolis 65-99 PM10, D8HourMax 0.00196 0.001238 Log-linear All year. 8-hour max
al. , MN CO 0 from 24-hour mean.

Pneumonia Moolgavkar et 1997 Minneapolis 65-99 PM10, D24HourMea 0.00380 0.001088 Log-linear
al. , MN SO2, n 0
NO2

Pneumonia Moolgavkar et 1997 Minneapolis 65-99 PM10, D8HourMax 0.00266 0.000762 Log-linear All year. 8-hour max
al. , MN SO2, 0 from 24-hour mean.
NO2

Chronic Lung Schwartz 1994 Detroit, MI 65-99 PM10 D24HourMea 0.00552 0.002085 Log-linear All year.
(less Asthma) n 3

Chronic Lung Schwartz 1994 Detroit, MI 65-99 PM10 D8HourMax 0.00342 0.001293 Log-linear All year. 8-hour max
(less Asthma) 4 from 24-hour mean.

Pneumonia Schwartz 1994 Detroit, MI 65-99 PM10 D24HourMea 0.00521 0.001300 Log-linear All year.
n 0

Pneumonia Schwartz 1994 Minneapolis 65-99 PM10 D24HourMea 0.00397 0.001865 Log-linear All year.
, MN n 7

Pneumonia Schwartz 1994 Detroit, MI 65-99 PM10 D8HourMax 0.00323 0.000806 Log-linear All year. 8-hour max
0 from 24-hour mean.

Pneumonia Schwartz 1994 Minneapolis 65-99 PM10 D8HourMax 0.00278 0.001305 Log-linear All year. 8-hour max
, MN 4 from 24-hour mean.

All Schwartz 1995 New 65-99 PM10 D24HourMea 0.00265 0.001398 Log-linear Warm season.
Respiratory Haven, CT n 2

All Schwartz 1995 Tacoma, 65-99 PM10 D24HourMea 0.00714 0.002565 Log-linear Warm season.
Respiratory WA n 7

All Schwartz 1995 New 65-99 PM10 D8HourMax 0.00177 0.000936 Log-linear Warm season. 8-hour
Respiratory Haven, CT 7 max from 24-hour
mean.

All Schwartz 1995 Tacoma, 65-99 PM10 D8HourMax 0.00493 0.001770 Log-linear Warm season. 8-hour
Respiratory WA 1 max from 24-hour
mean.

G.2.1 Burnett et al (2001)

Burnett et al. (2001) studied the association between air pollution and acute respiratory
hospital admissions (ICD codes 493, 466, 464.4, 480-486) in Toronto from 1980-1994,
among children less than 2 years of age. They collected hourly concentrations of the
gaseous pollutants, CO, NO2, SO2, and ozone. Daily measures of particulate matter were
estimated for the May to August period of 1992-1994 using TSP, sulfates, and coefficient
of haze data. The authors report a positive association between ozone in the May through
August months and respiratory hospital admissions, for several single days after elevated
ozone levels.
The strongest association was found using a five-day moving average of ozone. No
association was found in the September through April months. In co-pollutant models
with a particulate matter or another gaseous pollutant, the ozone effect was only slightly
diminished. The effects for PM and gaseous pollutants were generally significant in single

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pollutant models but diminished in co-pollutant models with ozone, with the exception of
CO. The C-R functions for ozone are based on a single pollutant and two co-pollutant
models, using the five-day moving average of one-hour max ozone.

Hospital Admissions, All Respiratory (ICD-9 codes 464, 466, 480-487, 493)
In a model with PM2.5, the coefficient and standard error are based on the percent increase
(33.0) and t-statistic (3.44) associated with a 45.2 ppb increase in the five-day moving
average of one-hour max ozone (Burnett et al., 2001, Table 3).

G.2.2 Moolgavkar et al (1997)

Moolgavkar et al. (1997) examined the relationship between air pollution and hospital
admissions (ICD codes 490-496) for individuals 65 and older in Minneapolis-St. Paul,
Minnesota, from January 1986 to December 1991. In a Poisson regression, they found no
significant effect for any of the pollutants (PM10, ozone, or CO). The effect for ozone was
marginally significant. The model with a 100 df smoother was reported to be optimal (p.
368). The health impact function for chronic lung disease is based on the results from a
three-pollutant model (ozone, CO, PM10) using the 100 df smoother; the function for
Pneumonia uses the 130 df smoother.

Hospital Admissions, Chronic Lung Disease (ICD-9 codes 490-496)

In a model with CO and PM10, the estimated coefficient and standard error are based on the
percent increase (4.2) and 95% confidence interval of the percent increase (-1.0-9.4)
associated with a change in daily average ozone levels of 15 ppb (Moolgavkar et al., 1997,
Table 4).

Hospital Admissions, Pneumonia (ICD-9 codes 480-487)

In a model with NO2, PM10,and SO2, the estimated coefficient and standard error are based
on the percent increase (5.7) and 95% confidence interval of the percent increase (2.5-8.9)
associated with an increase in daily average ozone levels of 15 ppb (Moolgavkar et al.,
1997, Table 4).

G.2.3 Schwartz (1994a)

Schwartz (1994a) examined the relationship between air pollution and hospital admissions
for individuals 65 and older in Minneapolis-St. Paul, Minnesota, from January 1986 to
December 1989. In single-pollutant Poisson regression models, both ozone and PM10 were
significantly associated with pneumonia admissions. In a two-pollutant model, Schwartz
found PM10 significantly related to pneumonia; ozone was weakly linked to pneumonia.

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The results were not sensitive to the methods used to control for seasonal patterns and
weather. The ozone C-R functions are based on the results of the single pollutant model
and the two-pollutant model (PM10 and ozone) with spline smoothing for temporal patterns
and weather.

Hospital Admissions, Pneumonia (ICD-9 codes 480-487)

In a model with PM10 and spline functions to adjust for time and weather, the coefficient
and standard error are based on the relative risk (1.22) and 95% confidence interval (1.02,
1.47) for a 50 ppb increase in daily average ozone levels (Schwartz, 1994a, Table 4).

G.2.4 Schwartz (1994b)

Schwartz (1994b) examined the relationship between air pollution and hospital admissions
(ICD codes 491-492, 494-496) for individuals 65 and older in Detroit, Michigan, from
January 1986 to December 1989. In a two-pollutant Poisson regression model, Schwartz
found both PM10 and ozone significantly linked to pneumonia and COPD. The authors
state that effect estimates were relatively unchanged compared to the unreported single
pollutant models. No significant associations were found between either pollutant and
asthma admissions. The C-R function for chronic lung disease incidence is based on the
results of the “basic” co-pollutant model (ozone and PM10) presented in Table 4 (p. 651).
The study also reports results using generalized additive models to fit time and temperature
variables, however no standard error or confidence intervals were reported.

Hospital Admissions, Chronic Lung Disease less Asthma (ICD-9 codes 490-492, 494-
496)
The coefficient and standard error for the “basic” model are reported in Table 4 (Schwartz,
1994b, p.651) for a one ppb change in daily average ozone.

Hospital Admissions, Pneumonia (ICD-9 codes 480-487)

The ozone C-R function for pneumonia incidence is based on the coefficient and standard
error for the “basic” co-pollutant model presented in Table 4 (Schwartz, 1994b, p. 651).

G.2.5 Schwartz (1995)

Studies have reported associations between short term changes in air pollution and
respiratory hospital admissions. This relationship was examined in two cities with
substantially different levels of sulphur dioxide (SO2) but similar levels of airborne
particles in an attempt to separate the effects of the two pollutants. Significant differences

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in weather between the two cities allowed the evaluation of that potential confounder also.
Daily counts of admissions to all hospitals for respiratory disease (ICD 9 460-519) were
constructed for persons aged 65 years and older in two cities - New Haven, Connecticut
and Tacoma, Washington.
Each city was analysed separately. Average daily concentrations of SO2, inhalable
particles (PM10), and ozone were computed from all monitors in each city, and daily
average temperature and humidity were obtained from the US weather service. Daily
respiratory admission counts were regressed on temperature, humidity, day of the week
indicators, and air pollution. A 19 day weighted moving regression filter was used to
remove all seasonal and subseasonal patterns from the data. Possible U- shaped
dependence of admissions on temperature was dealt with using indicator variables for eight
categories each of temperature and humidity.
Each pollutant was first examined individually and then multiple pollutant models were
fitted. All three pollutants were associated with respiratory hospital admissions of the
elderly. The PM10 associations were little changed by control for either ozone or SO2.
The ozone association was likewise independent of the other pollutants. The SO2
association was substantially attenuated by control for ozone in both cities, and by control
for PM10 in Tacoma. The magnitude of the effect was small (relative risk 1.06 in New
Haven and 1.10 in Tacoma for a 50 micrograms/m3 increase in PM10, for example) but,
given the ubiquitous exposure, this has some public health significance. The authors
concluded that air pollution concentrations within current guidelines were associated with
increased respiratory hospital admissions of the elderly. The strongest evidence for an
independent association was for PM10, followed by ozone.

Hospital Admissions, All Respiratory (ICD-9 codes 460-519) -- Tacoma

In a model with PM10, the coefficient and standard error are estimated from the relative
risk (1.20) and 95% confidence interval (1.06-1.37) for a 50 µg/m3 increase in average
daily ozone levels (Schwartz, 1995, Table 6, p. 535). To calculate the coefficient, a
conversion of 1.96 μg/m3 per ppb was used, based on a density of ozone of 1.96 grams per
liter (at 25 degrees Celsius).

Hospital Admissions, All Respiratory (ICD-9 codes 460-519) -- New Haven

In a model with PM10, the coefficient and standard error are estimated from the relative
risk (1.07) and 95% confidence interval (1.00-1.15) for a 50 µg/m3 increase in average
daily ozone levels (Schwartz, 1995, Table 3, p. 534). To calculate the coefficient, a
conversion of 1.96 μg/m3 per ppb was used, based on a density of ozone of 1.96 grams per
liter (at 25 degrees Celsius).

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G.3 Emergency Room Visits

Table G-3 summarizes the health impacts functions used to estimate the relationship
between ozone and emergency room (ER) visits. Below, we present a brief summary of
each of the studies and any items that are unique to the study.

Table G-3. Health Impact Functions for Ozone and Emergency Room Visits
Effect Author Year Lcoation Age Co-Poll Metric Beta Std Err Form Notes

Asthma Jaffe et al. 2003 Ohio cities 5-34 D8HourMax 0.003000 0.001531 Log-linear

Asthma Peel et al. 2005 Atlanta, GA 0-99 D8HourMax 0.000870 0.000529 Log-linear

Asthma Stieb et al. 1996 New Brunswick, 0-99 D1HourMax 0.000040 0.000020 Quadratic Warm season.
CAN

Asthma Stieb et al. 1996 New Brunswick, 0-99 D24HourMean 0.000100 0.000040 Quadratic Warm season.
CAN

Asthma Wilson et al. 2005 Portland, ME 0-99 D8HourMax 0.003000 0.001000 Log-linear

Asthma Wilson et al. 2005 Manchester, NH 0-99 D8HourMax -0.001000 0.002000 Log-linear

G.3.1 Jaffe et al (2003)

Jaffe et al. (2003) examined the relationship between ER visits and air pollution for
persons ages 5-34 in Cleveland, Columbus, and Cincinnati, Ohio, from 1991 through 1996.
In single-pollutant Poisson regression models, ozone and SO2 were linked to asthma visits,
and no significant effect was seen for NO2 and PM10.

Emergency Room Visits, Asthma

Assuming a 10 ppb increase in the daily 8-hour maximum ozone level, Jaffe et al (2003,
Table 3) reported a 3.0% change in asthma ER visits with a 95% confidence interval of
0.0% to 6.0%.

G.3.2 Peel et al (2005)

A number of emergency department studies have corroborated findings from mortality and
hospital admission studies regarding an association of ambient air pollution and respiratory
outcomes. More refined assessment has been limited by study size and available air quality
data. Measurements of 5 pollutants PM10, ozone, NO2, CO, and SO2 were available for
the entire study period (1 January 1993 to 31 August 2000); detailed measurements of
particulate matter were available for 25 months. The authors obtained data on 4 million
emergency department visits from 31 hospitals in Atlanta. Visits for asthma, chronic
obstructive pulmonary disease, upper respiratory infection, and pneumonia were assessed
in relation to air pollutants using Poisson generalized estimating equations. In
single-pollutant models examining 3-day moving averages of pollutants (lags 0, 1, and 2):
standard deviation increases of ozone, NO2, CO, and PM10 were associated with 1-3%

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increases in URI visits; a 2 microg/m increase of PM2.5 organic carbon was associated
with a 3% increase in pneumonia visits; and standard deviation increases of NO2 and CO
were associated with 2-3% increases in chronic obstructive pulmonary disease visits.
Positive associations persisted beyond 3 days for several of the outcomes, and over a week
for asthma. The results of this study contribute to the evidence of an association of several
correlated gaseous and particulate pollutants, including ozone, NO2, CO, PM, and organic
carbon, with specific respiratory conditions.

Emergency Room Visits, Asthma

The ozone coefficient and standard error are reported per 25 ppb increment of the
maximum daily 8-hour average ozone level (Peel et al., 2003, Table 4). We used the
results from the three cities combined. The relative risk is 1.022, with a 95 percent
confidence interval of 0.996 to 1.049.

G.3.3 Stieb (1996)

Stieb et al. (1996) examined the relationship between ER visits and air pollution for
persons of all ages in St. John, New Brunswick, Canada, from May through September in
1984-1992. Ozone was significantly linked to ER visits, especially when ozone levels
exceeded 75 ppb. The authors reported results from a linear model, quadratic model, and
linear-quadratic model using daily average and 1-hour maximum ozone. In the linear
model, ozone was borderline significant. In the quadratic and linear-quadratic models,
ozone was highly significant. This is consistent with the author’s conclusion that “only
ozone appeared to have a nonlinear relationship with visit rates” (p. 1356) and that
“quadratic, linear-quadratic, and indicator models consistently fit the data better than the
linear model ...” (p. 1358). The linear term in the linear-quadratic model is negative,
implying that at low ozone levels, increases in ozone are associated with decreases in risk.
Since this does not seem biologically plausible, the ozone health impact functions
described here are based on the results of the quadratic regression models presented in
Table 2 (Stieb et al., 1996, p. 1356).

Emergency Room Visits, Asthma

One-hour Max Function
The coefficient and standard error of the quadratic model are reported in Table 2 (Stieb et
al., 1996, p. 1356) for a 1 ppb increase in 1-hour daily maximum ozone levels. The C-R
function to estimate avoided emergency visits derived from a quadratic regression model is
shown below:

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Baseline Population: baseline population of St. John, New Brunswick (Stieb et al., 1996,
p. 1354) = 125,000
Population: population of all ages

Daily Average Function

The coefficient and standard error of the quadratic model are reported in Table 2 (p. 1356)
for a 1 ppb increase in daily average ozone levels. The C-R function to estimate avoided
emergency visits derived from a quadratic regression model is shown below:

Baseline Population: baseline population of St. John, New Brunswick (Stieb et al., 1996, p. 1354)
= 125,000
Population: population of all ages

G.3.4 Wilson et al (2005)

Daily emergency room (ER) visits for all respiratory (ICD-9 460-519) and asthma (ICD-9
493) were compared with daily SO2, ozone, and weather variables over the period
1998-2000 in Portland, Maine (population 248,000), and 1996-2000 in Manchester, New
Hampshire (population 176,000). Seasonal variability was removed from all variables
using nonparametric smoothed function (LOESS) of day of study. Generalized additive
models were used to estimate the effect of elevated levels of pollutants on ER visits.
Relative risks of pollutants were reported over their interquartile range (IQR, the 75th
-25th percentile pollutant values). I n Portland, an IQR increase in SO2 was associated
with a 5% (95% CI 2-7%) increase in all respiratory ER visits and a 6% (95% CI 1-12%)
increase in asthma visits. An IQR increase in O3 was associated with a 5% (95% CI
1-10%) increase in Portland asthmatic ER visits. No significant associations were found in
Manchester, New Hampshire, possibly due to statistical limitations of analyzing a smaller
population. The absence of statistical evidence for a relationship should not be used as
evidence of no relationship. This analysis reveals that, on a daily basis, elevated SO2 and
O3 have a significant impact on public health in Portland, Maine.

Emergency Room Visits, Asthma

The coefficient and standard error are taken from Wilson et al. (2005, Table 5).

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G.4 Minor Effects

Table G-4 summarizes the health impacts functions used to estimate the relationship
between ozone and minor effects. Below, we present a brief summary of each of the
studies and any items that are unique to the study.

Table G-4. Health Impact Functions for Ozone and Minor Effects
Effect Author Year Lcoation Age Co-Poll Metric Beta Std Err Form Notes

School Loss Chen et al. 2000 Washoe Co, 5-17 PM10, D1HourMax 0.01324 0.00498 Linear
Days, All Cause NV CO 7 5

School Loss Chen et al. 2000 Washoe Co, 5-17 PM10, D8HourMax 0.01576 0.00498 Linear All year. 8-hour
Days, All Cause NV CO 3 5 max from 1-hour
max.

Worker Crocker 1981 Nationwide 18-64 D24HourMea 0.14270 Linear All year.
Productivity and Horst n 0

Worker Crocker 1981 Nationwide 18-64 D8HourMax 0.09275 Linear All year. 8-hour
Productivity and Horst 5 max from 24-hour
mean.

School Loss Gilliland et 2001 Southern 5-17 D8HourMax 0.00782 0.00444 Log-linear All year. 8-hour
Days, All Cause al. California 4 5 max from 8-hour
mean.

School Loss Gilliland et 2001 Southern 5-17 D8HourMean 0.00815 0.00463 Log-linear
Days, All Cause al. California 0 0

Minor Restricted Ostro and 1989 Nationwide 18-64 PM2.5 D1HourMax 0.00220 0.00065 Log-linear
Activity Days Rothschild 0 8

Minor Restricted Ostro and 1989 Nationwide 18-64 PM2.5 D8HourMax 0.00259 0.00077 Log-linear 8-hour max from
Activity Days Rothschild 6 6 1-hour max.

G.4.1 Chen et al (2000)

Chen et al. (2000) studied the association between air pollution and elementary school
absenteeism (grades 1-6) in Washoe County, Nevada. Assuming that most children start
kindergarten at age 5, the corresponding ages for grades 1 through 6 would be 6 through
11. Daily absence data were available for all elementary schools in the Washoe Country
School District. The authors regressed daily total absence rate on the three air pollutants,
meteorological variables, and indicators for day of the week, month, and holidays. They
reported statistically significant associations between both ozone and CO and daily total
absence rate for grades one through six. PM10 was negatively associated with absence rate,
after adjustment for ozone, CO, and meteorological and temporal variables. The C-R
function for ozone is based on the results from a multiple linear regression model with CO,
ozone, and PM10.

School Loss Days, All Cause

The coefficient and standard error are presented in Table 3 (Chen et al., 2000, p. 1008) for
a unit ppm increase in the two-week average of daily one-hour maximum ozone

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concentration. This is converted to unit ppb increase by dividing by 1,000.

The reported coefficient represents an absolute increase in absenteeism rate for a unit
increase in ozone. If we apply this study to other locations, we assume that the same
absolute increase will occur for a unit increase in ozone, regardless of the baseline rate. If
the study location has a particularly high baseline rate, we may be overestimating decreases
in absenteeism nationally, and vice-versa. As an example, consider if the baseline
absenteeism rate were 10% in the study and 5% nationally. An absolute increase in
absence rate of 2% associated with a given increase in ozone reflects a relative increase in
absence rate of 20% for the study population. However, in the national estimate, we would
assume the same absolute increase of 2%, but this would reflect a relative increase in the
absenteeism rate of 40%.
An alternative approach is to estimate apply the relative increase in absenteeism rate in the
C-R function by adjusting the results by the ratio of the national absenteeism rate to the
study-specific rate. As a result, the percent increase in absenteeism rate associated with an
increase in ozone is extrapolated nationally rather than the absolute increase in
absenteeism rate. The incidence derivation section above describes the data used to
estimate national and study-specific absence rates.
In addition to this scaling factor, there are two other scaling factors which are applied to
the function. A scaling factor of 0.01 is used to convert the beta from a percentage (x 100)
per unit increase of ozone to a proportion per unit increase of ozone. As a result it can be
applied directly to the national population of school children ages 6 through 11 to estimate
the number of absences avoided.
The final scaling factor adjusts for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the ozone season (May 1 -
September 30), however, in reality, school absences will be avoided only on school days.
We assume that children are in school during weekdays for all of May, two weeks in June,
one week in August, and all of September. This corresponds to approximately 2.75
months out of the 5 month season, resulting in an estimate of 39.3% of days (2.75/5*5/7).
The C-R function parameters are shown below.
Population: population of children ages 6-11
Scaling Factor 1: Ratio of national school absence rate to study-specific school absence rate =
1.081. (National school absence rate of 5.5% obtained from the U.S. Department of
Education (1996, Table 42-1). Study-specific school absence rate of 5.09% obtained from
Chen et al. (2000, Table 1).)
Scaling Factor 2: Convert beta in percentage terms to a proportion = 0.01
Scaling Factor 3: Proportion of days that are school days in the ozone season = 0.393. (Ozone is
modeled for the 5 months from May 1 through September 30. We assume that children are
in school during weekdays for all of May, 2 weeks in June, 1 week in August, and all of
September. This corresponds to approximately 2.75 months out of the 5 month season,
resulting in an estimate of 39.3% of days (2.75/5*5/7).)

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G.4.2 Crocker and Horst (1981)

To monetize benefits associated with increased worker productivity resulting from
improved ozone air quality, we used information reported in Crocker and Horst (1981) and
summarized in EPA (1994). Crocker and Horst examined the impacts of ozone exposure
on the productivity of outdoor citrus workers. The study measured productivity impacts as
the change in income associated with a change in ozone exposure, given as the elasticity of
income with respect to ozone concentration (-0.1427). The relationship estimated by
Crocker and Horst between wages and ozone is a log-log relationship. Therefore the
elasticity of wages with respect to ozone is a constant, equal to the coefficient of the log of
ozone in the model. The reported elasticity translates a ten percent reduction in ozone to a
1.4 percent increase in income. Given the national median daily income for outdoor
workers engaged in strenuous activity reported by the U.S. Census Bureau (2002), $68 per
day (2000$), a ten percent reduction in ozone yields about $0.97 in increased daily wages. (
The national median daily income for workers engaged in “farming, forestry, and fishing”
from the U.S. Census Bureau (2002, Table 621, p. 403) is used as a surrogate for outdoor
workers engaged in strenuous activity.) We adjust the national median daily income
estimate to reflect regional variations in income using a factor based on the ratio of county
median household income to national median household income. No information was
available for quantifying the uncertainty associated with the central valuation estimate.
Therefore, no uncertainty analysis was conducted for this endpoint.

Worker Productivity
The C-R function for estimating changes in worker productivity is shown below:

Daily Income: median daily income for outdoor workers. (The national median daily income
for workers engaged in “farming, forestry, and fishing” was obtained from the U.S. Census
Bureau (2002, Table 621, p. 403) and is used as a surrogate for outdoor workers engaged
in strenuous activity. This national median daily income ($68) is then scaled by the ratio
of national median income to county median income to estimate county median daily
income for outdoor workers.)
Population: population of adults 18 to 64 employed as farm workers.

G.4.3 Gilliland et al (2001)

Gilliland et al. (2001) examined the association between air pollution and school
absenteeism among 4th grade school children (ages 9-10) in 12 southern Californian
communities. The study was conducted from January through June 1996. The authors
used school records to collect daily absence data and parental telephone interviews to
identify causes. They defined illness-related absences as respiratory or non-respiratory. A

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respiratory illness was defined as an illness that included at least one of the following:
runny nose/sneezing, sore throat, cough, earache, wheezing, or asthma attack. The authors
used 15 and 30 day distributed lag models to quantify the association between ozone, PM10
, and NO2 and incident school absences. Ozone levels were positively associated with all
school absence measures and significantly associated with all illness-related school
absences (non-respiratory illness, respiratory illness, URI and LRI). Neither PM10 nor NO2
was significantly associated with illness-related school absences, but PM10 was associated
with non-illness related absences. The health impact function for ozone is based on the
results of the single pollutant model.

School Loss Days

Gilliland et al. (2001) defines an incident absence as an absence that followed attendance
on the previous day and the incidence rate as the number of incident absences on a given
day over the population at risk for an absence on a given day (i.e. those children who were
not absent on the previous day). Since school absences due to air pollution may last longer
than one day, an estimate of the average duration of school absences could be used to
calculated the total avoided school loss days from an estimate of avoided new absences. A
simple ratio of the total absence rate divided by the new absence rate would provide an
estimate of the average duration of school absences, which could be applied to the estimate
of avoided new absences as follows:

Since the function is log-linear, the baseline incidence rate (in this case, the rate of new
absences) is multiplied by duration, which reduces to the total school absence rate.
Therefore, the same result would be obtained by using a single estimate of the total school
absence rate in the C-R function. Using this approach, we assume that the same
relationship observed between pollutant and new school absences in the study would be
observed for total absences on a given day. As a result, the total school absence rate is
used in the function below. The derivation of this rate is described in the section on
baseline incidence rate estimation.
For all absences, the coefficient and standard error are based on a percent increase of 16.3
percent (95% CI -2.6 percent, 38.9 percent) associated with a 20 ppb increase in 8-hour
average ozone concentration (2001, Table 6, p. 52).
A scaling factor is used to adjust for the number of school days in the ozone season. In the
modeling program, the function is applied to every day in the ozone season (May 1 -

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September 30), however, in reality, school absences will be avoided only on school days.
We assume that children are in school during weekdays for all of May, two weeks in June,
one week in August, and all of September. This corresponds to approximately 2.75
months out of the 5 month season, resulting in an estimate of 39.3% of days (2.75/5*5/7).
In addition, not all children are at-risk for a new school absence, as defined by the study.
On average, 5.5% of school children are absent from school on a given day (U.S.
Department of Education, 1996, Table 42-1). Only those who are in school on the
previous day are at risk for a new absence (1-0.055 = 94.5%). As a result, a factor of
94.5% is used in the function to estimate the population of school children at-risk for a
new absence.
Incidence Rate: daily school absence rate = 0.055 (U.S. Department of Education, 1996, Table
42-1)
Population: population of children ages 9-10 not absent from school on a given day = 94.5% of
children ages 9-10 (The proportion of children not absent from school on a given day (5.5%)
is based on 1996 data from the U.S. Department of Education (1996, Table 42-1).)
Scaling Factor: Proportion of days that are school days in the ozone season = 0.393
(Ozone is modeled for the 5 months from May 1 through September 30. We assume that
children are in school during weekdays for all of May, 2 weeks in June, 1 week in August,
and all of September. This corresponds to approximately 2.75 months out of the 5 month
season, resulting in an estimate of 39.3% of days (2.75/5*5/7). )

G.4.4 Ostro and Rothschild (1989)

Ostro and Rothschild (1989) estimated the impact of PM2.5 and ozone on the incidence of
minor restricted activity days (MRADs) and respiratory-related restricted activity days
(RRADs) in a national sample of the adult working population, ages 18 to 65, living in
metropolitan areas. The study population is based on the Health Interview Survey (HIS),
conducted by the National Center for Health Statistics. In publications from this ongoing
survey, non-elderly adult populations are generally reported as ages 18-64. From the study,
it is not clear if the age range stops at 65 or includes 65 year olds. We apply the C-R
function to individuals ages 18-64 for consistency with other studies estimating impacts to
non-elderly adult populations. The annual national survey results used in this analysis
were conducted in 1976-1981. Controlling for PM2.5, two-week average ozone had a
highly variable association with RRADs and MRADs. Controlling for ozone, two-week
average PM2.5 was significantly linked to both health endpoints in most years. The C-R
function for ozone is based on the co-pollutant model with PM2.5.

The study is based on a “convenience” sample of non-elderly individuals. Applying the

C-R function to this age group is likely a slight underestimate, as it seems likely that
elderly are at least as susceptible to ozone as individuals under 65. A number of studies
have found that hospital admissions for the elderly are related to ozone exposures (e.g.,
Schwartz, 1994b; Schwartz, 1995).

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Minor Restricted Activity Days

The coefficient and standard error used in the C-R function are based on a weighted
average of the coefficients in Ostro and Rothschild (1989, Table 4). The derivation of
these estimates is described below.
Incidence Rate: daily incidence rate for minor restricted activity days (MRAD) = 0.02137 (Ostro
and Rothschild, 1989, p. 243)
Population: adult population ages 18 to 64

The coefficient used in the C-R function is a weighted average of the coefficients in Ostro
and Rothschild (1989, Table 4) using the inverse of the variance as the weight. The
calculation of the MRAD coefficient and its standard error is exactly analogous to the
calculation done for the work-loss days coefficient based on Ostro (1987).

The standard error of the coefficient is calculated as follows, assuming that the estimated
year-specific coefficients are independent:

This reduces down to:

G.5 Converting Functions to 8-Hour Daily Maximum Metric

A number of health impact functions were converted from 1-hour maximum, 24-hour
average, and 8-hour average to the 8-hour maximum metric. To convert, say, a 1-hour
maximum function, we multiplied the 1-hour maximum coefficient with the ratio of the

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typical 1-hour maximum value to the typical 8-hour maximum value. We calculated ozone
metric ratios for each quarter and year in the period 2000-2007. We calculated ratios by
monitor, and by county, core business statistical area (CBSA), state, and nation.
For each monitor, a day was considered valid if it had at least 18 hourly values out of 24.
A quarter was considered valid if it had at least 85 percent valid days. Ratios are
calculated for the year, only if that year had four quarterly values. The CBSA codes, which
were defined by OMB on 6-6-03, were obtained from: http://www.census.gov/population/
estimates/metro-city/03msa.txt.
We chose the time period for the ratio calculation (e.g., spring and summer quarters) and
the locations based on the data used in each epidemiological study. Table G-5 presents the
8-hour adjustment used for each study. Tables G-6 through G-8 present supporting
documentation for some of the multi-city 8-hour adjustments.

Table G-5. Eight-Hour Adjustments by Study

Effect Author Year Lcoation Adjustment Factor Location Quarte Metric 8-Hour Notes
rs Adj

Mortality, Bell et al. 2004 95 US cities Nation 2-3 24HourMean 0.67

Non-Accidental

Mortality, All Bell et al. 2005 Meta-analysis From study. See comment. -- 24HourMean 0.53
Cause

HA, All Burnett et 2001 Toronto, CAN Buffalo-Cheektowaga-Tonawan 2-3 1HourMax 1.12
Respiratory al. da, NY MSA

School Loss Chen et al. 2000 Washoe Co, Washoe County 1-4 1HourMax 1.19
Days, All Cause NV

Worker Crocker 1981 Florida FL 1-4 24HourMean 0.65

Productivity and Horst

School Loss Gilliland et 2001 Southern Los Angeles-Long Beach-Santa 1-4 8HourMean 0.96 The statewide avg
Days, All Cause al. California Ana, CA MSA is 0.96.

Mortality, Huang et 2005 19 US cities See below See 24HourMean 0.66

Cardiopulmonary al. below

Mortality, Ito et al. 2005 6 US cities See below See 24HourMean 0.65
Non-Accidental below

Mortality, Ito et al. 2005 Meta-analysis From study. See comment. -- 24HourMean 0.67
Non-Accidental

Mortality, Ito et al. 2006 Meta-analysis From study. See comment. -- 1HourMax 1.33
Non-Accidental

Mortality, All Levy et al. 2005 Meta-analysis From study. See comment. -- 1HourMax 1.33
Cause

HA, Chronic Moolgavka 1997 Minneapolis, Minneapolis-St. 1-4 24HourMean 0.70 Data 2004-2007
Lung Disease r et al. MN Paul-Bloomington, MN-WI only.
MSA

HA, Pneumonia Moolgavka 1997 Minneapolis, Minneapolis-St. 1-4 24HourMean 0.70 Data 2004-2007
r et al. MN Paul-Bloomington, MN-WI only.
MSA

Minor Restricted Ostro and 1989 Nationwide Nation 1-4 1HourMax 1.18
Activity Days Rothschild

HA, Chronic Schwartz 1994 Detroit, MI Detroit-Warren-Livonia, MI 1-4 24HourMean 0.62 Data 2006 only.
Lung Disease MSA
(less Asthma)

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HA, Pneumonia Schwartz 1994 Detroit, MI Detroit-Warren-Livonia, MI 1-4 24HourMean 0.62 Data 2006 only.
MSA

HA, Pneumonia Schwartz 1994 Minneapolis, Minneapolis-St. 1-4 24HourMean 0.70 Data 2004-2007
MN Paul-Bloomington, MN-WI only.
MSA

HA, All Schwartz 1995 New Haven, New Haven-Milford, CT MSA 2-3 24HourMean 0.67
Respiratory CT

HA, All Schwartz 1995 Tacoma, WA Seattle-Tacoma-Bellevue, WA 2-3 24HourMean 0.69

Respiratory MSA

Mortality, Schwartz 2004 14 US cities See below See 1HourMax 0.67

Non-Accidental below

Table G-6. Eight-Hour Adjustment Details -- 6-City Study

City/County CBSAs or Counties Used in Ratio Average Quarters Used Study Metric 8-Hour Adj

Detroit Detroit-Warren-Livonia, MI MSA 2-3 24HourMean 0.63

Cook County Cook County 2-3 24HourMean 0.65

Houston Houston-Baytown-Sugar Land, TX MSA 2-3 24HourMean 0.59

Minneapolis Minneapolis-St. Paul-Bloomington, MN-WI MSA 2-3 24HourMean 0.70

Philadelphia Philadelphia-Camden-Wilmington, PA-NJ-DE-MD MSA 2-3 24HourMean 0.65

St. Louis St. Louis, MO-IL MSA 2-3 24HourMean 0.64

Average 0.64

Table G-7. Eight-Hour Adjustment Details -- 14-City Study

City/County CBSAs or Counties Used in Ratio Average Quarters Used Study Metric 8-Hour Adj Notes

Birmingham Birmingham-Hoover, AL MSA 2-3 1HourMax 1.15

Boulder Boulder, CO MSA 2-3 1HourMax 1.15

Canton Canton-Massillon, OH MSA 2-3 1HourMax 1.12

Chicago Chicago-Naperville-Joliet, IL-IN-WI MSA 2-3 1HourMax 1.16

Cincinnati Cincinnati-Middletown, OH-KY-IN MSA 2-3 1HourMax 1.15

Colorado Springs Colorado Springs, CO MSA 2-3 1HourMax 1.11

Columbus Columbus, OH MSA 2-3 1HourMax 1.13

Detroit Detroit-Warren-Livonia, MI MSA 2-3 1HourMax 1.17

Houston Houston-Baytown-Sugar Land, TX MSA 2-3 1HourMax 1.22

New Haven New Haven-Milford, CT MSA 2-3 1HourMax 1.17

Pittsburgh Pittsburgh, PA MSA 2-3 1HourMax 1.15

Provo Provo-Orem, UT MSA 3 1HourMax 1.13 Only quarter 3 available

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Seattle Seattle-Tacoma-Bellevue, WA MSA 2-3 1HourMax 1.15

Spokane Spokane, WA MSA 3 1HourMax 1.08 Only quarter 3 available

Average 1.15

Table G-8. Eight-Hour Adjustment Details -- 19-City Study

City/County CBSAs or Counties Used in Ratio Average Quarters Used Study Metric 8-Hour Adj Notes

Atlanta Atlanta-Sandy Springs-Marietta, GA MSA 2-3 24HourMean 0.59

Chicago Chicago-Naperville-Joliet, IL-IN-WI MSA 2-3 24HourMean 0.65

Cleveland Cleveland-Elyria-Mentor, OH MSA 2-3 24HourMean 0.69

Dallas/Ft Worth Dallas-Fort Worth-Arlington, TX MSA 2-3 24HourMean 0.67

Detroit Detroit-Warren-Livonia, MI MSA 2-3 24HourMean 0.63

Houston Houston-Baytown-Sugar Land, TX MSA 2-3 24HourMean 0.59

Los Angeles and Santa

Ana/Anaheim have same
Los Angeles Los Angeles-Long Beach-Santa Ana, CA MSA 2-3 24HourMean 0.59 CBSA.

Santa
Ana/Anaheim Los Angeles-Long Beach-Santa Ana, CA MSA 2-3 24HourMean 0.59

Miami-Fort Lauderdale-Miami Beach, FL

Miami MSA 2-3 24HourMean 0.71

New York New York-Newark-Edison, NY-NJ-PA MSA 2-3 24HourMean 0.66

Philadelphia-Camden-Wilmington,
Philadelphia PA-NJ-DE-MD MSA 2-3 24HourMean 0.65

Phoenix Phoenix-Mesa-Scottsdale, AZ MSA 2-3 24HourMean 0.66

Pittsburgh Pittsburgh, PA MSA 2-3 24HourMean 0.61

San Bernardino Riverside-San Bernardino-Ontario, CA MSA 2-3 24HourMean 0.65

San Antonio San Antonio, TX MSA 2-3 24HourMean 0.66

San Diego San Diego-Carlsbad-San Marcos, CA MSA 2-3 24HourMean 0.70

Oakland San Francisco-Oakland-Fremont, CA MSA 2-3 24HourMean 0.70

San Jose San Jose-Sunnyvale-Santa Clara, CA MSA 2-3 24HourMean 0.64

Seattle Seattle-Tacoma-Bellevue, WA MSA 2-3 24HourMean 0.69

Keeping 1 Los Angeles keeps

Average 0.65 8-hour adj at 0.65.

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 Appendix H: Health Valuation Functions in U.S. Setup

Appendix H: Health Valuation Functions in U.S.

Setup
This appendix presents the unit values that are available in BenMAP for each of the health
endpoints included in the current suite of health impact functions. Wherever possible, we
present a distribution of the unit value, characterizing the uncertainty surrounding any
point estimate. The mean of the distribution is taken as the point estimate of the unit
value, and the distribution itself is used to characterize the uncertainty surrounding the unit
value, which feeds into the uncertainty surrounding the monetary benefits associated with
reducing the incidence of the health endpoint. Below we give detailed descriptions of the
derivations of unit values and their distributions, as well as tables listing the unit values
and their distributions, available for each health endpoint. The definitions of the
distributions and their parameters is given in Table H-1.

Table H-1. Unit Value Uncertainty Distributions and Their Parameters

Distribution * Parameter 1 (P1) Parameter 2 (P2)

Normal standard deviation –

Triangular minimum value maximum value

Lognormal ** mean of corresponding normal standard deviation of corresponding

distribution normal distribution

Uniform minimum value maximum vaue

Weibull *** α β

* In all cases, BenMAP calculates the mean of the distribution, which

is used as the “point estimate” of the unit value.

** If Y is a normal random variable, and Y = logeX, then X is

lognormally distributed. Equivalently, X is lognormally distributed if
X = eY, where Y is normally distributed.
*** The Weibull distribution has the following probability density

function:

H.1 Mortality
The economics literature concerning the appropriate method for valuing reductions in
premature mortality risk is still developing. The adoption of a value for the projected
reduction in the risk of premature mortality is the subject of continuing discussion within
the economics and public policy analysis communities. Issues such as the appropriate
discount rate and whether there are factors, such as age or the quality of life, that should be
taken into consideration when estimating the value of avoided premature mortality are still

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under discussion. BenMAP currently offers a variety of options reflecting the uncertainty
surrounding the unit value for premature mortality.

H.1.1 Value of a Statistical Life Based on 26 Studies

One unit value available in BenMAP is $6.3 million. This estimate is the mean of a
distribution fitted to 26 “value of statistical life” (VSL) estimates that appear in the
economics literature and that have been identified in the Section 812 Reports to Congress
as “applicable to policy analysis.” This represents an intermediate value from a variety of
estimates, and it is a value EPA has frequently used in Regulatory Impact Analyses (RIAs)
as well as in the Section 812 Retrospective and Prospective Analyses of the Clean Air Act.

The VSL approach and the set of selected studies mirrors that of Viscusi (1992) (with the
addition of two studies), and uses the same criteria as Viscusi in his review of value-of-life
studies. The $6.3 million estimate is consistent with Viscusi’s conclusion (updated to
2000$) that “most of the reasonable estimates of the value of life are clustered in the $3.8
to $8.9 million range.” Five of the 26 studies are contingent valuation (CV) studies, which
directly solicit WTP information from subjects; the rest are wage-risk studies, which base
WTP estimates on estimates of the additional compensation demanded in the labor market
for riskier jobs. Because this VSL-based unit value does not distinguish among people
based on the age at their death or the quality of their lives, it can be applied to all
premature deaths.

H.1.2 Value of a Statistical Life Based on Selected Studies

In addition to the value of a statistical life based on the results of 26 studies, we have
included three alternatives based loosely on the results of recent work by Mrozek and
Taylor (2002) and Viscusi and Aldy (2003). Each of the four alternatives has a mean value
of $5.5 million (2000$), but with a different distributions: normal, uniform, triangular, and
beta. Table H-2 presents the distribution parameters for the suite of mortality valuations
currently available in BenMAP.

Table H-2. Unit Values Available for Mortality

Basis for Estimate * Age Range at Unit Value Distribution of Parameters of Distribution
Death (VSL) Unit Value
(2000$)
min. max. P1 P2
VSL, based on 26 value-of-life studies. 0 99 $6,324,101 Weibull 5.32E-6 1.509588
VSL based on range from $1 million to $10 0 99 $5,500,000 Normal 2,295,960.54 --
million – 95% CI of assumed normal
distribution.
VSL based on range from $1 million to $10 0 99 $5,500,000 Uniform 1,000,000 10,000,000
million – assumed uniform distribution.

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Basis for Estimate * Age Range at Unit Value Distribution of Parameters of Distribution
Death (VSL) Unit Value
(2000$)
min. max. P1 P2
VSL based on range from $1 million to $10 0 99 $5,500,000 Triangular 1,000,000 10,000,000
million – assumed triangular distribution.

*The original value of a statistical life was calculated in 1990 $. We have used
a factor of 1.3175, based on the All-Items CPI-U.

H.2 Chronic Illness

This sub-section presents the unit values developed for chronic bronchitis, chronic asthma,
and non-fatal myocardial infarctions.

H.2.1 Chronic Bronchitis

PM-related chronic bronchitis is expected to last from the initial onset of the illness
throughout the rest of the individual’s life. WTP to avoid chronic bronchitis would
therefore be expected to incorporate the present discounted value of a potentially long
stream of costs (e.g., medical expenditures and lost earnings) as well as WTP to avoid the
pain and suffering associated with the illness. Both WTP and COI estimates are currently
available in BenMAP.

H.2.1.1 Unit Value Based on Two Studies of WTP

Two contingent valuation studies, Viscusi et al. (1991) and Krupnick and Cropper (1992),
provide estimates of WTP to avoid a case of chronic bronchitis. Viscusi et al. (1991) and
Krupnick and Cropper (1992) were experimental studies intended to examine new
methodologies for eliciting values for morbidity endpoints. Although these studies were
not specifically designed for policy analysis, they can be used to provide reasonable
estimates of WTP to avoid a case of chronic bronchitis. As with other contingent valuation
studies, the reliability of the WTP estimates depends on the methods used to obtain the
WTP values. The Viscusi et al. and the Krupnick and Cropper studies are broadly
consistent with current contingent valuation practices, although specific attributes of the
studies may not be.
The study by Viscusi et al. (1991) uses a sample that is larger and more representative of
the general population than the study by Krupnick and Cropper (1992), which selects
people who have a relative with the disease. However, the chronic bronchitis described to
study subjects in the Viscusi study is severe, whereas a pollution-related case may be less
severe.
The relationship between the severity of a case of chronic bronchitis and WTP to avoid it
was estimated by Krupnick and Cropper (1992). We used that estimated relationship to
derive a relationship between WTP to avoid a severe case of chronic bronchitis, as
described in the Viscusis study, and WTP to avoid a less severe case. The estimated
relationship (see Table 4 in Krupnick and Cropper) can be written as:

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where a denotes all the other variables in the regression model and their coefficients, ß is
the coefficient of sev, estimated to be 0.18, and sev denotes the severity level (a number
from 1 to 13). Let x (< 13) denote the severity level of a pollution-related case of chronic
bronchitis, and 13 denote the highest severity level (as described in Viscusi et al., 1991).
Then

and

Subtracting one equation from the other,

or

Exponentiating and rearranging terms,

There is uncertainty surrounding the exact values of WTP13; x, and ß, and this uncertainty
can be incorporated in the equation, if you request that the analysis be carried out in
“uncertainty mode.” The distribution of WTP to avoid a severe case of chronic bronchitis,
WTP13 ,is based on the distribution of WTP responses in the Viscusi et al. (1991) study.
The distribution of x, the severity level of an average case of pollution-related chronic
bronchitis, is modeled as a triangular distribution centered at 6.5, with endpoints at 1.0 and
12.0. And the distribution of ß is normal with mean = 0.18 and std. dev.= 0.0669 (the
estimate of b and standard error reported in Krupnick and Cropper, 1992).
In uncertainty mode, BenMAP uses a Monte Carlo approach. On each Monte Carlo
iteration, random draws for these three variables are made, and the resulting WTPx is

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calculated from the equation above. Because this function is non-linear, the expected
value of WTP for a pollution-related case of CB cannot be obtained by using the expected
values of the three uncertain inputs in the function (doing that will substantially understate
mean WTP). A Monte Carlo analysis suggests, however, that the mean WTP to avoid a
case of pollution-related chronic bronchitis is about $340,000. Therefore, if you request
that the analysis be carried out in “point estimate” mode, that is the unit value that is used.

H.2.1.2 Alternative Cost of Illness Estimates

Cost of illness estimates for chronic bronchitis were derived from estimates of annual
medical costs and annual lost earnings by Cropper and Krupnick (1990). This study
estimated annual lost earnings resulting from chronic bronchitis as a function of age at
onset of the illness, for the following age categories: 25-43, 35-44, 45-54, and 55-65 (see
Cropper and Krupnick, Table 8). Annual medical expenses were estimated for 10-years
age groups (0-9, 10-19, 20-29, ..., 80-89). We derived estimates of the present discounted
value of the stream of medical and opportunity costs for people whose age of onset is 30,
40, 50, 60, 70, and 80. Medical costs (which are in 1977$ in the Cropper and Krupnick
study) were inflated to 2000$ using the CPI-U for medical care; lost earnings (opportunity
costs) were inflated to 2000$ using the Employment Cost Index for Wages and Salaries.
Life expectancies were assumed to be unaffected by the illness. For example, an
individual at age 70 has a life expectancy of 14.3 more years, and we assumed that
someone whose age of onset of chronic bronchitis is 70 will also live for 14.3 more years.
( Source of life expectancies: National Center for Health Statistics, 1999, Table 5.) We
also assumed that opportunity costs at ages 66 and over were zero. Present discounted
values were calculated using three and seven percent discount rates.
For each of the two discount rates, there are three cost of illness unit values for chronic
bronchitis available in BenMAP, for the following age categories: 27-44, 45-64, and 65+.
These are the age categories that were used in the epidemiological study that estimated a
concentration-response function for chronic bronchitis (Abbey et al., 1995b). The
estimate for the 27-44 age group is an average of the present discounted values calculated
for ages 30 and 40; the estimate for the 45-64 age category is an average of the present
discounted values calculated for ages 50 and 60; and the estimate for the 65+ age category
is an average of the present discounted values calculated for ages 70 and 80. The suite of
unit values available for use in BenMAP are shown in Table H-3 below.

Table H-3. Unit Values Available for Chronic Bronchitis

Present Present
Age of Onset
Discounted Discounted
Basis for Estimate Value of Value of Unit Value Distribution
Medical Opportunity
min. max.
Costs Costs

WTP: average severity 30 99 N/A N/A $340,482 custom

COI: med costs + wage loss, 3% DR 27 44 $18,960 $135,463 $154,422 none

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 Appendix H: Health Valuation Functions in U.S. Setup

Present Present
Age of Onset
Discounted Discounted
Basis for Estimate Value of Value of Unit Value Distribution
Medical Opportunity
min. max.
Costs Costs

45 64 $23,759 $76,029 $99,788 none

65 99 $11,088 $0 $11,088 none

COI: med costs + wage loss, 7% DR 27 44 $7,886 $80,444 $88,331 none

45 64 $14,390 $59,577 $73,967 none

65 99 $9,030 $0 $9,030 none

H.2.2 Chronic Bronchitis Reversals

The unit value for chronic bronchitis reversals assumes that this is chronic bronchitis with
a severity level of 1. The method for generating a distribution of unit values in BenMAP is
therefore the same as the WTP-based unit value method for chronic bronchitis (see above),
with x=1. The mean of this distribution is $150,221.

H.2.3 Chronic Asthma

Two studies have estimated WTP to avoid chronic asthma in adults. Blumenschein and
Johannesson (1998) used two different contingent valuation (CV) methods, the
dichotomous choice method and a bidding game, to estimate mean willingness to pay for a
cure for asthma. The mean WTP elicited from the bidding game was $189 per month, or
$2,268 per year (in 1996$). The mean WTP elicited from the dichotomous choice
approach was $343 per month, or $4,116 per year (in 1996$). Using $2,268 per year, a
three percent discount rate, and 1997 life expectancies for males in the United States
(National Center for Health Statistics, 1999, Table 5), the present discounted value of the
stream of annual WTPs is $47,637 (in 2000$).
O’Conor and Blomquist (1997) estimated WTP to avoid chronic asthma from estimates of
risk-risk tradeoffs. Combining the risk-risk tradeoffs with a statistical value of life, the
annual value of avoiding asthma can be derived. Assuming a value of a statistical life of
$6 million, they derived an annual WTP to avoid asthma of $1500 (O'Connor and
Blomquist, 1997, p. 677). For a value of a statistical life of $5,894,400 (in 1997 $), the
corresponding implied annual value of avoiding chronic asthma, based on O’Conor and
Blomquist would be $1,474. Assuming a three percent discount rate and 1997 life
expectancies for males in the United States, the present discounted value of the stream of
annual WTPs would be $30,257 (in 2000$). A unit value, based on a three percent
discount rate, is the average of the two estimates, or $38,947. Following the method used
for the §812 Prospective analysis, the uncertainty surrounding the WTP to avoid a case of
chronic asthma among adult males was characterized by a triangular distribution on the
range determined by the two study-specific WTP estimates.
A second unit value, using a seven percent discount rate, is also available for use in
BenMAP. The method used to derive this unit value is the same as that described above

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for the three percent discount rate unit value. The unit values available for use in BenMAP
are summarized in Table H-4 below.

Table H-4. Unit Values Available for Chronic Asthma

Age Range Distribution of Unit Parameters of Distribution
Basis for Estimate Unit Value
min. max. Value P1 P2

WTP: 3% DR (Discount Rate) 27 99 $38,947 triangular $30,257 $47,637

WTP: 7% DR 27 99 $25,357 triangular $19,699 $31,015

H.2.4 Non-Fatal Myocardial Infarctions (Heart Attacks)

In the absence of a suitable WTP value for reductions in the risk of non-fatal heart attacks,
there are a variety of cost-of-illness unit values available for use in BenMAP. These
cost-of-illness unit values incorporate two components: the direct medical costs and the
opportunity cost (lost earnings) associated with the illness event. Because the costs
associated with a heart attack extend beyond the initial event itself, the unit values include
costs incurred over five years. Using age-specific annual lost earnings estimated by
Cropper and Krupnick (1990), and a three percent discount rate, we estimated the
following present discounted values in lost earnings over 5 years due to a heart attack:
$8,774 for someone between the ages of 25 and 44, $12,932 for someone between the ages
of 45 and 54, and $74,746 for someone between the ages of 55 and 65. The corresponding
age-specific estimates of lost earnings using a seven percent discount rate are $7,855,
$11,578, and $66,920, respectively. Cropper and Krupnick do not provide lost earnings
estimates for populations under 25 or over 65. As such we do not include lost earnings in
the cost estimates for these age groups.
We have found three possible sources of estimates of the direct medical costs of a
myocardial infarction (MI) in the literature:
 Wittels et al. (1990) estimated expected total medical costs of MI over 5 years to be
$51,211 (in 1986$) for people who were admitted to the hospital and survived
hospitalization. (There does not appear to be any discounting used.) Wittels et al. was
used to value coronary heart disease in the 812 Retrospective Analysis of the Clean Air
Act. Using the CPI-U for medical care, the Wittels estimate is $109,474 in year 2000$.
This estimated cost is based on a medical cost model, which incorporated therapeutic
options, projected outcomes and prices (using “knowledgeable cardiologists” as
consultants). The model used medical data and medical decision algorithms to estimate
the probabilities of certain events and/or medical procedures being used. The authors
note that the average length of hospitalization for acute MI has decreased over time
(from an average of 12.9 days in 1980 to an average of 11 days in 1983). Wittels et al.
used 10 days as the average in their study. It is unclear how much further the length of
stay (LOS) for MI may have decreased from 1983 to the present. The average LOS for
ICD code 410 (MI) in the year-2000 AHQR HCUP database is 5.5 days. However, this

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may include patients who died in the hospital (not included among our non-fatal MI
cases), whose LOS was therefore substantially shorter than it would be if they hadn’t
died.
 Eisenstein et al. (2001) estimated 10-year costs of $44,663, in 1997$ (using a three
percent discount rate), or $49,651 in 2000$ for MI patients, using statistical prediction
(regression) models to estimate inpatient costs. Only inpatient costs (physician fees and
hospital costs) were included.
 Russell et al. (1998) estimated first-year direct medical costs of treating nonfatal MI of
$15,540 (in 1995$), and $1,051 annually thereafter. Converting to year 2000$, that
would be $18,880 for a 5-year period, using a three percent discount rate, or $17,850,
using a seven percent discount rate.
The age group-specific estimates of opportunity cost over a five-year period are combined
with the medical cost estimates from each of the three studies listed above. Because
opportunity costs are derived for each of five age groups, there are 3 x 5 = 15 unit values
for each of 2 discount rates, or 30 unit values available for use in BenMAP. These are
given in Table H-5 below.
Note that we were unable to achieve complete consistency, unfortunately, because of
limitations in the input studies. For example, although we calculated opportunity costs
over a five-year period using a 3 percent and a 7 percent discount rate, we were not able to
do the same for medical costs, except for the medical costs estimated by Russell et al. (in
which they estimate an annual cost). Wittels et al. appear to have used no discounting in
their estimate; Eisenstein et al. used a 3 percent discount rate. Similarly, although almost
all cost estimates (opportunity costs and medical costs) are for a 5-year period, the medical
cost estimate reported by Eisenstein et al. is for a 10-year period. There was no reasonable
method for inferring from that study what costs over a 5-year period would be.

Table H-5. Unit Values Available for Myocardial Infarction

Age Range Opportunity Cost
Basis of Estimate Medical Cost * Total Cost
Min Max **

COI: 5 yrs med, 5 yrs wages, 3% 0 24 $109,474 $0 $109,474

DR, Wittels (1990)
25 44 $109,474 $9,033 $118,507
45 54 $109,474 $13,313 $122,787
55 65 $109,474 $76,951 $186,425
66 99 $109,474 $0 $109,474
COI: 10 yrs med, 5 yrs wages, 3% 0 24 $49,651 $0 $49,651
DR, Eisenstein (2001)
25 44 $49,651 $9,033 $58,683
45 54 $49,651 $13,313 $62,964
55 65 $49,651 $76,951 $126,602
66 99 $49,651 $0 $49,651

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COI: 5 yrs med, 5 yrs wages, 3% 0 24 $22,331 $0 $22,331

DR, Russell (1998)
25 44 $22,331 $9,033 $31,363
45 54 $22,331 $13,313 $35,644

55 65 $22,331 $76,951 $99,281

66 99 $22,331 $0 $22,331
COI: 5 yrs med, 5 yrs wages, 7% 0 24 $109,474 $0 $109,474
DR, Wittels (1990)
25 44 $109,474 $8,087 $117,561
45 54 $109,474 $11,919 $121,393
55 65 $109,474 $68,894 $178,368
66 99 $109,474 $0 $109,474
COI: 10 yrs med, 5 yrs wages, 7% 0 24 $49,651 $0 $49,651
DR, Eisenstein (2001)
25 44 $49,651 $8,087 $57,738
45 54 $49,651 $11,919 $61,570
55 65 $49,651 $68,894 $118,545
66 99 $49,651 $0 $49,651
COI: 5 yrs med, 5 yrs wages, 7% 0 24 $21,113 $0 $21,113
DR, Russell (1998)
25 44 $21,113 $8,087 $29,200
45 54 $21,113 $11,919 $33,032
55 65 $21,113 $68,894 $90,007
66 99 $21,113 $0 $21,113

* From Cropper and Krupnick (1990). Present discounted value of 5 yrs

of lost earnings, at 3% and 7% discount rate, adjusted from 1977$ to
2000$ using CPI-U “all items”.
** An average of the 5-year costs estimated by Wittels et al. (1990) and
Russell et al. (1998). Note that Wittels et al. appears not to have used
discounting in deriving a 5-year cost of $109,474; Russell et al.
estimated first-year direct medical costs and annual costs thereafter. The
resulting 5-year cost is $22,331, using a 3% discount rate, and $21,113,
using a 7% discount rate. Medical costs were inflated to 2000$ using
CPI-U for medical care.

H.3 Hospital Admissions & Emergency Room Visits

This section presents the values for avoided hospital admissions, as well as avoided
emergency room visits. We assume that hospital admissions due to acute exposure to air
pollution pass through the emergency room. However, the value of hospital admissions
that we have calculated here does not account for the cost incurred in the emergency room
visit.

H.3.1 Hospital Admissions

As suggested above, the total value to society of an individual’s avoidance of a hospital
admission can be thought of as having two components: (1) the cost of illness (COI) to
society, including the total medical costs plus the value of the lost productivity, as well as

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(2) the WTP of the individual, as well as that of others, to avoid the pain and suffering
resulting from the illness.
In the absence of estimates of social WTP to avoid hospital admissions for specific
illnesses (components 1 plus 2 above), estimates of total COI (component 1) are available
for use in BenMAP as conservative (lower bound) estimates. Because these estimates do
not include the value of avoiding the pain and suffering resulting from the illness
(component 2), they are biased downward. Some analyses adjust COI estimates upward by
multiplying by an estimate of the ratio of WTP to COI, to better approximate total WTP.
Other analyses have avoided making this adjustment because of the possibility of
over-adjusting -- that is, possibly replacing a known downward bias with an upward bias.
Based on Science Advisory Board (SAB) advice, the COI values currently available for use
in BenMAP are not adjusted.
Unit values are based on ICD-code-specific estimated hospital charges and opportunity
cost of time spent in the hospital (based on the average length of a hospital stay for the
illness). The opportunity cost of a day spent in the hospital is estimated as the value of the
lost daily wage, regardless of whether or not the individual is in the workforce.
For all hospital admissions endpoints available in BenMAP, estimates of hospital charges
and lengths of hospital stays were based on discharge statistics provided by the Agency for
Healthcare Research and Quality’s Healthcare Utilization Project (2000). The total COI
for an ICD-code-specific hospital stay lasting n days is estimated as the mean hospital
charge plus n times the daily lost wage. Year 2000 county-specific median annual wages
divided by (52*5) were used to estimate county-specific median daily wages. (The source
for median is Geolytics, 2001.) Because wage data used in BenMAP are county-specific,
the unit value for a hospital admission varies from one county to another.
Most hospital admissions categories considered in epidemiological studies consisted of
sets of ICD codes. The unit value for the set of ICD codes was estimated as the weighted
average of the ICD-code-specific COI estimates. The weights were the relative
frequencies of the ICD codes among hospital discharges in the United States, as estimated
by the National Hospital Discharge Survey (Owings and Lawrence, 1999, Table 1). The
hospital admissions for which unit values are available in BenMAP are given in Table H-6.
Although unit values available for use in BenMAP are county-specific, the national median
daily wage was used to calculate opportunity costs and total costs for the table below, to
give a general idea of the cost of illness estimates for the different hospital admissions
endpoints.
The mean hospital charges and mean lengths of stay provided by (AHRQ 2000) are based
on a very large nationally representative sample of about seven million hospital discharges,
and are therefore the best estimates of mean hospital charges and mean lengths of stay
available, with negligible standard errors.

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Table H-6. Unit Values Available for Hospital Admissions

EndPoint ICD Codes Age Range Mean Mean Total Cost of
Hospital Length of Illness (Unit
min. max. Charge * Stay (days) * Value) **

HA, All Cardiovascular 390-429 65 99 $20,607 5.07 $21,191

HA, All Cardiovascular 390-429 0 99 $20,873 4.71 $21,415

HA, All Cardiovascular 390-429 20 64 $22,300 4.15 $22,778

HA, Congestive Heart Failure 428 65 99 $14,573 5.60 $15,218

HA, Dysrhythmia 427 0 99 $14,811 3.70 $15,237

HA, Ischemic Heart Disease 410-414 65 99 $25,322 4.81 $25,876

HA, All Respiratory 460-519 65 99 $17,600 6.88 $18,393

HA, All Respiratory 460-519 0 99 $14,999 5.63 $15,647

HA, All Respiratory 460-519 0 2 $7,416 2.97 $7,759

HA, Asthma 493 0 64 $7,448 2.95 $7,788

HA, Asthma 493 65 99 $11,417 4.99 $11,991

HA, Asthma 493 0 99 $8,098 3.30 $8,478

HA, Chronic Lung Disease 490-496 65 99 $12,781 5.59 $13,425

HA, Chronic Lung Disease 490-496 0 99 $10,882 4.59 $11,412

HA, Chronic Lung Disease 490-496 20 64 $10,194 4.04 $10,660

HA, Chronic Lung Disease (less 490-492, 494-496 65 99 $12,993 5.69 $13,648
Asthma)

HA, Chronic Lung Disease (less 490-492, 494-496 0 99 $12,742 5.45 $13,370
Asthma)

HA, Chronic Lung Disease (less 490-492, 494-496 20 64 $11,820 4.48 $11,820
Asthma)

HA, Pneumonia 480-487 65 99 $17,030 7.07 $17,844

HA, Pneumonia 480-487 0 99 $14,693 5.92 $15,375

* Source of hospital charges and lengths of stay: Agency for Healthcare

Research and Quality. 2000. HCUPnet, Healthcare Cost and Utilization
Project. http://www.agrq.gov/data/hcup/hcupnet.htm .
** The opportunity cost of a day spent in the hospital was estimated, for
this exhibit, at the median daily wage of all workers, $115.20, regardless
of age. The median daily wage was calculated by dividing the median
weekly wage ($576 in 2000$) by 5. The median weekly wage was
obtained from U.S. Census Bureau, Statistical Abstract of the United
States: 2001, Section 12, Table 621: “Full-Time Wage and Salary
Workers – Numbers and Earnings: 1985 to 2000.” Actual unit values
used in BenMAP are based on county-specific wages, and are therefore
county-specific.

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H.3.2 Emergency Room Visits for Asthma

Two unit values are currently available for use in BenMAP for asthma emergency room
(ER) visits. One is $311.55, from Smith et al., 1997, who reported that there were
approximately 1.2 million asthma-related ER visits made in 1987, at a total cost of $186.5
million, in 1987$. The average cost per visit was therefore $155 in 1987$, or $311.55 in
2000 $ (using the CPI-U for medical care to adjust to 2000$). The uncertainty surrounding
this estimate, based on the uncertainty surrounding the number of ER visits and the total
cost of all visits reported by Smith et al. is characterized by a triangular distribution
centered at $311.55, on the interval [$230.67, $430.93].
A second unit value is $260.67 from Stanford et al. (1999). This study considered
asthmatics in 1996-1997, in comparison to the Smith et al. (1997) study, which used 1987
National Medical Expenditure Survey (NMES) data). In comparing their study, the
authors note that the 1987 NMES, used by Smith et al., “may not reflect changes in
treatment patterns during the 1990s.” In addition, its costs are the costs to the hospital (or
ER) for treating asthma rather than charges or payments by the patient and/or third party
payer. Costs to the ER are probably a better measure of the value of the medical resources
used up on an asthma ER visit (see above for a discussion of costs versus charges).
The unit values and the corresponding distributions available in BenMAP for
asthma-related ER visits are summarized in Table H-7.

Table H-7. Unit Values Available for Asthma-Related ER Visits

Basis for Estimate Age Range Unit Value Distribution of Unit Parameters of Distribution
Value
min. max. P1 P2

COI: Smith et al. (1997) 0 99 $312 triangular $231 $431

COI: Standford et al. (1999) 0 99 $261 normal 5.22 –

H.4 Acute Symptoms and Illness Not Requiring Hospitalization

Several acute symptoms and illnesses have been associated with air pollution, including
acute bronchitis in children, upper and lower respiratory symptoms, and exacerbation of
asthma (as indicated by one of several symptoms whose occurrence in an asthmatic
generally suggests the onset of an asthma episode). In addition, several more general
health endpoints which are associated with one or more of these acute symptoms and
illnesses, such as minor restricted activity days, school loss days, and work loss days, have
also been associated with air pollution. We briefly discuss the derivation of the unit values
for each of these acute symptoms and illnesses. Tables H-8 and H-9 summarize the values.

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Table H-8. Unit Values Available for Acute Symptoms and Illnesses
Parameters of
Age Range
Health Unit Distribution Distribution
Basis for Estimate *
Endpoint Value of Unit Value
min. max. P1 P2

Acute Bronchitis WTP: 1 day illness, CV studies 0 17 $59 uniform 17.51 101.11

WTP: 6 day illness, CV studies 0 17 $356 uniform 105.06 606.64

WTP: 28 symptom-days, Dickie 0 17 $374 lognormal 5.947 0.0907

and Ulery

Any of 19 WTP: 1 day illness, CV studies 18 65 $24 uniform 0 48.25

Respiratory
Symptoms

Minor Restricted WTP: 1 day, CV studies 18 99 $51 triangular 20.71 80.37

Activity Days
WTP: 3 symptoms 1 day, Dickie 18 99 $98 lognormal 4.6088 0.0649
and Ulery (2002).

Lower WTP: 1 day, CV studies 0 17 $16 uniform 6.94 24.47

Respiratory
Symptoms WTP: 2 symptoms 1 day, Dickie 0 17 $187 lognormal 5.2556 0.07048
and Ulery (2002).

WTP: 2 x 1 day, CV studies 0 17 $31 uniform 13.89 48.93

School Loss Described in text. 0 17 $75 none N/A N/A

Days

Upper WTP: 1 day, CV studies 0 17 $25 uniform 9.22 43.11

Respiratory
Symptoms WTP: 2 symptoms 1 day, Dickie 0 17 $187 lognormal 5.2556 0.07048
and Ulery (2002)

WTP: 2 x 1 day, CV studies 0 17 $49 uniform 18.45 86.22

Work Loss Days Median daily wage, 18 65 $115 none N/A N/A
** county-specific

* All unit values pulled from a lognormal distribution from Model 1,

Table III in Dickie and Ulery are multiplied by 0.973811 to adjust for a
difference in mean household income between the study participants and
the general population. The unit values shown here have already been
adjusted.

** Unit values for work loss days are county-specific, based on

county-specific median wages. The unit value shown here is the national
median daily wage, given for illustrative purposes only.

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Table H-9. Unit Values Available for Asthma-related Acute Symptoms and Illnesses
Age Parameters of
Health Range Unit Unit Value Distribution
Basis for WTP Estimate*
Endpoint Value Distribution
min. max. P1 P2

Asthma Bad asthma day, Rowe and Chestnut 18 99 $43 uniform 15.56 70.88
Attacks; (1986)
Cough;
Moderate or 1 symptom-day, Dickie and Ulery (2002) 18 99 $74 lognormal 4.321 0.0957
Worse; One
or more
Bbad asthma day, Rowe and Chestnut 0 17 $43 uniform 15.56 70.88
symptoms;
(1986)
Shortness of
Breath;
Wheeze 2 x bad asthma day, Rowe and Chestnut 0 17 $86 uniform 31.12 141.77
(1986)

1 symptom-day, Dickie and Ulery (2002) 0 17 $156 lognormal 5.074 0.0925

*All unit values pulled from a lognormal distribution from Model 1,

Table III in Dickie and Ulery, 2002, are multiplied by 0.973811 to
adjust for a difference in mean household income between the study
participants and the general population. The unit values shown here
have already been adjusted.

H.4.1 Acute Bronchitis in Children

Estimating WTP to avoid a case of acute bronchitis is difficult for several reasons. First,
WTP to avoid acute bronchitis itself has not been estimated. Estimation of WTP to avoid
this health endpoint therefore must be based on estimates of WTP to avoid symptoms that
occur with this illness. Second, a case of acute bronchitis may last more than one day,
whereas it is a day of avoided symptoms that is typically valued. Finally, the C-R function
used in the benefit analysis for acute bronchitis was estimated for children, whereas WTP
estimates for those symptoms associated with acute bronchitis were obtained from adults.
Three unit values are available in BenMAP for acute bronchitis in children. In previous
benefit analyses, EPA used a unit value of $59.31. This is the midpoint between a low
estimate and a high estimate. The low estimate is the sum of the midrange values
recommended by IEc (1994) for two symptoms believed to be associated with acute
bronchitis: coughing and chest tightness. The high estimate was taken to be twice the
value of a minor respiratory restricted activity day. For a more complete description of the
derivation of this estimate, see Abt Associates (2000, p. 4-30).
The above unit value assumes that an episode of acute bronchitis lasts only one day.
However, this is generally not the case. More typically, it can last for 6 or 7 days. A
simple adjustment, then, would be to multiply the original unit value of $59.31 by 6 or 7.
A second unit value of $356 (=$59.31 x 6) was therefore derived.
Finally, as noted above, the epidemiological study relating air pollution to the incidence of
acute bronchitis referred to children specifically. The value of an avoided case should

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therefore be WTP to avoid a case in a child, which may be different from WTP to avoid a
case in an adult. Recent work by Dickie and Ulery (2002) suggests, in fact, that parents are
generally willing to pay about twice as much to avoid sickness in their children as in
themselves. In one of several models they estimated, the natural logarithm of parents’
WTP was related both to the number of symptom-days avoided and to whether it was their
child or themselves at issue. Dickie and Ulery noted that “experiencing all of the
symptoms [considered in their study – cough and phlegm, shortness of breath/wheezing,
chest pain, and fever] for 7 days, or 28 symptom-days altogether, is roughly equivalent to a
case of acute bronchitis ...” Using this model, and assuming that a case of acute bronchitis
can be reasonably modeled as consisting of 28 symptom-days, we estimated parents’ WTP
to avoid a case of acute bronchitis in a child to be $374. This is the third unit value
available in BenMAP.
The mean household income among participants in the Dickie and Ulery CV survey was
slightly higher than the national average. We therefore adjusted all WTP estimates that
resulted from their models downward slightly, using an income elasticity of WTP of 0.147,
the average of the income elasticities estimated in the four models in the study. The
adjustment factor thus derived was 0.9738.

H.4.2 Upper Respiratory Symptoms (URS) in Children

In past benefit analyses, EPA based willingness to pay to avoid a day of URS on
symptom-specific WTPs to avoid those symptoms identified as part of the URS complex
of symptoms. Pope et al. (1991) defined a day of URS as consisting of one or more of the
following symptoms: runny or stuffy nose; wet cough; and burning, aching, or red eyes.
The three contingent valuation (CV) studies shown in Table H-10 have estimated WTP to
avoid various morbidity symptoms that are either within the URS symptom complex
defined by Pope et al., or are similar to those symptoms.

Table H-10. Median WTP Estimates and Derived Midrange Estimates (in 1999 $)

Symptom * Dickie et al. Tolley et al. (1986) Loehman et al. Mid-Range

(1979) Estimate

Throat congestion 4.81 20.84 - 12.75

Head/sinus congestion 5.61 22.45 10.45 12.75

Coughing 1.61 17.65 6.35 8.93

Eye irritation - 20.03 - 20.03

Headache 1.61 32.07 - 12.75

Shortness of breath 0.00 - 13.47 6.37

Pain upon deep inhalation (PDI) 5.63 - - 5.63

Wheeze 3.21 - - 3.21

Coughing up phlegm 3.51 ** - - 3.51

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Symptom * Dickie et al. Tolley et al. (1986) Loehman et al. Mid-Range

(1979) Estimate

Chest tightness 8.03 - - 8.03

* All estimates are WTP to avoid one day of symptom. Midrange

estimates were derived by IEc (1993).
** 10% trimmed mean.

The three individual symptoms that were identified as most closely matching those listed
by Pope et al. for URS are cough, head/sinus congestion, and eye irritation, corresponding
to “wet cough,” “runny or stuffy nose,” and “burning, aching or red eyes,” respectively. A
day of URS could consist of any one of the seven possible “symptom complexes”
consisting of at least one of these three symptoms. The original unit value for URS was
based on the assumption that each of these seven URS complexes is equally likely. This
unit value for URS, $24.64, is just an average of the seven estimates of mean WTP for the
different URS complexes.
The WTP estimates on which the first unit value is based were elicited from adults,
whereas the health endpoint associated with air pollution in the epidemiological study is in
children. As noted above, recent research by Dickie and Ulery (2002) suggests that
parental WTP to avoid symptoms and illnesses in their children is about twice what it is to
avoid those symptoms and illnesses in themselves. We therefore derived a second unit
value of $49.28 (=2 x $24.64) from the first unit value.
A third unit value was derived by using Model 1, Table III in Dickie and Ulery (2002) (the
same model used for acute bronchitis), assuming that a day of URS consists of 2
symptoms. As noted above, this model relates parental WTP to the number of
symptom-days avoided and to whether it is the parent or the child at issue. The unit value
derived from this model is $187.
A WTP estimate elicited from parents concerning their WTP to avoid symptoms in their
children may well include some calculation of lost earnings resulting from having to lose a
day of work. Estimates from the Dickie and Ulery model therefore (appropriately)
probably include not only their WTP to have their children avoid the pain and suffering
associated with their illness, but also the opportunity cost of a parent having to stay home
with a sick child.

H.4.3 Lower Respiratory Symptoms (LRS) in Children

The three unit values for LRS in children currently available in BenMAP follow the same
pattern as those for URS in children. In past benefit analyses, EPA based willingness to
pay to avoid a day of LRS on symptom-specific WTPs to avoid those symptoms identified
as part of the LRS complex of symptoms. Schwartz et al. (1994) defined a day of LRS as
consisting of at least two of the following symptoms: cough, chest tightness, coughing up
phlegm, and wheeze. Of the symptoms for which WTP estimates are available (listed in
Table H-10), those that most closely match the symptoms listed by Schwartz et al. are

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coughing, chest tightness, coughing up phlegm, and wheeze. A day of LRS, as defined by
Schwartz et al., could consist of any one of 11 possible combinations of at least two of
these four symptoms. In the absence of any further information, each of the 11 possible
“symptom clusters” was considered equally likely. The original unit value for LRS,
$15.57, is just an average of the eleven estimates of mean WTP for the different LRS
symptom clusters.
A second unit value is twice the original unit value, or $31.15, based on the evidence from
Dickie and Ulery (2002) that parents are willing to pay about twice as much to avoid
symptoms and illness in their children as in themselves. The third unit value is based on
Model 1, Table III in Dickie and Ulery, assuming that, as for URS, a day of LRS consists
of 2 symptoms. As noted above, this model relates parental WTP to the number of
symptom-days avoided and to whether it is the parent or the child at issue. The unit value
derived from this model is $187.

H.4.4 Any of 19 Respiratory Symptoms

The presence of “any of 19 acute respiratory symptoms” is a somewhat subjective health
effect used by Krupnick et al. (1990). Moreover, not all 19 symptoms are listed in the
Krupnick et al. study. It is therefore not clear exactly what symptoms were included in the
study. Even if all 19 symptoms were known, it is unlikely that WTP estimates could be
obtained for all of the symptoms. Finally, even if all 19 symptoms were known and WTP
estimates could be obtained for all 19 symptoms, the assumption of additivity of WTPs
becomes tenuous with such a large number of symptoms. The likelihood that all 19
symptoms would occur simultaneously, moreover, is very small.
Acute respiratory symptoms must be either upper respiratory symptoms or lower
respiratory symptoms. In the absence of further knowledge about which of the two types
of symptoms is more likely to occur among the “any of 19 acute respiratory symptoms,”
we assumed that they occur with equal probability. Because this health endpoint may also
consist of combinations of symptoms, it was also assumed that there is some (smaller)
probability that upper and lower respiratory symptoms occur together. To value avoidance
of a day of “the presence of any of 19 acute respiratory symptoms” we therefore assumed
that this health endpoint consists either of URS, or LRS, or both. We also assumed that it
is as likely to be URS as LRS and that it is half as likely to be both together. That is, it was
assumed that “the presence of any of 19 acute respiratory symptoms” is a day of URS with
40 percent probability, a day of LRS with 40 percent probability, and a day of both URS
and LRS with 20 percent probability. Using the point estimates of WTP to avoid a day of
URS and LRS derived above, the point estimate of WTP to avoid a day of “the presence of
any of 19 acute respiratory symptoms” is:
(0.40)($24.64) + (0.40)($15.57) + (0.20)($24.64 + $15.57) = $24.12.

Because this health endpoint is only vaguely defined, and because of the lack of
information on the relative frequencies of the different combinations of acute respiratory
symptoms that might qualify as “any of 19 acute respiratory symptoms,” the unit dollar
value derived for this health endpoint must be considered only a rough approximation.

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H.4.5 Work Loss Days (WLDs)

Work loss days are valued at a day’s wage. BenMAP calculates county-specific median
daily wages from county-specific annual wages by dividing by (52*5), on the theory that a
worker’s vacation days are valued at the same daily rate as work days.

H.4.6 Minor Restricted Activity Days (MRADs)

Two unit values are currently available in BenMAP for MRADs. No studies are reported
to have estimated WTP to avoid a minor restricted activity day (MRAD). However, IEc
(1993) derived an estimate of WTP to avoid a minor respiratory restricted activity day
(MRRAD), using WTP estimates from Tolley et al. (1986) for avoiding a three-symptom
combination of coughing, throat congestion, and sinusitis. This estimate of WTP to avoid
a MRRAD, so defined, is $38.37 (1990 $). Although Ostro and Rothschild (1989)
estimated the relationship between PM2.5 and MRADs, rather than MRRADs (a
component of MRADs), it is likely that most of the MRADs associated with exposure to
PM2.5 are in fact MRRADs. The original unit value, then, assumes that MRADs associated
with PM exposure may be more specifically defined as MRRADs, and uses the estimate of
mean WTP to avoid a MRRAD.
Any estimate of mean WTP to avoid a MRRAD (or any other type of restricted activity day
other than WLD) will be somewhat arbitrary because the endpoint itself is not precisely
defined. Many different combinations of symptoms could presumably result in some
minor or less minor restriction in activity. Krupnick and Kopp (1988) argued that mild
symptoms will not be sufficient to result in a MRRAD, so that WTP to avoid a MRRAD
should exceed WTP to avoid any single mild symptom. A single severe symptom or a
combination of symptoms could, however, be sufficient to restrict activity. Therefore
WTP to avoid a MRRAD should, these authors argue, not necessarily exceed WTP to
avoid a single severe symptom or a combination of symptoms. The “severity” of a
symptom, however, is similarly not precisely defined; moreover, one level of severity of a
symptom could induce restriction of activity for one individual while not doing so for
another. The same is true for any particular combination of symptoms.
Given that there is inherently a substantial degree of arbitrariness in any point estimate of
WTP to avoid a MRRAD (or other kinds of restricted activity days), the reasonable bounds
on such an estimate must be considered. By definition, a MRRAD does not result in loss
of work. WTP to avoid a MRRAD should therefore be less than WTP to avoid a WLD.
At the other extreme, WTP to avoid a MRRAD should exceed WTP to avoid a single mild
symptom. The highest IEc midrange estimate of WTP to avoid a single symptom is $20.03
(1999 $), for eye irritation. The point estimate of WTP to avoid a WLD in the benefit
analysis is $83 (1990 $). If all the single symptoms evaluated by the studies are not severe,
then the estimate of WTP to avoid a MRRAD should be somewhere between $16 and $83.
Because the IEc estimate of $38 falls within this range (and acknowledging the degree of
arbitrariness associated with any estimate within this range), the IEc estimate is used as the
mean of a triangular distribution centered at $38, ranging from $16 to $61. Adjusting to

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2000 $, this is a triangular distribution centered at $50.55, ranging from $21 to $80.
A second unit value is based on Model 1, Table III in Dickie and Ulery (2002). This
model estimates the natural logarithm of parents’ WTP to avoid symptoms as a linear
function of the natural logarithm of the number of symptom-days avoided and whether or
not the person avoiding the symptoms is the parent or the child. The unit value derived
from this model, assuming that an MRAD consists of one day of 3 symptoms in an adult, is
$98.

H.4.7 Asthma Exacerbation

Several respiratory symptoms in asthmatics or characterizations of an asthma episode have
been associated with exposure to air pollutants. All of these can generally be taken as
indications of an asthma exacerbation (“asthma attack”) when they occur in an asthmatic.
BenMAP therefore uses the same set of unit values for all of the variations of “asthma
exacerbation” that appear in the epidemiological literature.
Two unit values are currently available in BenMAP for asthma exacerbation in adults, and
three are currently available for asthma exacerbation in children. In past benefit analyses,
EPA based willingness to pay to avoid an asthma exacerbation on four WTP estimates
from Rowe and Chestnut (1986) for avoiding a “bad asthma day.” The mean of the four
average WTPs is $32 (1990 $), or $43 in 2000$. The uncertainty surrounding this estimate
was characterized by a continuous uniform distribution on the range defined by the lowest
and highest of the four average WTP estimates from Rowe and Chestnut, [$12, $54] in
1990$, or [$16, $71] in 2000 $. This unit value is available for both adults and children.
A second unit value for adults was derived by using Model 1, Table III in Dickie and Ulery
(2002) -- the same model used for acute bronchitis, LRS, and URS -- assuming that an
asthma exacerbation consists of 1 symptom-day. As noted above, this model relates
parental WTP to the number of symptom-days avoided and to whether it is the parent or
the child at issue. The unit value derived from this model for adults is $74.
Two additional unit values are available for children. One of these is twice the original unit
value, or $86, based on the evidence from Dickie and Ulery (2002) that parents are willing
to pay about twice as much to avoid symptoms and illness in their children as in
themselves. The third unit value is based on Model 1, Table III in Dickie and Ulery (the
same model used for asthma exacerbation in adults, only now with the “adult or child”
variable set to 1 rather than 0). The unit value derived from this model is $156.

H.4.8 School Loss Days

There is currently one unit value available in BenMAP for school loss days, based on (1)
the probability that, if a school child stays home from school, a parent will have to stay
home from work to care for the child, and (2) the value of the parent’s lost productivity.
We first estimated the proportion of families with school-age children in which both
parents work, and then valued a school loss day as the probability of a work loss day
resulting from a school loss day (i.e., the proportion of households with school-age

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children in which both parents work) times a measure of lost wages.

From the U.S. Bureau of the Census (2002) we obtained (1) the numbers of single,
married, and “other” (i.e., widowed, divorced, or separated) women with children in the
workforce, and (2) the rates of participation in the workforce of single, married, and
“other” women with children. From these two sets of statistics, we calculated a weighted
average participation rate of 72.85 percent, as shown in Table H-11.
Our estimated daily lost wage (if a mother must stay at home with a sick child) is based on
the median weekly wage among women age 25 and older in 2000 . This median weekly
wage is $551. Dividing by 5 gives an estimated median daily wage of $103. The expected
loss in wages due to a day of school absence in which the mother would have to stay home
with her child is estimated as the probability that the mother is in the workforce times the
daily wage she would lose if she missed a day = 72.85% of $103, or $75. We currently
have insufficient information to characterize the uncertainty surrounding this estimate.

Table H-11. Women with Children: Number and Percent in the Labor Force, 2000,
and Weighted Average Participation Rate
Implied Total
Women in Labor Participation Population-Weigh
Number in Implied Percent in
Force Rate ted Average
Population (in Population
(millions) * (%) * Participation Rate
Category millions)
[=sum (2)*(4) over
(1) (2) (3) = (1)/(2) (4)
rows]
Single 3.1 73.9% 4.19 11.84% --
Married 18.2 70.6% 25.78 72.79% --
Other ** 4.5 82.7% 5.44 15.36% --
Total -- -- 35.42 -- 72.85%

* Source: U.S. Bureau of the Census (2002).

** Widowed, divorced, or separated.

A unit value based on the approach described above is likely to understate the value of a
school loss day in two ways. First, it omits WTP to avoid the symptoms/illness which
resulted in the school absence. Second, it effectively gives zero value to school absences
which do not result in a work loss day. The unit value of $75 is therefore considered an
“interim” value until such time as alternative means of estimating this unit value become
available.

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Appendix I: Population & Other Data in U.S.

Setup
This section describes the population and monitor data in the United States setup.
 Population Data. This describes how BenMAP forecasts population; the block-level and
county-level data underlying the forecasts; and the PopGrid software application, which
aggregates block-level population data to whatever grid definition might be needed.
 Monitor Data. The default United States setup has ozone, PM2.5, PM10 and lead
monitor data for the years 2000-2007. Data for CO, NO2, and SO2 are available at the
BenMAP website: http://www.epa.gov/air/benmap/.

I.1 Population Data in U.S. Setup

The U.S. setup in BenMAP calculates health impacts for any desired grid definition, so
long as you have a shapefile for that grid definition and population data for that grid
definition. In this description, we use the term “population grid cell” to refer to a cell (e.g.,
county) within a grid definition. The foundation for calculating the population level in the
population grid-cells is 2000 Census block data. A separate application developed by Abt
Associates, called “PopGrid,” described below, combines the Census block data with any
user-specified set of population grid-cells, so long as they are defined by a GIS shape file.
Unfortunately, PopGrid relies on extremely large census files that are too large to include
with BenMAP -- hence the need for the separate application. If you are interested in
PopGrid, please email: benmap@epa.gov.
Within any given population grid-cell, BenMAP has 304 unique race-ethnicity-gender-age
groups: 19 age groups by 2 ethnic groups by gender by 4 racial groups (19*2*2*4=304).
Exhibit B-1 presents the 304 population variables available in BenMAP. As discussed
below, these variables are available for use in developing age estimates in whatever
grouping desired by you.

Exhibit I-1 Demographic Groups and Variables Available in BenMAP

Racial/Ethnic Group Ethnicity Age Gender

White, African American, Hispanic, <1, 1-4, 5-9, 10-14, 15-19, 20-24, 25-29, 30-34, Male,
Asian, American Indian, Non-Hispani 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, Female
Other, Hispanic c 70-74, 75-79, 80-84, 85+

In this section on population data in the U.S. setup, we describe:

 Forecasting Population. This describes how BenMAP forecasts population.

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 Data Needed. This section describes the block-level and county-level data underlying
the forecasts.
 PopGrid. This section reviews the PopGrid software application, which aggregates
block-level population data to whatever grid definition might be needed.

I.1.1 How BenMAP Forecasts Population

In calculating the population in age groups that may include a portion of one of the pre-specified
demographic groups in Exhibit I-1, BenMAP assumes the population is uniformly distributed in
the age group. For example, to calculate the number of children ages 3 through 12, BenMAP
calculates:

1 3
age312   age14  age59   age1014 .
2 5

To estimate population levels for the years after the last Census in 2000, BenMAP scales the 2000
Census-based estimate with the ratio of the county-level forecast for the future year of interest
over the 2000 county-level population level. Woods & Poole (2007) provides the
county-level population forecasts used to calculate the scaling ratios; these data are
discussed in detail below.
In the simplest case, where one is forecasting a single population variable, say, children
ages 4 to 9 in the year 2010, CAMPS calculates:

age4 9 , county, 2010

age4 9 , g , 2010  age4 9 , g , 2000 
age4 9 , county, 2000

where the gth population grid-cell is wholly located within a given county.
In the case, where the gth grid-cell includes “n” counties in its boundary, the situation is
somewhat more complicated. BenMAP first estimates the fraction of individuals in a
given age group (e.g., ages 4 to 9) that reside in the part of each county within the gth
grid-cell. BenMAP calculates this fraction by simply dividing the population all ages of a
given county within the gth grid-cell by the total population in the gth grid-cell:
ageall, g in county c
fraction of age4 9 , g in county c 
ageall, g

Multiplying this fraction with the number of individuals ages 4 to 9 in the year 2000 gives
an estimate of the number of individuals ages 4 to 9 that reside in the fraction of the county
within the gth grid-cell in the year 2000:

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age4 9 , g in countyc , 2000  age4 9 , g , 2000  fraction age4 9 , g in countyc

To then forecast the population in 2010, we scale the 2000 estimate with the ratio of the
county projection for 2010 to the county projection for 2000:

age4 9 , countyc , 2010

age4 9 , g in countyc , 2010  age4 9 , g in countyc , 2000  .
age4 9 , countyc , 2000

Combining all these steps for “n” counties within the gth grid-cell, we forecast the
population of persons ages 4 to 9 in the year 2010 as follows:
n total pop g in county c age4 9 , county c , 2010
age4 9 , g , 2010  age4 9 , g , 2000  
c 1 total pop g age4 9 , county c , 2000

In the case where there are multiple age groups and multiple counties, BenMAP first
calculates the forecasted population level for individual age groups, and then combines the
forecasted age groups. In calculating the number of children ages 4 to 12, BenMAP
calculates:

n total pop g in county c age4 9 , county c , 2010

age4 9 , g , 2010  age4 9 , g , 2000  
c 1 total pop g age4 9 , county c , 2000

n total pop g in county c age1014, county c , 2010

age1014, g , 2010  age1014, g , 2000  
c 1 total pop g age1014, county c , 2000

3
age4 12 , g , 2010  age4 9 , g , 2010   age1014 , g , 2010 .
5

Since the Woods and Poole (2007) projections only extend through 2030, we used the
existing projections and constant growth factors to provide additional projections. To
estimate population levels beyond 2030, CAPMS linearly extrapolates from the final two
years of data. For example, to forecast population in 2035, CAPMS calculates:

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 
age49, 2035  age49, 2030  5 age49, 2030  age49, 2029 .

I.1.2 Data Needed for Forecasting

Underlying the population forecasts in BenMAP there are block-level databases used to
provide year 2000 population estimates and a county-level database of forecast ratios.
Both files have the same set of 304 race-ethnicity-gender-age population groups.
The block-level data is typically not used directly in BenMAP, and instead is used with the
PopGrid software (described below) to provide year 2000 estimates for a grid definition of
interest (e.g., 12 kilometer CMAQ grid). The output from PopGrid with the year 2000
population estimates can then be loaded into BenMAP.
The county-level data comes pre-installed in the U.S. setup, and is not something that the
user needs to load herself. These data are simply county-level ratios of a "future" year
(2000-2030) and year 2000 population data for each county and each of the 304 race-
ethnicity-gender-age population groups.
We describe the development of each databases below.

I.1.2.1 Block-Level Census 2000

There are about five million "blocks" in the United States, and for each block we have 304
race-ethnicity-gender-age groups. The block-level population database is created
separately for each state, in order to make the data more manageable. (A single national
file of block data would be about six gigabytes.)
The initial block file from the U.S. Census Bureau is not in the form needed. The block
data has 7 racial categories and 23 age groups, as opposed to the 4 and 19 used in
BenMAP. Table I-4 summarizes the initial set of variables and the final desired set of
variables.

Table I-4 Race, Ethnicity and Age Variables in 2000 Census Block Data

Type Race Ethnicity Gender Age

Initial White Alone, Black Alone, Native -- Male, 0-4, 5-9, 10-14, 15-17, 18-19, 20,
Variables American Alone, Asian Alone, Pacific Female 21, 22-24, 25-29, 30-34, 35-39,
(SF1 file) Islander / Hawaiian Alone, Other 40-44, 45-49, 50-54, 55-59,
Alone, Two or More Alone 60-61, 62-64, 65-66, 67-69,
70-74, 75-79, 80-84 85+
Final White, African-American, Hispanic, Female, <1, 1-4, 5-9, 10-14, 15-19, 20-24,
Desired Asian-American, Native-American Non-Hispan Male 25-29, 30-34, 35-39, 40-44,
Variables ic 45-49, 50-54, 55-59, 60-64,
65-69, 70-74, 75-79, 80-84, 85+

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The initial set of input files are as follows.

 Census 2000 block-level file (Summary File 1)
Data: ftp.census.gov/census_2000/datasets/Summary_File_1
Docs: http://www.census.gov/prod/cen2000/doc/sf1.pdf

 Census 2000 tract-level file (Summary File 4)

Data: ftp.census.gov/census_2000/datasets/Summary_File_4
Docs: http://www.census.gov/prod/cen2000/doc/sf4.pdf

 Census 2000 MARS national-level summary

Docs: http://www.census.gov/popest/archives/files/MRSF-01-US1.pdf

The SF4 and MARS data, as described below, are needed to reorganize the variables that
come initially in the SF1 file. (For the sake of completeness, we note that there exists a
county-level Census 2000 MARS file, however, due to major population count
discrepancies between the county-level MARS file and block-level SF1 file, we used only
the nation-level summary table. Tables in MARS documentation file did not have the
discrepancies that the county-level file had. We were unable to get an adequate
explanation of this from the US Census.)
The steps in preparing the data are as follows:

1. Adjust Age-classifications:
We combined some age groups in the SF1 data to match the age groups wanted for
BenMAP. For example, we combined age groups 15-17 and 18-19 to create the 15-19 age
group used in BenMAP. Then, in the case of the 0-4 age group, we split it into <1 and 1-4
using the county-level SF4 data, which gave us the fraction of 0-4 year-olds who are <1.

2. Fill in Missing Racial-Ethnic Interactions:

We used the county-level SF4 data to calculate the fraction of Hispanics in each
ethnically-aggregated subpopulation from the block-level data, by age and sex. We used
these fractions to distribute each age-sex-race-block-level datum into Hispanics and
non-Hispanics.
This process tended to underestimate the number of Hispanics. Therefore, we made a
correction. We calculated the ratio of total Hispanics in a state to the estimated Hispanics
in a state. In each age-sex-race-block-level datum, if the resulting total of Hispanics is not
greater than the total number of people in the datum, we increased the number of people
according to this ratio.

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3. Assign "Other" and "Multi-Racial" to the Remaining Four Racial Categories:

We assign the “Other" race category in two steps. First, based on the national MARS data,
we estimated how many people in the “multi-racial” category checked off “some other
race” as one of their races, for Hispanics and non-Hispanics separately. In each
age-sex-race-block-level datum, we added those people to “other race” category to create
the re-distribution pool, analogously to the method implemented by Census while creating
MARS data (see U.S. Census Bureau, 2002a, Table 1, below). Second, based on the
national re-allocation fractions for Hispanics and non-Hispanics (derived from the MARS
data), we assigned the “Other” race into the four races of interest and “multi-race”.
After the assignment of the "Other" race category, we then assigned “multi-racial” category
to the four racial categories categories, using state fractions of these races in each
age-sex-race-block-level datum.

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I.1.2.2 County-Level Forecasts

Woods & Poole (2006) developed county-level forecasts for each year from 2000 through
2030, by age and gender for non-Hispanic White, African-American, Asian-American, and
Native-American and for all Hispanics. As discussed below, the adjustments necessary to
prepare the data for use in BenMAP are relatively straightforward. The starting data is the
following:

 Woods & Poole county-level files

Data: L:\project data\Benmap\Database Development\Population\Woods and Poole
from 2007-2008\Data\
Docs: http://www.woodsandpoole.com/pdfs/CED07.pdf

For each non-Hispanic subset of the population and each year from 2000-2030, we divided
the Woods and Poole population for that year by the Woods and Poole population for that
subset in 2000. These serve as the growth coefficients for the non-Hispanic subsets of each
race. We used a similar calculation to determine the growth rates for the Hispanic
population. We assume that each Hispanic race grows at the same rate, and use these
growth rates for the Hispanic subsets of each race.

Matching Age Groups Used in BenMAP

There are 86 age groups, so it is a simple matter of aggregating age groups to match the 19
used in BenMAP.

Matching Counties Used in U.S. Census

The county geographic boundaries used by Woods & Poole are somewhat more aggregated
than the county definitions used in the 2000 Census (and BenMAP), and the FIPS codes
used by Woods and Poole are not always the standard codes used in the Census. To make
the Woods and Poole data consistent with the county definitions in BenMAP, we
disaggregated the Woods and Poole data and changed some of the FIPS codes to match the
U.S. Census.

Calculating Growth Ratios with Zero Population in 2000

There are a small number of cases were the 2000 county population for a specific
demographic group is zero, so the ratio of any future year to the year 2000 data is
undefined. In these relatively rare cases, we set the year 2000 ratio and all subsequent
ratios to 1, assuming no growth.

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I.1.3 PopGrid
If the geographic center of a Census block falls within a population grid-cell, PopGrid
assigns the block population to this particular population grid-cell. Note that the grid-cells
in an air quality model, such as CMAQ, may cross multiple county boundaries. PopGrid
keeps track of the total number of people in each race-ethnic group by county within a
particular population grid-cell. Of course, when the population grid-cell is for U.S.
counties, then there is only a single county associated with the population grid-cell.
However, with air quality models, there can clearly be multiple counties in a population
grid-cell.
Keeping track of the total number of people in a county is necessary when forecasting
population, as the population forecast for a given grid cell is equal to the year 2000
population estimate from the Census Bureau multiplied by the ratio of future-year to year
2000 county population estimates from Woods & Poole. BenMAP assumes that all
age-gender groups within a given race-ethnic group have the same geographic distribution.

I.1.3.1 How to Use PopGrid

After installing PopGrid, double-click on the PopGrid executable "PopGrid4.exe." The
following screen will appear:

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The Census Data Files Directory box points PopGrid to where the block data are located
that PopGrid uses. Make sure that the files in this directory are unzipped. This data folder
should look something like the following:

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The Result Population File box provides the path and the name of the file that you want
to create. In the example above, PopGrid is being used to estimate population for the
intersection of air basins and counties in California (CA_AirBasin_by_County).
Click on the Step 2: Shape File tab. Choose the shapefile that you want to use. The
example for air basins and counties in California looks as follows:

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After choosing your shapefile, go to the Step 3: Run tab, which should look as follows:

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Click Run. PopGrid will now begin processing. It can take a very long time to run. When
PopGrid has finished running, check the log file. The log file notes the start time, the files
that PopGrid used, and the end time. Also, at the very end of the log file, PopGrid notes
the number of people that PopGrid assigned to your grid definition ("Population covered
by grid") and the number of people that PopGrid determined are outside of your grid
definition ("Population outside grid").

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I.1.3.2 PopGrid Output

PopGrid generates two files. One file has the number of people in each grid cell for each
of the 304 race-ethnicity-gender-age demographic groups available in PopGrid. Table I-1
presents an example of what the population file looks like from PopGrid. The Row and
Column uniquely identify each grid cell. Note that the Race, Ethnicity, Gender and
AgeRange variables are precisely defined (see section on loading population data
LoadData_Setups_Population).

Table I-1. Population File Fragment from PopGrid

Row Column Year Population Race Ethnicity Gender AgeRange
58 81 2000 1.54 WHITE HISPANIC MALE 0TO0
58 81 2000 0.03 BLACK HISPANIC MALE 0TO0
58 81 2000 0.01 NATAMER HISPANIC MALE 0TO0
58 81 2000 0.01 ASIAN HISPANIC MALE 0TO0
58 81 2000 4.86 WHITE HISPANIC MALE 1TO4
58 81 2000 0.12 BLACK HISPANIC MALE 1TO4
58 81 2000 0.03 NATAMER HISPANIC MALE 1TO4
58 81 2000 0.03 ASIAN HISPANIC MALE 1TO4

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58 81 2000 6.79 WHITE HISPANIC MALE 5TO9

58 81 2000 0.21 BLACK HISPANIC MALE 5TO9
58 81 2000 0.05 NATAMER HISPANIC MALE 5TO9
58 81 2000 0.05 ASIAN HISPANIC MALE 5TO9
58 81 2000 0.90 WHITE HISPANIC MALE 10TO14
58 81 2000 0.04 BLACK HISPANIC MALE 10TO14
58 81 2000 0.01 NATAMER HISPANIC MALE 10TO14
58 81 2000 0.01 ASIAN HISPANIC MALE 10TO14
58 81 2000 3.44 WHITE HISPANIC MALE 15TO19
58 81 2000 0.15 BLACK HISPANIC MALE 15TO19
58 81 2000 0.04 NATAMER HISPANIC MALE 15TO19
58 81 2000 0.04 ASIAN HISPANIC MALE 15TO19
58 81 2000 1.49 WHITE HISPANIC MALE 20TO24
58 81 2000 0.06 BLACK HISPANIC MALE 20TO24
58 81 2000 0.02 NATAMER HISPANIC MALE 20TO24
58 81 2000 0.03 ASIAN HISPANIC MALE 20TO24
58 81 2000 1.93 WHITE HISPANIC MALE 25TO29
58 81 2000 0.04 BLACK HISPANIC MALE 25TO29
58 81 2000 0.01 NATAMER HISPANIC MALE 25TO29
58 81 2000 0.01 ASIAN HISPANIC MALE 25TO29
58 81 2000 1.87 WHITE HISPANIC MALE 30TO34
58 81 2000 0.08 BLACK HISPANIC MALE 30TO34

PopGrid generates a second file that keeps track of the fraction of the total population in
each of the eight race-ethnic groups that comes from each county in the United States.
Table I-2 presents a sample. The SourceCol and SourceRow uniquely identify each
county, and the TargetCol and TargetRow uniquely identify each grid cell. The Value
variable gives the fraction of the total population in the grid cell for a given race-ethnic
group that comes from the "source" county.
When a grid cell lies completely within a county, then the fraction will be 1. When a grid
cell is in more than county, then the sum of the fractions across the counties for a given
race-ethnic group must sum to one. In Table I-2, you can see that for grid cell
(TargetCol=123, TargetRow=18) that the fraction of Asian Non-Hispanic coming from
county (SourceCol=16, SourceRow=71) is 0.49 and for county (SourceCol=49,
SourceRow=3) the fraction is 0.51. In this case, about half the population of Asian
Non-Hispanics comes from each of the two counties. In the case of Black Hispanics, the
fraction from county (SourceCol=16, SourceRow=71) is only 0.12, with most Black
Hispanics in this grid cell coming from county (SourceCol=49, SourceRow=3).

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Table I-2. Population-Weight File Fragment from PopGrid

SourceCol SourceRow TargetCol TargetRow Race Ethnicity Value Year
16 71 123 18 ASIAN NON-HISPANIC 0.49 2000
16 71 123 18 ASIAN HISPANIC 0.21 2000
16 71 123 18 BLACK NON-HISPANIC 0.49 2000
16 71 123 18 BLACK HISPANIC 0.12 2000
16 71 123 18 NATAMER NON-HISPANIC 0.98 2000
16 71 123 18 NATAMER HISPANIC 0.43 2000
16 71 123 18 WHITE NON-HISPANIC 0.23 2000
16 71 123 18 WHITE HISPANIC 0.06 2000
49 3 123 18 ASIAN NON-HISPANIC 0.51 2000
49 3 123 18 ASIAN HISPANIC 0.79 2000
49 3 123 18 BLACK NON-HISPANIC 0.51 2000
49 3 123 18 BLACK HISPANIC 0.88 2000
49 3 123 18 NATAMER NON-HISPANIC 0.02 2000
49 3 123 18 NATAMER HISPANIC 0.57 2000
49 3 123 18 WHITE NON-HISPANIC 0.77 2000
49 3 123 18 WHITE HISPANIC 0.94 2000
6 23 45 1 ASIAN NON-HISPANIC 0.00 2000
6 23 45 1 ASIAN HISPANIC 0.00 2000
6 23 45 1 BLACK NON-HISPANIC 0.00 2000
6 23 45 1 BLACK HISPANIC 0.00 2000
6 23 45 1 NATAMER NON-HISPANIC 1.00 2000
6 23 45 1 NATAMER HISPANIC 1.00 2000
6 23 45 1 WHITE NON-HISPANIC 1.00 2000
6 23 45 1 WHITE HISPANIC 1.00 2000
6 23 45 2 ASIAN NON-HISPANIC 1.00 2000
6 23 45 2 ASIAN HISPANIC 1.00 2000
6 23 45 2 BLACK NON-HISPANIC 1.00 2000
6 23 45 2 BLACK HISPANIC 1.00 2000
6 23 45 2 NATAMER NON-HISPANIC 1.00 2000
6 23 45 2 NATAMER HISPANIC 1.00 2000
6 23 45 2 WHITE NON-HISPANIC 1.00 2000
6 23 45 2 WHITE HISPANIC 1.00 2000

I.2 Monitor Data in U.S. Setup

BenMAP-ready data files were created from 2000 through 2007 data, as reported to the U.
S. Environmental Protection Agency’s (EPA) Air Quality System (AQS), for PM2.5,
PM10 STP and LC, lead TSP, ozone, NO2, SO2, and CO. Table I-5 summarizes the data
sources and vintage of the processed data.

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Table I-5. Underlying data sources for BenMAP air quality data files.

The AQS data were uploaded to the STI Air Quality Archive (AQA) Oracle database. The
AQA database performs additional quality control (QC) checks against the AQS data, such
as uniqueness by AQS site, method, parameter occurrence code (POC), and duration
codes; checks of minimum and maximum values; and maximum rate of change between
consecutive data values (where appropriate). The specific QC checks imposed on the
BenMAP data are outlined in Table I-6. No maximum value filters were applied to the
concentration data. High aerosol concentration values caused by dust storms or other
exceptional events are included in the BenMAP-ready data files.

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Table I-6. Pollutant-specific QC checks performed in AQA

I.2.1 Data Processing

STI developed data processing procedures consistent with those used in the past by Abt
Associates to create air quality data for files for use in the BenMAP model. Critical data
processing rules implemented in the deliverable data are listed below:
 Data delivered by STI are reported with consistent units: μg/m3 for aerosols; ppb for
ozone, NO2, and SO2; and ppm for CO.
 The “monitor name” field is populated by concatenating the AQS site, parameter, and
POC codes.
 The “monitor description” field is populated with the following metadata: method code,
land use, location setting, POC, and AQS parameter code. The AQS probe location and
monitoring objective code fields are left blank in STI-processed data.
 The data were formatted with one record per site, pollutant, POC, and year for use in the
BenMAP program. Data for 365 days, or 8,760 hourly values, are expected per record.
This format is satisfied regardless of leap years; an average of February 28 and 29 data
are reported.

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 The monitoring method is allowed to change over the course of a year. To provide a
more complete record, data with multiple method codes for a given site, parameter, POC,
and year were combined and the first reported method code was reported in the
BenMAP-ready data files.
 Aerosol data collected with 24-hr sample durations were used before data collected with
underlying 1-hr sample durations.One-hour sampling duration data are used for ozone,
NO2, SO2,, and CO.

I.2.2 Output Files

Table I-7 lists the number of monitors by pollutant and year, represented in the resulting
BenMAP-ready data files.

Table I-7. Number of monitors by pollutant, AQS parameter code, and year included
in the BenMAP-ready data files

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Appendix J: Uncertainty & Pooling

This Appendix discusses the treatment of uncertainty in BenMAP, both for incidence changes and
associated dollar benefits. Some background is then given on pooling methodology. Finally, the
mechanics of the various Pooling Methods available in BenMAP are discussed in detail, including
Subjective Weight based pooling, Fixed Effects pooling, Random / Fixed Effects pooling, and
independent and dependent Sum and Subtraction.

J.1 Uncertainty
Although there are several sources of uncertainty affecting estimates of incidence changes
and associated benefits, the sources of uncertainty that are most readily quantifiable in
benefit analyses are uncertainty surrounding the health impact functions and uncertainty
surrounding unit dollar values. The total dollar benefit associated with a given endpoint
group depends on how much the endpoint group will change in the control scenario (e.g.,
how many premature deaths will be avoided) and how much each unit of change is worth
(e.g., how much a statistical death avoided is worth).
Both the uncertainty about the incidence changes and uncertainty about unit dollar values
can be characterized by distributions. Each “uncertainty distribution” characterizes our
beliefs about what the true value of an unknown (e.g., the true change in incidence of a
given health effect) is likely to be, based on the available information from relevant
studies. Although such an “uncertainty distribution” is not formally a Bayesian posterior
distribution, it is very similar in concept and function (see, for example, the discussion of
the Bayesian approach in Kennedy 1990, pp. 168-172). Unlike a sampling distribution
(which describes the possible values that an estimator of an unknown value might take on),
this uncertainty distribution describes our beliefs about what values the unknown value
itself might be.
Such uncertainty distributions can be constructed for each underlying unknown (such as a
particular pollutant coefficient for a particular location) or for a function of several
underlying unknowns (such as the total dollar benefit of a regulation). In either case, an
uncertainty distribution is a characterization of our beliefs about what the unknown (or the
function of unknowns) is likely to be, based on all the available relevant information.
Uncertainty statements based on such distributions are typically expressed as 90 percent
credible intervals. This is the interval from the fifth percentile point of the uncertainty
distribution to the ninety-fifth percentile point. The 90 percent credible interval is a “
credible range” within which, according to the available information (embodied in the
uncertainty distribution of possible values), we believe the true value to lie with 90 percent
probability. The uncertainty surrounding both incidence estimates and dollar benefits
estimates can be characterized quantitatively in BenMAP. Each is described separately
below.

J.1.1 Characterization of Uncertainty Surrounding Incidence Changes

To calculate point estimates of the changes in incidence of a given adverse health effect

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associated with a given set of air quality changes, BenMAP performs a series of
calculations at each grid-cell. First, it accesses the health impact functions needed for the
analysis, and then it accesses any data needed by the health impact functions. Typically,
these include the grid-cell population, the change in population exposure at the grid-cell,
and the appropriate baseline incidence rate. BenMAP then calculates the change in
incidence of adverse health effects for each selected health impact function. The resulting
incidence change is stored, and BenMAP proceeds to the next grid-cell, where the above
process is repeated.
In Latin Hypercube mode, BenMAP reflects the uncertainty surrounding estimated
incidence changes (resulting from the sampling uncertainty surrounding the pollutant
coefficients in the health impact functions used) by producing a distribution of possible
incidence changes rather than a single point estimate. To do this, it uses the distribution (
Dist Beta) associated with the pollutant coefficient (Beta, or β), and potentially the point
estimate (Beta) and two parameters (P1Beta, P2Beta). Typically, pollutant coefficients are
normally distributed, with mean Beta and standard deviation P1Beta.
BenMAP uses an N-point Latin Hypercube to represent the underlying distribution of β
and to create a corresponding distribution of incidence changes in each population grid
cell, where N is specified by you. The Latin Hypercube method represents an underlying
distribution by N percentile points of the distribution, where the nth percentile point is
equal to:

The Latin Hypercube method is used to enhance computer processing efficiency. It is a

sampling method that divides a probability distribution into intervals of equal probability,
with an assumption value for each interval assigned according to the interval’s probability
distribution. Compared with conventional Monte Carlo sampling, the Latin Hypercube
approach is more precise over a fewer number of trials because the distribution is sampled
in a more even, consistent manner (Decisioneering, 1996, pp. 104-105).
Suppose, for example, that you elect to use a 20-point Latin Hypercube. BenMAP would
then represent the distribution of β by 20 percentile points, specifically the 2.5th, 7.5th, ...,
97.5th. To do this, the inverse cumulative distribution function specified by the distribution
of β is called with the input probability equal to each the 20 percentile points. BenMAP
then generates an estimate of the incidence change in a grid-cell for each of these values of
β, resulting in a distribution of N incidence changes. This distribution is stored, and
BenMAP proceeds to the next population grid-cell, where the process is repeated.

J.1.2 Characterization of Uncertainty Surrounding Dollar Benefits

The uncertainty distribution of the dollar benefits associated with a given health or welfare
effect is derived from the two underlying uncertainty distributions – the distribution of the
change in incidence of the effect (number of cases avoided) and the distribution of the

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value of a case avoided (the “unit value”). The derivation of the uncertainty distribution
for incidence change is described above. The distributions used to characterize the
uncertainty surrounding unit values are described in detail in the appendix on the
Economic Value of Health Effects. As noted in that Appendix, a variety of distributions
have been used to characterize the uncertainty of unit values, including uniform, triangular,
normal, and Weibull.
To represent the underlying distribution of uncertainty surrounding unit values, a 100-point
Latin Hypercube is generated in the same way described in the previous section for the
distribution of β. That is, the unit value distribution is represented using the 0.5th, 1.5th, ...,
and 99.5th percentile values of its distribution.
A distribution of the uncertainty surrounding the dollar benefits associated with a given
endpoint is then derived from Latin Hypercube values generated to represent the change in
incidence and the Latin Hypercube values generated to represent the unit value
distribution. To derive this new distribution, each of the 100 unit values is multiplied by
each of the N incidence change values, yielding a set of 100 * N dollar benefits. These
values are sorted low to high and binned down to a final distribution of N dollar benefit
values.

J.1.3 Characterization of Uncertainty Surrounding QALY Estimates

The uncertainty distribution of the QALY estimates associated with a given health effect is
similar to that for dollar benefits. That is, it is derived from the two underlying uncertainty
distributions – the distribution of the change in incidence of the effect (number of cases
avoided) and the distribution of the QALYs per case avoided. The derivation of the
uncertainty distribution for incidence change is described above. The distributions used to
characterize the uncertainty surrounding QALYs are described in detail in the appendix on
the Economic Value of Health Effects. As noted in that Appendix, a variety of
distributions have been used to characterize the uncertainty of unit values, including
uniform, triangular, normal, and Weibull.
To represent the underlying distribution of uncertainty surrounding unit values, a 100-point
Latin Hypercube is generated in the same way described in the previous section for the
distribution of β. That is, the unit value distribution is represented using the 0.5th, 1.5th, ...,
and 99.5th percentile values of its distribution.
A distribution of the uncertainty surrounding the QALYs associated with a given endpoint
is then derived from Latin Hypercube values generated to represent the change in incidence
and the Latin Hypercube values generated to represent the QALY distribution. To derive
this new distribution, each of the 100 QALY weights is multiplied by each of the N
incidence change values. These values are sorted low to high and binned down to a final
distribution of QALY values.

J.2 Pooling
There is often more than one study that has estimated a health impact function for a given

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pollutant-health endpoint combination. Each study provides an estimate of the pollutant

coefficient, β, along with a measure of the uncertainty of the estimate. Because uncertainty
decreases as sample size increases, combining data sets is expected to yield more reliable
estimates of β, and therefore more reliable estimates of the incidence change predicted
using β. Combining data from several comparable studies in order to analyze them
together is often referred to as meta-analysis.
For a number of reasons, including data confidentiality, it is often impractical or
impossible to combine the original data sets. Combining the results of studies in order to
produce better estimates of β provides a second-best but still valuable way to synthesize
information . This is referred to as pooling. Pooling β’s requires that all of the studies
contributing estimates of β use the same functional form for the health impact function.
That is, the β’s must be measuring the same thing.
It is also possible to pool the study-specific estimates of incidence change derived from the
health impact functions, instead of pooling the underlying β’s themselves. For a variety of
reasons, this is often possible when it is not feasible to pool the underlying β’s. For
example, if one study is log-linear and another is linear, we could not pool the β’s because
they are not different estimates of a coefficient in the same health impact function, but are
instead estimates of coefficients in different health impact functions. We can, however,
calculate the incidence change predicted by each health impact function (for a given
change in pollutant concentration and, for the log-linear function, a given baseline
incidence rate), and pool these incidence changes. BenMAP allows the pooling of
incidence changes predicted by several studies for the same pollutant-health endpoint
group combination. It also allows the pooling of the corresponding study-specific estimates
of monetary benefits.
As with estimates based on only a single study, BenMAP allows you to characterize the
uncertainty surrounding pooled estimates of incidence change and/or monetary benefit. To
do this, BenMAP pools the study-specific distributions of incidence changes (or monetary
benefit or QALYs) to derive a pooled distribution. This pooled distribution incorporates
information from all the studies used in the pooling procedure.

J.2.1 Weights Used for Pooling

The relative contribution of any one study in the pooling process depends on the weight
assigned to that study. A key component of the pooling process, then, is the determination
of the weight given to each study. There are various methods that can be used to assign
weights to studies. Below we discuss the possible weighting schemes that are available in
BenMAP.

J.2.1.1 Subjective Weights

BenMAP allows you the option of specifying the weights to be used. Suppose, for
example, you want to simply average all study-specific results. You would then assign a
weight of 1/N to each of the N study-specific distributions that are to be pooled. Note that
subjective weights are limited to two decimal places, and are normalized to sum to one, if

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they do not already sum to one.

J.2.1.2 Automatically Generated Weights

A simple average has the advantage of simplicity but the disadvantage of not taking into
account the uncertainty of each of the estimates. Estimates with great uncertainty
surrounding them are given the same weight as estimates with very little uncertainty. A
common method for weighting estimates involves using their variances. Variance takes
into account both the consistency of data and the sample size used to obtain the estimate,
two key factors that influence the reliability of results. BenMAP has two methods of
automatically generating pooling weights using the variances of the input distributions -
Fixed Effects Pooling and Random / Fixed Effects Pooling.
The discussion of these two weighting schemes is first presented in terms of pooling the
pollutant coefficients (the β’s), because that most closely matches the discussion of the
method for pooling study results as it was originally presented by DerSimonian and Laird.
We then give an overview of the analogous weighting process used within BenMAP to
generate weights for incidence changes rather than β’s.

J.2.1.3 Fixed-Effect Weights

The fixed effects model assumes that there is a single true concentration-response
relationship and therefore a single true value for the parameter β that applies everywhere.
Differences among β’s reported by different studies are therefore simply the result of
sampling error. That is, each reported β is an estimate of the same underlying parameter.
The certainty of an estimate is reflected in its variance (the larger the variance, the less
certain the estimate). Fixed effects pooling therefore weights each estimate under
consideration in proportion to the inverse of its variance.
Suppose there are n studies, with the ith study providing an estimate βi with variance vi (I = 1,
..., n). Let

denote the sum of the inverse variances. Then the weight, wi , given to the ith estimate, βi , is:

This means that estimates with small variances (i.e., estimates with relatively little
uncertainty surrounding them) receive large weights, and those with large variances receive
small weights.

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The estimate produced by pooling based on a fixed effects model, then, is just a weighted
average of the estimates from the studies being considered, with the weights as defined
above. That is:

The variance associated with this pooled estimate is the inverse of the sum of the inverse
variances:

Exhibit J-2 shows the relevant calculations for this pooling for three sample studies.

Exhibit J-2. Example of Fixed Effects Model Calculations

Study βi vi 1/vi wi wi*βi

1 0.75 0.1225 8.16 0.016 0.012
2 1.25 0.0025 400 0.787 0.984
3 1.00 0.0100 100 0.197 0.197
Sum ∑ = 508.16 ∑ = 1.000 ∑ = 1.193

The sum of weighted contributions in the last column is the pooled estimate of β based on
the fixed effects model. This estimate (1.193) is considerably closer to the estimate from
study 2 (1.25) than is the estimate (1.0) that simply averages the study estimates. This
reflects the fact that the estimate from study 2 has a much smaller variance than the
estimates from the other two studies and is therefore more heavily weighted in the pooling.

The variance of the pooled estimate, vfe, is the inverse of the sum of the variances, or
0.00197. (The sums of the βi and vi are not shown, since they are of no importance. The
sum of the 1/vi is S, used to calculate the weights. The sum of the weights, wi , i=1, ..., n,
is 1.0, as expected.)

J.2.1.4 Random- / Fixed-Effect Weights

An alternative to the fixed effects model is the random effects model, which allows the possibility
that the estimates βi from the different studies may in fact be estimates of different parameters,

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rather than just different estimates of a single underlying parameter. In studies of the effects of
PM10 on mortality, for example, if the composition of PM10 varies among study locations the
underlying relationship between mortality and PM10 may be different from one study location to
another. For example, fine particles make up a greater fraction of PM10 in Philadelphia than in El
Paso. If fine particles are disproportionately responsible for mortality relative to coarse particles,
then one would expect the true value of β in Philadelphia to be greater than the true value of β in
El Paso. This would violate the assumption of the fixed effects model.

The following procedure can test whether it is appropriate to base the pooling on the random
effects model (vs. the fixed effects model):

A test statistic, Qw , the weighted sum of squared differences of the separate study estimates from
the pooled estimate based on the fixed effects model, is calculated as:

Under the null hypothesis that there is a single underlying parameter, β, of which all the βi ’s are
estimates, Qw has a chi-squared distribution with n-1 degrees of freedom. (Recall that n is the
number of studies in the meta-analysis.) If Qw is greater than the critical value corresponding to
the desired confidence level, the null hypothesis is rejected. That is, in this case the evidence does
not support the fixed effects model, and the random effects model is assumed, allowing the
possibility that each study is estimating a different β. (BenMAP uses a five percent one-tailed
test).

The weights used in a pooling based on the random effects model must take into account not only
the within-study variances (used in a meta-analysis based on the fixed effects model) but the
between-study variance as well. These weights are calculated as follows:

Using Qw , the between-study variance, η2, is:

It can be shown that the denominator is always positive. Therefore, if the numerator is negative
(i.e., if Qw < n-1), then η2 is a negative number, and it is not possible to calculate a random effects
estimate. In this case, however, the small value of Qw would presumably have led to accepting
the null hypothesis described above, and the meta-analysis would be based on the fixed effects
model. The remaining discussion therefore assumes that η2 is positive.

Given a value for η2 , the random effects estimate is calculated in almost the same way as the
fixed effects estimate. However, the weights now incorporate both the within-study variance (vi)
and the between-study variance ( η2). Whereas the weights implied by the fixed effects model
used only vi, the within-study variance, the weights implied by the random effects model use vi +η
2.

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Let vi* = vi +η2. Then:

The estimate produced by pooling based on the random effects model, then, is just a
weighted average of the estimates from the studies being considered, with the weights as
defined above. That is:

The variance associated with this random effects pooled estimate is, as it was for the fixed
effects pooled estimate, the inverse of the sum of the inverse variances:

The weighting scheme used in a pooling based on the random effects model is basically the same
as that used if a fixed effects model is assumed, but the variances used in the calculations are
different. This is because a fixed effects model assumes that the variability among the estimates
from different studies is due only to sampling error (i.e., each study is thought of as representing
just another sample from the same underlying population), while the random effects model
assumes that there is not only sampling error associated with each study, but that there is also
between-study variability -- each study is estimating a different underlying β. Therefore, the sum
of the within-study variance and the between-study variance yields an overall variance estimate.

Fixed Effects and Random / Fixed Effects Weighting to Pool Incidence Change
Distributions and Dollar Benefit Distributions
Weights can be derived for pooling incidence changes predicted by different studies, using
either the fixed effects or the fixed / random effects model, in a way that is analogous to
the derivation of weights for pooling the â’s in the C-R functions. As described above,
BenMAP generates a Latin Hypercube representation of the distribution of incidence
change corresponding to each health impact function selected. The means of those

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study-specific Latin Hypercube distributions of incidence change are used in exactly the
same way as the reported â’s are used in the calculation of fixed effects and random effects
weights described above. The variances of incidence change are used in the same way as
the variances of the â’s. The formulas above for calculating fixed effects weights, for
testing the fixed effects hypothesis, and for calculating random effects weights can all be
used by substituting the mean incidence change for the ith health impact function for âi and
the variance of incidence change for the ith health impact function for vi.200
Similarly, weights can be derived for dollar benefit distributions. As described above,
BenMAP generates a Latin Hypercube representation of the distribution of dollar benefits .
The means of those Latin Hypercube distributions are used in exactly the same way as the
reported â’s are used in the calculation of fixed effects and random effects weights
described above. The variances of dollar benefits are used in the same way as the
variances of the â’s. The formulas above for calculating fixed effects weights, for testing
the fixed effects hypothesis, and for calculating random effects weights can all be used by
substituting the mean dollar benefit change for the ith valuation for âi and the variance of
dollar benefits for the ith valuation for vi.
BenMAP always derives Fixed Effects and Random / Fixed Effects weights using
nationally aggregated results, and uses those weights for pooling at each grid cell (or
county, etc. if you choose to aggregate results prior to pooling). This is done because
BenMAP does not include any regionally based uncertainty – that is, all uncertainty is at
the national level in BenMAP, and all regional differences (population, for example) are
treated as certain.

J.2.2 Mechanics of Pooling in BenMAP

Once weights are generated for each input distribution, BenMAP has three options for
using these weights to combine the input distributions into a single new distribution.
These options are referred to as Advanced Pooling Methods.
Round Weights to Two Digits
This is BenMAP’s default Advanced Pooling Method, and is always the method used
when Subjective Weights are used. The first step is converting the weights to two digit
integers by multiplying them by 100 and rounding to the nearest integer. If all the integral
weights thus generated are divisible by the smallest weight, they are each divided by that
smallest weight. For example, if the original weights were 0.1, 0.2, 0.3, and 0.4, the
resulting integral weights would be 10/10, 20/10, 30/10, and 40/10 (or 1, 2, 3, and 4).
BenMAP then creates a new distribution by sampling each entire input distribution
according to its weight. That is, in the above example the first distribution would be
sampled once, the second distribution twice, and so forth. The advantage of sampling
whole distributions is that it preserves the characteristics (i.e., the moments - the mean, the
variance, etc.) of the underlying distributions. Assuming n latin hypercube points, the
resulting distribution will contain a maximum of 100 * n values, which are then sorted low
to high and binned down to n values, which will represent the new, pooled distribution.

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Round Weights to Three Digits

This Advanced Pooling Method is essentially the same as rounding weights to two digits,
except that the weights are converted to three digit integers, and so forth. That is, the
weights are multiplied by 1000 and rounded to the nearest integer. Again, if all the integral
weights thus generated are divisible by the smallest weight, they are each divided by that
smallest weight. Assuming n Latin Hypercube points, the resulting distribution with this
Advanced Pooling Method can contain a maximum of 1000 * n values, which are sorted
low to high and binned down to n values, which represent the new, pooled distribution.
Exact Weights for Monte Carlo
This Advanced Pooling Method uses a Monte Carlo method to combine the input
distributions. Using this method, on each of many iterations, (1) an input distribution is
selected (with the probability of selection equal to the weight assigned to the distribution),
and (2) a value is randomly drawn from that distribution. Values chosen in this way are
placed into a temporary pooled distribution, which will have one point per iteration of the
Monte Carlo method. The number of iterations is specified by the user, and defaults to
5,000. After the temporary distribution is fully generated, it is sorted low to high and
binned down to n values (where n is the number of Latin Hypercube Points chosen for the
analysis).

J.2.3 Summing Distributions

Sometimes rather than pooling distributions we want to add them. For example, some
studies have estimated a health impact function for hospital admissions for COPD and
another health impact function for hospital admissions for pneumonia. From each of these
health impact functions, BenMAP can derive the corresponding distributions for incidence
change. Hospital admissions for COPD and pneumonia are two of the most important
components of respiratory hospital admissions, and we may want to estimate the number of
cases of “respiratory hospital admissions,” as characterized by being either COPD or
pneumonia. To do this we would add the two distributions.
Summing across distributions can be done in one of two ways: We can assume the two
distributions are independent of each other or dependent. Which is the more reasonable
assumption depends on the particulars of the distributions being summed.
Assuming Independence
This is the Sum (Independent) Pooling Method. To sum two distributions that are
independent, on each of many iterations of a Monte Carlo procedure, BenMAP (1)
randomly selects a value from the first input distribution, (2) randomly selects a value from
the second input distribution, and (3) adds the two values together. To sum N distributions
that are independent, BenMAP follows an analogous procedure in which, on each iteration
it makes a random selection from each of the input distributions and then adds the results
together. When the Monte Carlo procedure is completed, all such generated results are
sorted low to high and binned down to the appropriate number of latin hypercube points.
The number of iterations is determined by the Monte Carlo Iterations setting.

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Assuming Dependence
This is the Sum (Dependent) Pooling Method. Recall that the uncertainty distributions in
BenMAP are latin hypercube representations, consisting of N percentile points. To sum
two distributions assumed to be dependent, BenMAP simply generates a new N point latin
hypercube where each point is the sum of the corresponding points from the input latin
hypercubes. That is, the first point in the new latin hypercube is the sum of the first points
in the two input latin hypercubes, and so forth. To sum n distributions that are assumed to
be dependent, BenMAP follows an analogous procedure in which each point in the new
latin hypercube is the sum of the corresponding points from each of the input latin
hypercubes.

J.2.4 Subtracting Distributions

In some cases, you may want to subtract one or more distribution(s) from another. For
example, one study may have estimated a health impact function for minor restricted
activity days (MRADs), and another study may have estimated a health impact function for
asthma “episodes.” You may want to subtract the change in incidence of asthma episodes
from the change in incidence from MRADs before estimating the monetary value of the
MRADs, so that the monetary value of asthma episodes avoided will not be included.
Subtracting across distributions can be done in one of two ways: we can assume the two
distributions are independent of each other or dependent. Which is the more reasonable
assumption depends on the particulars of the distributions being subtracted.
Assuming Independence
This is the Subtraction (Independent) Pooling Method. To subtract one distribution from
another, assuming independence, on each of many iterations of a Monte Carlo procedure,
BenMAP (1) randomly selects a value from the first input distribution, (2) randomly
selects a value from the second input distribution, and (3) subtracts the second value from
the first. To subtract N distributions from another distribution, assuming independence,
BenMAP follows an analogous procedure in which, on each iteration it makes a random
selection from each of the input distributions and then subtracts the second through the Nth
from the first. When the Monte Carlo procedure is completed, all such generated results
are sorted low to high and binned down to the appropriate number of Latin Hypercube
points. The number of iterations is determined by the Monte Carlo Iterations setting.
Assuming Dependence
This is the Subtraction (Dependent) Pooling Method (see Chapter 6 for details). Recall
that the uncertainty distributions in BenMAP are Latin Hypercube representations,
consisting of N percentile points. To subtract one distribution from another, assuming
them to be dependent, BenMAP simply generates a new N point Latin Hypercube where
each point is the result of subtracting the corresponding point of the second input Latin
Hypercube from the corresponding point of the first input Latin Hypercube. That is, the
first point in the new Latin Hypercube is the result of subtracting the first point in the
second Latin Hypercube from the first point of the first Latin Hypercube, and so forth. To

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subtract n distributions from another distribution, assuming dependence, BenMAP follows

an analogous procedure in which each point in the new Latin Hypercube is the result of
subtracting the corresponding points of the second through the Nth input Latin Hypercubes
from the corresponding point of the first.

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 Appendix K: Command Line BenMAP

Appendix K: Command Line BenMAP

The command line version of BenMAP is capable of performing all of the functions of the
GUI-based version. It is most useful for large, complex analyses that require generation of
a substantial number of files. This appendix describes the syntax and use of the command
line version.

K.1 Overview
The overall format of the file is a variable definitions section followed by a commands
section.
Comment statements are supported at any point in the file. Lines beginning with a pound
character (#) are considered comment lines and will be ignored during file parsing.
Additionally, LOAD <filename> statements are supported at any point in the file. These
work as string replacements – the contents of the file specified by <filename> are simply
inserted into the main file. Multi-level LOAD statements are supported, but no attempt is
made to detect cycles (two files referencing each other with LOAD statements, for
example).
The control file is, in general, not case sensitive. In the case of user-defined strings,
(variable values, etc.), it is preserved.

K.2 Variables
The variable definitions section is optional, and if present will consist of a single line with
the word “Variables” on it, followed by one or more lines that define variables. A variable
definition consists of a variable name and a variable value. When parsing lines in the
commands section of the control file, all occurrences of the variable name will be replaced
by the variable value.
All variable names must begin and end with the percent character (%).
Variable Name/Value replacement will be done in multiple passes (until no variable names
remain), so variable values may contain other variable names. No attempt will be made to
detect cycles, however, so be careful not to introduce them. For example, avoid variable
definitions like the following:

%BENMAPDIR% %AQGDIR%\
%AQGDIR% %BENMAPDIR%\Air Quality Grids

Variable values must be contained in a single line, and will consist of the first

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non-whitespace character after the variable name through the newline character. Watch
out for undesired trailing whitespaces!

K.3 Commands
The commands section is required, and will consist of one or more command sections.
There are five types of command sections:

SETACTIVESETUP
CREATE AQG
RUN CFG
RUN APV
GENERATE REPORT

This section will discuss each one in turn.

In general, in command sections, there must be at least one white space between each
token (where a token is either a command, a parameter name, or a parameter value).
Additional white space is ignored, including newline characters. To include white space in
a parameter value, you must enclose the parameter in double quotes. The double quotes
will not be included in the parameter value in this case (If you wish to include beginning
and trailing double quotes in a parameter value, put two in a row at the beginning and end
– e.g. ““Look at all those double quotes.””).

K.3.1 Set Active Setup

For the US version of the BenMAP command line executable the only valid value is
United States. The SETACTIVESETUP section is required.
Example
-ActiveSetup “United States”
K.3.2 Create AQG
This section initiates the creation of one or more air quality grids (normally one, potentially
two in the case of monitor rollback grid creation – see below). It always starts with the
words CREATE AQG. It must then include the following options, in any order:

-Filename <filename>
-Gridtype <gridtype>

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-Pollutant <pollutant>

The Filename value is the name of the air quality grid that will be created.
The GridType value must be one found in the BenMAP database. The actual values for
this parameter are found on the Modify Setup screen in the Grid Definitions list box.
Supported Pollutant values are:
-Ozone
-PM10
-PM2.5

These values are also found on the Modify Setup screen in the Pollutants list box.
After these required options, the type of grid creation must be identified, and then the
parameters for that grid creation type must be specified. There are four air quality grid
creation types:
-ModelDirect
-MonitorDirect
-MonitorModelRelative
-MonitorRollback

K.3.2.1 Model Direct

This section initiates the creation of a model direct air quality grid.

This creation type has two required parameters:

-ModelFilename <filename>
-DSNName <ODBC DSN name>

and one optional parameter:

-TableName <tablename>

Supported DSNName values are:

“Excel Files” Excel Spreadsheet (.xls)
“Text Files” Comma-delimited (.csv) files

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“MS Access Database” Access Database (.mdb)

If the DSNName is “Excel Files” and there is more than one worksheet in the workbook or
“MS Access Database” and there is more than one table in the database then the
TableName parameter must indicate the worksheet or table name.

K.3.2.2 Monitor Direct

This section initiates the creation of a monitor direct air quality grid.

The required parameters are:

-MonitorDataType <DataSource descriptor>
-InterpolationMethod <Interpolation Method>

Valid values for MonitorDataType are:

-Library
-DatabaseRows
-DatabaseColumns
-TextFile

Valid values for Interpolation method are:

-ClosestMonitor
-VNA

If MonitorDataType is Library then the following parameters are required:

-MonitorDataSet <Monitor Dataset Name>
MonitorDataSet is the Dataset name of Monitor data stored in the BenMAP database.
These values can be found on the Modify Setup screen in Monitor Datasets list box.
-MonitorYear <Year>
MonitorYear specifies the year of interest in the monitor library.

If MonitorDataType is DatabaseRows then the following parameters are required:

-MonitorFile <filename>
-DSNName <ODBC DSN name>

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and one optional parameter:

-TableName <tablename>

Supported DSNName values are:

-“Excel Files” Excel Spreadsheet (.xls)
-“Text Files” Comma-delimited (.csv) files
-“MS Access Database” Access Database (.mdb)

If the DSNName is “Excel Files” and there is more than one worksheet in the workbook or
“MS Access Database” and there is more than one table in the database then the
TableName parameter must indicate the worksheet or table name.
If MonitorDataType is DatabaseColumns then the same parameters for MonitorDataType
DatabaseRows are required along with the following:
-MonitorDefFilename
-DefDSNName
-DefTableName

These parameters behave the same as the corresponding DatabaseRows parameters.

If MonitorDataType is TextFile the following parameter is required:
-MonitorFile <filename>
MonitorFile specifies a comma separated values (*.csv, generally) file containing monitor
data.

Optional Parameters:
-MaxDistance <real>
Specifies the maximum distance (in kilometers) to be used in ClosestMonitor
interpolation or VNA interpolation. Monitors outside this distance will not be considered
in the interpolation procedure.
-MaxRelativeDistance <real>
Specifies the maximum relative distance to be used in VNA interpolation, where
relative distance is the multiple of the distance to the closest monitor used in the
interpolation procedure.
-WeightingMethod <method>

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Specifies the weighting procedure used for monitors in VNA interpolation. Supported
values are InverseDistance and InverseDistanceSquared. If this parameter is not specified,
InverseDistance weighting is used.

K.3.2.3 Monitor Model Relative

This section initiates the creation of a monitor model relative air quality grid. This
creation type has all the same required and optional parameters as the MonitorDirect
creation type. In addition, it has two/three new required parameters.

Required Parameters:
-ScalingMethod <scaling method>
Supported scaling methods are Spatial, Temporal, and Both.
-BaseYearFilename <filename>
Specifies the base year adjustment file to use in monitor scaling.
-BaseYearDSNName <ODBC DSN Name>
Supported –BaseYearDSNName values are
“Excel Files” Excel Spreadsheet (.xls)
“Text Files” Comma-delimited (.csv) files
“MS Access Database” Access Database (.mdb)

When the ScalingMethod is Temporal or Both, the FutureYearFileName and

FutureYearDSNName parameters are required. These specify the future year adjustment
file to use in monitor scaling.

K.3.2.4 Monitor Rollback

// MonitorRollback
SpatialScaling = '-SpatialScaling';
BaselineFilename = '-BaselineFilename';

// RollbackOptions
Percentage = '-Percentage';
Increment = '-Increment';

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 Appendix K: Command Line BenMAP

// RollbackToStandardOptions
Standard = '-Standard';
Metric = '-Metric';
Ordinality = '-Ordinality';
InterdayRollbackMethod = '-InterdayRollbackMethod';
IntradayRollbackMethod = '-IntradayRollbackMethod';

K.3.3 Run CFG

The command line version of BenMAP does not support creation of new .cfg files, both
because this would be quite cumbersome to do in plain text, and because it probably is not
needed. Slight modifications of existing .cfg files are supported, and it is thought that at
this point this should be enough.
As such, the only required parameter to run a configuration is the configuration filename.
Optional parameters allow the slight modifications mentioned above.

Required Parameters
-CFGFilename <filename>
Specifies the .cfg file to run.
-ResultsFilename <filename>
Specifies the .cfgr file to save the results in.

Optional Parameters
-BaselineAQG <filename>
Specifies the baseline air quality grid file to use when running the configuration – overrides
whatever value is present in the .cfg file.
-ControlAQG <filename>
Specifies the control air quality grid file to use when running the configuration – overrides
whatever value is present in the .cfg file.
-Year <Integer>
Year in which to run the configuration (this will affect the population numbers used) –
overrides whatever value is present in the .cfg file. Supported values are 1990 and up.
-LatinHypercubePoints <integer>
Number of latin hypercube points to generate when running the configuration (zero means
run in point mode), overrides whatever value is present in the .cfg file.

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-Threshold <real>
Threshold to use when running the configuration – overrides whatever value is present in the
.cfg file.

K.3.4 Run APV

The command line version of BenMAP does not support creation of new .apv files, both
because this would be quite cumbersome to do in plain text, and because it probably is not
needed. Slight modifications of existing .apv files are supported, and it is thought that at
this point this should be enough.
As such, the only required parameter to run an APV configuration is the APV
configuration filename. Optional parameters allow the slight modifications mentioned
above.

Required Parameters
-APVFilename <filename>
Specifies the .apv file to run.
-ResultsFilename <filename>
Specifies the .apvr file to save the results in.

Optional Parameters
-CFGRFilename <filename>
Specifies the .cfgr file to use when running the APV configuration – note that this file must
contain the same set of results which the .cfgr file originally used to generate the .apv file
contained. Overrides whatever value is present in the .apv file.
-IncidenceAggregation <aggregation level>
Level to aggregate incidence results to before pooling them. Supported values are None,
County, State, and Nation. Overrides whatever value is present in the .apv file.
-ValuationAggregation <aggregation level>
Level to aggregate valuation results to before pooling them. Supported values are None,
County, State, and Nation (though the value must be greater than or equal to
IncidenceAggregation). Overrides whatever value is present in the .apv file.
-RandomSeed <integer>
Random seed to use for all procedures requiring pseudo-random numbers (e.g. monte carlo
procedures). Overrides the default behavior, which is to generate a new random
seed each time the APV configuration is run.
-DollarYear <integer>
Year in which dollar figures should be reported. Supported values are 1980 – 2001.
Overrides whatever value is present in the .apv file.

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 Appendix K: Command Line BenMAP

K.3.5 Generate Report

Reports come in three main varieties – Audit Trail Reports, which can be generated from
any BenMAP file; Configuration Results Reports, which can be generated from .cfgr files;
and APV Configuration Results Reports, which can be generated from .apvr files. All
these report types need an input filename and an output filename. CFGR reports and
APVR reports additionally take many optional parameters.

The format for each report type is:

GENERATE REPORT <ReportType>

-InputFile <filename>
-ReportFile <filename>
<optional parameters>

Supported ReportType values are: AuditTrail, CFGR, and APVR.

K.3.5.1 Audit Trail

Audit trail reports require only the parameters described in the "Generate Report" section.

K.3.5.2 CFGR Report

A CFGR report may be generating using only the parameters described in the "Generate
Report" section. However, there are also a number of additional options, described below.

Optional Parameters
-GridFields <comma separated field names>
Specifies the set of grid fields to include in the report. Grid fields include Column and Row.
If this parameter is not present, all fields will be included in the report.
-CustomFields <comma separated field names>
Specifies the set of custom fields (C-R Function identifiers, in this case) to include in the
report. If this parameter is not present, all fields will be included in the report.
-ResultFields <comma separated field names>
Specifies the set of result fields to include in the report. Result fields include Point Estimate,
Population, Delta, Mean, Standard Deviation, Variance, and Latin Hypercube Points. If this

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 Appendix K: Command Line BenMAP

parameter is not present, all fields will be included in the report.

-Grouping <grouping method>
Specifies the grouping for the results – Gridcell, then C-R Function, or C-R Function, then
Gridcell. Supported values are GridcellFirst, GridcellLast. The default value is GridcellFirst.
-DecimalDigits <integer>
Specifies the number of digits after the decimal point to include in the report. Supported
values are zero to eight. The default value is four.

K.3.5.3 APVR Report

Required Parameters
APVR Reports require one additional parameter beyond those required for Audit Trail or
CFGR Reports.
-ResultType <result type>
Specifies the result type for which a report should be created. Supported result types are:
IncidenceResults, AggregatedIncidence, PooledIncidence,Valuation, AggregatedValuation,
PooledValuation, QALYValuation, AggregatedQALYValuation and
PooledQALYValuation.

Optional Parameters
All of the CFGR report parameters are supported for APVR reports as well, except that
Population and Delta are not supported ResultField elements.
-Totals <total type>
Specifies the type of totals which should be included in the report. Supported types are
Dependent and Independent. Totals can only be generated for valuation results (Valuation,
AggregatedValuation, and PooledValuation result types).

K.4 Example 1

VARIABLES

%CFG% C:\BenMAP\CommandLine\Configurations\PM25 Wizard.cfg

%APV% C:\BenMAP\CommandLine\Configurations\PM25 Wizard.apv
%RESULTSDIR% C:\BenMAP\Temp
%REPORTDIR% C:\BenMAP\Temp
%AQG% C:\BenMAP\CommandLine\Air Quality Grids

COMMANDS

SETACTIVESETUP

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 Appendix K: Command Line BenMAP

-ActiveSetup "United States"

CREATE AQG

-Filename %AQG%\PM25_2002Baseline_50km.aqg
-GridType "CMAQ 12km"
-Pollutant PM2.5

MonitorDirect

-InterpolationMethod VNA_Alt
-MonitorDataType Library
-MonitorDataSet "EPA Standard Monitors"
-MonitorYear 2002
-MaxDistance 50

CREATE AQG

-Filename %AQG%\PM25_2002Control_50km.aqg
-GridType "CMAQ 12km"
-Pollutant PM2.5

MonitorRollback

-InterpolationMethod VNA_Alt
-MonitorDataType Library
-MonitorDataSet "EPA Standard Monitors"
-MonitorYear 2002
-RollbackGridType State
-MaxDistance 50

RollbackToStandardOptions

-Standard 65
-Metric D24HourMean
-InterdayRollbackMethod Quadratic

RUN CFG

-CFGFilename %CFG%
-ResultsFilename %RESULTSDIR%\PM25_2002_50km.cfgr
-BaselineAQG %AQG%\PM25_2002Baseline_50km.aqg
-ControlAQG %AQG%\PM25_2002Control_50km.aqg

RUN APV

-APVFilename %APV%
-ResultsFilename %RESULTSDIR%\PM25_2002_50km.apvr
-CFGRFilename %RESULTSDIR%\PM25_2002_50km.cfgr
-IncidenceAggregation Nation
-ValuationAggregation Nation

GENERATE REPORT APVR

-InputFile %RESULTSDIR%\PM25_2002_50km.apvr
-ReportFile %REPORTDIR%\PM25_2002_50km_IncidenceNation.csv

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 Appendix K: Command Line BenMAP

-ResultType PooledIncidence
-CustomFields "Endpoint Group,Author,Start Age,Endpoint,Qualifier,Pooling
Window"
-ResultFields "Mean,Standard Deviation,Latin Hypercube Points"
-DecimalDigits 0

GENERATE REPORT APVR

-InputFile %RESULTSDIR%\PM25_2002_50km.apvr
-ReportFile %REPORTDIR%\PM25_2002_50km_ValuationNation.csv
-ResultType PooledValuation
-CustomFields "Endpoint Group,Author,Start Age,Endpoint,Qualifier,Pooling
Window"
-ResultFields "Mean,Standard Deviation,Latin Hypercube Points"
-DecimalDigits 0

K.5 Example 2

VARIABLES

%CFG% C:\BenMAP\CommandLine\Configurations\PM25 Wizard.cfg

%APV% C:\BenMAP\CommandLine\Configurations\PM25 Wizard.apv
%RESULTSDIR% C:\BenMAP\Temp
%REPORTDIR% C:\BenMAP\Temp
%AQG% C:\BenMAP\CommandLine\Air Quality Grids

COMMANDS

SETACTIVESETUP

-ActiveSetup "United States"

CREATE AQG

-Filename %AQG%\PM25_2004Baseline.aqg
-GridType "County"
-Pollutant PM2.5

MonitorDirect

-InterpolationMethod VNA_Alt
-MonitorDataType Library
-MonitorDataSet "EPA Standard Monitors"
-MonitorYear 2004

CREATE AQG

-Filename %AQG%\PM25_2004_Control.aqg
-GridType "County"
-Pollutant PM2.5

MonitorRollback

-InterpolationMethod VNA_Alt
-MonitorDataType Library

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 Appendix K: Command Line BenMAP

-MonitorDataSet "EPA Standard Monitors"

-MonitorYear 2004
-RollbackGridType State
-MaxDistance 50

RollbackToStandardOptions

-Standard 35
-Metric D24HourMean
-InterdayRollbackMethod Quadratic

RUN CFG

-CFGFilename %CFG%
-ResultsFilename %RESULTSDIR%\PM25_2004.cfgr
-BaselineAQG %AQG%\PM25_2004Baseline.aqg
-ControlAQG %AQG%\PM25_2004Control.aqg

RUN APV

-APVFilename %APV%
-ResultsFilename %RESULTSDIR%\PM25_2004.apvr
-CFGRFilename %RESULTSDIR%\PM25_2004.cfgr
-IncidenceAggregation Nation
-ValuationAggregation Nation

GENERATE REPORT APVR

-InputFile %RESULTSDIR%\PM25_2004.apvr
-ReportFile %REPORTDIR%\PM25_2004_IncidenceNation.csv
-ResultType PooledIncidence
-CustomFields "Endpoint Group,Author,Start Age,Endpoint,Qualifier,Pooling
Window"
-ResultFields "Mean,Standard Deviation,Latin Hypercube Points"
-DecimalDigits 0

GENERATE REPORT APVR

-InputFile %RESULTSDIR%\PM25_2004.apvr
-ReportFile %REPORTDIR%\PM25_2004_ValuationNation.csv
-ResultType PooledValuation
-CustomFields "Endpoint Group,Author,Start Age,Endpoint,Qualifier,Pooling
Window"
-ResultFields "Mean,Standard Deviation,Latin Hypercube Points"
-DecimalDigits 0

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 Appendix L: Function Editor

Appendix L: Function Editor

The function editor is used to develop both health impact functions and valuation
functions. This appendix describes the syntax of this editor.

L.1 User Defined Variables

In addition to pre-defined variables that you can select from the Available Variables list,
you can create your own variables in the C-R Function Editor.
A variable is an identifier whose value can change at runtime. Put differently, a variable is
a name for a location in memory; you can use the name to read or write to the memory
location. Variables are like containers for data, and, because they are typed, they tell the
compiler how to interpret the data they hold.
The basic syntax for a variable declaration is
var identifierList: type;

where identifierList is a comma-delimited list of valid identifiers and type is any valid
type. For example,
var I: Integer;

declares a variable I of type Integer, while

var X, Y: Real;

declares two variables--X and Y--of type Real.

Consecutive variable declarations do not have to repeat the reserved word var:
var
X, Y, Z: Double;
I, J, K: Integer;
Digit: 0..9;
IndicatorName: String;
Okay: Boolean;

Variables can be initialized at the same time they are declared, using the syntax
var identifier: type = constantExpression;

where constantExpression is any constant expression representing a value of type type.

Thus the declaration

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 Appendix L: Function Editor

var I: Integer = 7;

is equivalent to the declaration and statement

var I: Integer;
...
I := 7;

Multiple variable declarations (such as var X, Y, Z: Real;) cannot include initializations, nor
can declarations of variant and file-type variables.

L.2 The Script Language

In the C-R Function Editor, you can evaluate complex block of statements.
You can use constructions like:
If...then...else;
for I:= ... to .. do ;
while... do ;
repeat .... until...;
break;
assignment (...:=....;)
try...finally...end;
try...except...end;

Each function you create can be a single statement or a block of statements.

When you specify it as a block of statements, your script must conform to the rules of the
script language, as follows:
1. Each single statement must end with a semicolon (;)
2. You can use the following statements:
variable := expression;
If logical expression then statement(s) [else statement(s)];
for variable := from_expression to/downto to_expression do statement(s);
while logical_expression do statement(s);
repeat statement(s) until logical_expression;
try statement(s) finally statement(s) end;
try statement(s) except statement(s) end;
inline comments: // comment... until the end of the line

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 Appendix L: Function Editor

nested comments: { nested comment }

Statement(s) in the above declarations states that you can specify either a single statement
or a block of statements. The block of statements must be enclosed in begin ... end
keywords. It is not necessary to enclose the body of the function in begin .. end. Cycle
statements can use break keyword to break the cycle (break must also end with
semicolon.)

L.3 Operands
Expressions may contain the following constant and variable types:
Integer numbers;
Floating point numbers;
Scientific numbers;

Decimal separator for all floating point and scientific-format numbers in expressions, is
independent of the Regional Settings of Windows and always is a decimal point ('.').
Boolean values - TRUE or FALSE;
Date type values - values of that type must be put in quotes ( ' ' ), and also date separator
character is independent of the Regional Settings of Windows and always is a slash - /, i.e.
- '01/01/2005'
String values - values of that type must be put in double quotes (" "); If a string contains
double quotes, you should double them(i.e., "this is a ""string"" ");

L.4 Operations
Arithmetical
+, -, *, /;
div - integer division;
mod - modulo;
^ - power of;
- - negate;

Logical
<, <=, >=, >, <>, =;
and, or, xor, not;

Bitwise

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 Appendix L: Function Editor

and, or, xor;

~ - negate;

L.5 Arithmetic Functions

ABS(X) absolute value

SQR(X) square = X^2 = X*X
SQRT(X) square root
SIGN(X) sign of X; =1 for X>0, =0 for X=0,
=-1 for X<0
ZERO(X) =0 for X=0, =1 for X<>0
TRUNC(X)=INT(X) integer part
FRAC(X) fractional part
ROUND(X) rounds X to the nearest integer
value
CEIL(X) always returns "ceil" integer value
FLOOR(X) always returns "floor" integer
value
DEC(X) decrements a value X by 1 and
returns a new value
INC(X) increments a value X by 1 and
returns a new value
ARG(X,Y) argument(phase) of X and Y
RADIUS(X,Y) = sqrt(sqr(X)+sqr(Y))
POWER(X,Y) raises X to a power of Y (Y is a
floating point value)
IPOWER(X,Y) raises X to a power of Y (Y is a
integer value)
X^Y raises X to a power of Y (same as
above two functions)
EXP(X) exponent

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 Appendix L: Function Editor

LN(X) natural logarithm

LG(X) decimal logarithm
LOG(X) base 2 logarithm
SIN(X) sine
COS(X) cosine
TAN(X) tangent
COTAN(X) cotangent
ASIN(X) arcsine
ACOS(X) arccosine
ATAN(X) arctangent
SINH(X) hyperbolic sine
COSH(X) hyperbolic cosine
TANH(X) hyperbolic tangent

L.6 Aggregate Functions

AVG(X1,X2,...) returns average value of (unlimited number of) arguments.

MAX(X1,X2,...) maximum of (unlimited number of) arguments.
MIN(X1,X2,...) minimum of (unlimited number of) arguments.
SUM(X1,X2,...) sum of (unlimited number of) arguments.
PROD(X1,X2,..) product of (unlimited number of) arguments.

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 References

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