Measures of association

by Fisaha.H(BSc. Mphil)

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 Learning Objectives

List common measures of association and measures

of public health impact

Calculate and interpret risk ratio and odds ratio and

describe their use

Calculate and interpret attributable risk percent and

vaccine efficacy**** describe their use
 Measures of Association
Why do we need them?

Move from descriptive to analytical epidemiology.

Comparisons within and between populations.

Risk factor identification.

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 Measurements in Epidemiology
Measures of disease occurrence

Prevalence

Incidence

Mortality
Rates, Proportions, Ratios

Measures of Association

– Rate ratio, (relative risk, risk ratio), odds ratio

Etiologic (attributable) risk 4

 Association
Definition
• Statistical relationship between two or more
variables
• Probability of occurrence of an outcome depends
on
– Presence of one or more characteristics

– Occurrence of one or more events

– Quantity of one or more other variables

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Epidemiologic Measures of association
Quantifies or expresses the strength of the
relationship between an "exposure" and
“outcome” of interest

Quantifies the difference in occurrence of

disease or death between two groups of people
who differ on "exposure“

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 Measures of association…

Disease frequency between two populations can be

compared by
Ratio Measures: relative risk (risk ratio, rate ratio,
odds ratio)
Difference Measures: excess risk
These measures may be applied at:
Individual Level
Population Level
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 “Exposure”
Exposure in usual sense

 e.g., ingestion of contaminated food

 e.g., droplets from someone with active pulmonary
tuberculosis
 Behaviors
 e.g., sharing needles, drinking alcohol etc
 Treatment
 e.g., intervention - education program
 Trait
 e.g., genotype
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 “Outcome”
 Disease
– e.g., rubella
– e.g., diabetes

 Event
– e.g., injury from land mine

 Condition
– e.g., blindness

 Death

 Others
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 Description of Relationships
• Variables can be related or unrelated to another
description
• If related, variables can be

– positively or negatively related

– strongly or weakly related (one variable can have

large or small effect on the other)

– significantly or not significantly related

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Relationships between variables
;Statistically Significant or Not?

• Statistically significant

 association is unlikely to be due to chance

But remember:

Statistically significant does not mean important

Not significant does not mean unimportant

Not significant does not mean no association

Statistically significant does not mean causal

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 Measures of association…

To aid in the calculation of measures of

association, epidemiologic data are often
presented in the form of a two-by-two table( four-
fold or contingency table)
Presentation of data in a two-by-two table

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"Every epidemiologic study can be
summarized in a 2-by-2 table.“

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 two-by-two table….

In cohort studies with variable lengths of follow-up,

a variation of the two-by-two table is used for data
presentation, since the numbers of person-time
units for exposed and none exposed subjects are
provided rather than the total numbers of
individuals in each group

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 two-by-two table…..

Disease
Yes No Person-time
units
a -
Exposure
Yes c - PY1
No PYo
a+c PY1 + PYo
 
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 Risk

# new cases during a specified period

population at risk during the specified period

= "Attack rate“
= Probability of getting disease
= Risk of disease
= Cumulative incidence

= Incidence proportion
1. Relative Risk

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 Relative Risk
Risk: The probability of an event occurring

Risk Ratio: The ratio of two risks

A measure of the strength of association based on

prospective studies.

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 RR…
Indicate the likelihood of developing the disease in the
exposed group relative to those who are not exposed

Estimates the magnitude of an association between

exposure and disease

It is defined as the ratio of the incidence of disease in the

exposed group (expressed as Ie) divided by the
corresponding incidence of disease in the non exposed
group (Io)
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 Relative Risk
RR = incidence of a disease among exposed (a/(a+b)) Re
incidence of a disease among non-exposed (c/(c+d)) R è

RR = R e / Rè Disease
Yes (+) No (-)
K
Exposure a b a+b n
Yes (+)
. a . c d o
c+d
RR = w
No (-)
. a+b
n
.

. c .

– It is a directcmeasurement
+d of a risk

It is usually used in Cohort and experimental study

design
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 Relative Risk…
Table 1: data from a cohort study of oral
contraceptive (OC) use and bacteruria among
women aged 16-49 years

Bacteruria
Yes No Total

Current OC use
Yes 27 455 482
No 77 1831 1908
Total 104 2286 2390
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 Relative Risk…
RR = a/(a+b) =27/482 =1.4
c/(c+d) 77/1908
• Interpretation – OC users had 1.4 times the risk or
were 40 percent (i.e 1.4 minus the null value of 1.0)
more likely to develop bacteruria than nonusers
• For cohort studies with person-time units of
follow-up, the RR is calculated analogously as the
ratio of the incidence density in those exposed to
that among those non exposed.
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 Example conti….

Table 2: Data from a cohort study of postmenopausal

hormone use and coronary heart disease among
female nurses

Coronary heart disease

Yes No Person-years

Postmenopausal
hormone use
Yes 30 - 54,308.7
No 60 - 51,477.5
Total 90 105,786.2
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 Example Conti….
RR = Ie =IDe = a/PY1 = 30/54,308.7 = 0.5

Io IDo c/PYo 60/51,477.5

Interpretation: women who used postmenopausal

hormones had 0.5 times, or only half, risk of
developing coronary heart disease compared with
nonusers.

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 Exercises

Relative risk of death among diabetic men vs.

non-diabetic men

RR = 100/189 = 0.529 = 52.9% = 2.1

811/31510.257 25.7%
 Interpret ???

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 Interpretation of RR

A RR of 1 indicates no association

RR > 1 indicates a positive association, or an

increased risk among those exposed to a factor.

RR < 1 indicates negative association, which

means the exposure is preventive
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 Interpretation…
In general the strength of association can be

considered:

High - if the RR is 3.0 or more

Moderate – if the RR is from 1.5 to 2.9

Weak – if the RR is from 1.2 to 1.4

The further away from 1, the stronger the association

between exposure and disease
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2. Odds ratio

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 Odds ratio

Odds: The ratio of the probability of an event's

occurring to the probability of its not occurring

Odds Ratio: The ratio of two odds

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 Odds ratio, cross product ratio…

An indirect measure of a risk in a disease of rare

occurrence.

It is usually used in a case-control and cross-sectional

analytic study designs.

Cases and controls are predetermined and we are

calculating to determine whether cases or controls
are more exposed to a postulated risk factor.
 OR…
In case control study it is usually not possible to calculate the
rate of development of disease given the presence or absence of
exposure

The RR can be estimated by calculating the ratio of the odds of

exposure among the cases to the odds of exposure among the
controls
OR = a/c = ad

b/d bc

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 OR…
 Example

Comparison is made between the number of

people having contact with CSW within the cases
and number of people having contact with CSW
among the controls.

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 Example cont…
Table 3: Data from a case-control study of current oral
contraceptive (OC) use and MI in premenopausal female
nurses

Myocardial infarction
Yes No Total

Current OC use
Yes 23 304 327
No 133 2816 2949
Total 156 3120 3276

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 Example cont…

OR = ad = (23)(2816) = 1.6

bc (304)(133)
Interpretation: women who had MI were 1.6
times more likely to use OCP than individuals
with out MI.

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OR can be used as a valid estimate of
the RR
When the disease is uncommon;

When subjects selected as cases are incident cases;

and

When the cases and controls are from the population.

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 When Can the Odds Ratio be Used
to Approximate the Relative Risk?
D+ D- Total Risk
E+ a b a+b a/a+b

E- c d c+d c/c+d
a a
RR = a+b ≈ b ≈ ad = OR
c c bc
c+d d
For a rare disease, a <<< b, so a+b ≈ b
c <<< d, so c+d ≈ d
Example of the “Rare Disease” Assumption

D+ D- Total Risk
E+ 90 499,950 500,040 0.00018
E– 10 499,950 499,960 0.00002

RR = 90/ 500,040 = 0.00018 = 9.0

10/ 499,960 0.00002

OR = ad = (90)(499,950) = 9.0
bc (499,950)(10)
Example of the “Rare Disease” Assumption

D+ D- Total Risk
E+ 90 50 140 0.643

E- 10 50 60 0.167

RR = 90/140 = 0.643 = 3.9

10/60 0.167
OR = ad = (90)(50) = 9.0
bc (50)(10)
 Comments about Odds Ratio
Approximates Risk Ratio when disease is rare

Can be calculated from case-control and cross-

sectional study (where Risk Ratio, Rate Ratio
cannot be done)

Has good statistical properties

For simple analyses, should not be used if risk ratio

can be calculated

Always further from 1.0, especially if disease is

NOT rare
3. Attributable risk/Risk difference

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 Attributable Risk

The amount of disease that can be attributed to a

certain exposure

Measures of Public Health Impact

Places exposure–disease associations in public health

perspective

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 Attributable Risk (AR) or (RD)
provides information about the absolute effect of
the exposure  AR = Ie – Io

In a cohort study, AR is calculated as the difference

of cumulative incidences (risk difference) or
incidence density (rate difference) depending on
the study design

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 AR/RD…
AR quantifies disease burden in exposed
group attributable to exposure

It provides answers to questions;

What is the risk attributed to the exposure?

What is the excess risk due to the exposure?

It is calculated as risk difference (RD)

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Attributable Risk

I exposed – I unexposed

I = Incidence
 AR cont…
For example in the study of OC use and
bacteruria:
AR=27/482 – 77/1908 = 0.01566 = 1566/105
Interpretation: the excess occurrence of
bacteruria among OC users attributable to
their OC use is 1566 per 100,000.
AR is used to quantify the risk of disease in the
exposed group that can be considered
attributable to the exposure by removing the risk
of disease that would have occurred anyway due
to other causes (the risk in the non-exposed).
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 AR cont…

The interpretation of the AR is dependent on the

assumption that a cause-effect relationship exists
between exposure and disease

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 AR cont…

If AR is greater than 0, this indicates the number

of cases of the disease among the exposed that
can be attributable to the exposure itself, or
alternatively, the number of cases of the disease
among the exposed that could be eliminated if
the exposure were eliminated

Thus, the AR can be useful as a measure of the

public health impact of a particular exposure

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 Interpretation
No

0
Negative Positive

AR = 0
 No Association

AR > 0
 Positive association

AR < 0
Negative association
4.Attributable Risk Percent (AR%)

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 Attributable Risk Percent (AR%)
Also called, attributable fraction/ etiologic fraction.

Determined by dividing the attributable risk by rate

of occurrence among the exposed.

It is the proportion of the disease in the specific

population that is attributable to the exposure.

Useful tool for assessing priority in public health

action.

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 AR%...
estimate the proportion of the disease among the
exposed that is attributable to the exposure, or
the proportion of the disease in that group that
could be prevented by eliminating the exposure
 AR% = AR x 100 = (Ie – Io) x 100
Ie Ie
Example: In the cohort study of OC use and
bacteruria,
AR% = 1566/105 x 1OO = 27.96%
27/482
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 AR% …
Interpretation:

If OC use does cause bacteruria, about 28% of

bacteruria among women who use OCs can be
attributable to their OC use and could therefore
be eliminated if they did not use OCs

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 AR% …
For most case-control studies, the AR cannot be
calculated because the incidence rates among the
exposed and non exposed groups are not
available.
It is, however, possible to calculate the AR% using
the following formula
AR% = (OR – 1) x 100
OR
Example: From the data on OC use and MI, the
OR of MI associated with current OC use was 1.6,
yielding AR% of 37.5%
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 AR% cont…
Interpretation
If OC use causes MI, nearly 38% of MIs among
young women who used OCs could be
attributable to that exposure or could be
eliminated if they were to stop using OCs
If the exposure is preventive, so that Ie is less
than Io, the AR is meaningless.
-However, an analogous measure, the
Preventive Fraction (PF)****, can be defined
 PF = Io – Ie
Io
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5. Population Attributable Risk (PAR)

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 Population Attributable Risk (PAR)
It is measure of the excess rate of a disease in total study
population which is attributable to an exposure
Calculated by multiplying the attributable risk by the
proportion of the population exposed.
It can also be calculated by the rate of the disease
among the total population minus the rate in non-
exposed group.

PAR = Attributable Risk x Proportion of exposed population

PAR = Incidence total popn. – incidence in non-exposed

Population Attributable Rate or Risk (PAR)..

Estimates the proportion of disease occurring in

the total population attributable to the exposure
Helps to determine which exposures have the
most relevance to the health of a community
PAR = IT - Io
Alternatively PAR = (AR) (Pe)
IT -is the overall incidence rate of disease in a population
Io - the incidence rate among the non exposed
Pe - the proportion of individuals in the total population
who have the exposure

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 PAR…
Example: the PAR of bacteruria associated with OC use
(Table 1) is:

PAR = IT - Io = 104/2390 – 77/1908 = 316/105/year

 Or alternatively

PAR = (AR) (Pe) = 1566/105 X (482/2390)=

316/105/year
• -Thus, if OC use were stopped, the excess annual
incidence rate of bacteruria that could be eliminated among
women in this study is 316 per 100,000. 59
6.Population Attributable Risk Percent (PAR
%)

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 4. Population Attributable Risk Percent
(PAR%)
It measures the proportion of disease in a total
population that is attributable to an exposure.

Calculated by dividing the PAR by the incidence of

the disease in the total population and multiplied by
100.
PAR% = Attributable Risk - Proportion of exposed pop. X 100
Risk in population

PAR % = PAR x 100

Risk in population
 (PAR%)

Expresses the proportion of disease in the study

population that is attributable to the exposure and
thus could be eliminated if the exposure were
eliminated.

 PAR% = PAR x 100

IT

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 PAR%...

For example: in the cohort study of OC use and

bacteruria (Table 1)

PAR% = 316 x 100 = 7.3%

4351.5

Thus, if OC use causes bacteruria, about 7 percent

of all the bacteruria in the study population could
be prevented if OC use were eliminated.
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 Exercise-I
“In a low land district, in northern Ethiopia, a total of
25,000 healthy children between 5 and 14 years were
followed for three months. 8,000 of the children were
with in 5 km of a dam constructed for agricultural
irrigation. At the end of the third month a total of 480
children from the nearest to the dam, and 300 children
from these who were far from the dam got malaria.”

Describe the study design?

What measure of association could be done?
Illustrate using a 2x2 table?
Calculate the appropriate Relative Ratio?
Calculate the AR?
 Exercise-II
In an elementary school found in rural Ethiopia, 30 children
between 10 and 13 years who never have sexual intercourse
were found to have HIV positive, another 180 children of
the same age group were negative. Out of the 30 HIV
positives, 24 have history of cultural cuttings or tutoring
where as only 20 out of the 180 with negative test have
history of the above cultural cuttings or tutoring.

Describe the study design?

What measure of association could be done?
Illustrate using a 2x2 table?
Calculate the appropriate Relative Ratio?
Calculate the AR?
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