Measures of association
By Samuel D.(MPH)
Objectives
By the end of this chapter you will be able to:
Organize disease frequency data into a two-by-two table.
List common measures of association and measures of
public health impact
Calculate and interpret absolute and relative measure of
comparison and describe their use
Measures of association
Association
Statistical relationship between two or more variables
Epidemiologic Measure of Association
Quantifies or expresses the strength of the relationship
between an "exposure" and “outcome” of interest as
compared to another
Requires comparing two groups:
Indications of how more or less likely one is to develop
disease
Exposed Vs Unexposed
With outcome Vs Without Outcome
Measures of association….
Exposure examples
in usual sense
ingestion of contaminated food
droplets from someone with active pulmonary tuberculosis
Behaviors
sharing needles, drinking alcohol, multiple sexual partner etc
Treatment
intervention - education program
Trait -genotype
Measures of association
….
Outcome
Disease : e.g., malaria, TB, diabetes
Event: e.g., injury from land mine, car accident
Condition: e.g., blindness
Death
Other
Measures of association….
Types of measures:
Relative difference: risk ratio, rate ratio, odds ratio
► based on the ratio of two measures of disease frequency
exposed / unexposed
Absolute difference: risk difference, rate difference
► difference between two measures of disease frequency
exposed – unexposed
Epidemiologic data are often presented in the form of a two-
by- two table (four-fold or contingency table)
Generally we can have r-by-c table-(row by column)
Measures of
association….
Presentation of data in a two-by-two
table
Disease
Yes No Total
Exposure a b
Yes a+b
No c D c+ d
Total a+c b+d a+b+c+
d
What is every letter and summation of letters stand for? Think for a
while and compare your attempt with the provided
Measures of
Cells association….
A= Exposed, and diseased
B= Exposed, Not diseased
C= Not exposed, but diseased
D= Not exposed, Not diseased
Marginal totals
a+b= Exposed
c+d= Non-exposed
a+c= Diseased
b+d= Non-diseased
Grand total
n = a+b+c+d
Measures of association….
Presentation of data in a 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 non-exposed
subjects are provided rather than the total numbers of
individuals in each group.
Presentation of data in a two-by-two
table
Diseas
e Yes No Person-time units
Exposure
ye PY1
s
N
PY2
o
a+ -
PY=person- c
year
How strong is the association?
Relative risk (Risk ratio)
Indicate the likelihood of developing the disease in
the exposed group relative to those who are not
exposed
used for longitudal study
For a cohort study with count data RR = Ie = a/(a+b)
Io c/(c+d)
Example
Table 1: data from a cohort study of oral
contraceptive (OC) use and bacteruria among
women aged 16-49 years
Bacteruria
Current OC use Total
Yes No
Yes 27 455 482
No 77 1831 1908
Total 104 2286 2390
Calculate RR and interprate it?
Example
RR = a/(a+b) = 27/482 =1.4
c/(c+d) 77/1908
Interpretation –
OC usershad 1.4 times riskof developing bacteruria than
nonusers
OC users were 40 percent (i.e 1.4 minus the null value of 1.0)
MORE likely to develop bacteruria than nonusers.
OR 60% LESS likely to develop bacteruria among OC users.
Examples
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
Example cont…
RR = Ie =IDe = a/PY1 = 30/54,308.7 = 0.5 Io = IDo c/PY2
60/51,477.5
Interpretation: women who used postmenopausal
hormones had
0.5 times, or only half, the riskof developing coronary
heart
disease compared with nonusers.
Example cont…
RR= 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
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 to1.4
Odds ratio(OR)
In case control study RR can be estimated by calculating the
ratio of the odds of exposure among the cases to that among
the controls
OR = a/c = ad
b/d bc
OR indicates the likelihood of having been exposed among
cases relative to controls
Risk = the chances of something happening / the chances of all things
happening
Odds = the chances of something happening /the chances of it not
happening
Odds ratio…
Example:
Table 3:Data from a case-control study of current oral
contraceptive (OC) use and MI in pre-menopausal female
nurses.
Myocardial infarction
Yes No Total
Current OC use
Yes 23 304 327
No 133 2816 2949
Total 156 3120 3276
Odds ratio…
OR = = (23)(2816) =
ad 1.6
bc (304)(133)
Interpretation: womenwho were current OC usershad
a
risk of MI 1.6 times that of nonusers
Odds ratio…
OR is a valid estimator of RR if:
Cases are incident and drawn from a known and
defined population
Controls are drawn from the samedefined population
and would have been in the case group if they had the
disease;
Controls are selected in an unbiased way
the disease is rare
What is the excess risk among
exposed individuals?
Attributable risk(AR)
Definition:
The amount of disease that canbe attributed to a
certain exposure.
Places exposure–disease associations from public health
perspective
Quantifies expected reduction in disease occurrence if
harmful exposure could be eliminated
It is calculated as risk difference (RD)
Risk Difference = Risk in exposed - Risk in non-exposed
= A / (A + B) – C / (C + D)
Example
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
Attributable risk(AR)….
AR=27/482 - 77/1908 = 0.01566 = 1566/105
Interpretation: The excess occurrence of
Bacteriuria among OC users attributable to their
OC use is 1566 per 100,000.
Attributable Risk…
Relative Risk: (Multiplicative)
RR=Ie / Io
(strength, cause ?
)
Attributable Risk: (Additive)
AR=Ie-Io
(impact?).
Attributable Risk…
The interpretation of the AR is dependent on the assumption
that a cause- effect relationship exists between exposure and
disease
AR=0 - no association
AR > 0 indicates
I. the number of cases of the disease among the exposed
that can be attributable to the exposure itself, OR
II. 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
Presence of associations
Relative risk 1
Odds Ratio 1
Attributable risk 0
What proportion of cases is attributed to the
actual exposure among exposed people?
Attributable Risk Percent (AR%)
AR% is an attributable risk expressed as a percentage of risk
in exposed
What is the proportion of disease among the exposed which "X" can
be attributed to the exposure?
Synonyms
Attributable proportion
Attributable fraction
Etiologic fraction (EF)
AR% = AR x 100 = (Ie – Io) x 100
Ie Ie
AR%….
For most case-control studies, the AR cannot be calculated
It is, however, possible to calculatethe AR% using the
following formula
AR% = (OR – 1) x 100
OR
Example:From the data on OC useand MI, the OR of MI
associated with current OC use was 1.6,
yielding AR% of 37.5%
AR%...
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
What is the excess risk among the
general population that is due to
exposure of interest?
Population Attributable Rate or Risk (PAR)
• estimates the excess rate of disease in the total study
population that is attributable to the exposure.
• helps to determine which exposures have the most
relevance to the health of a community
• PAR = IT - I
o
• Alternatively PAR = (AR) (Pe) e=proportion of the population that is exposed
PAR…
• Example: the PAR of bacteruria associated with OC use
(Table 1) is:
• PAR = IT - I = 104/2390 – 77/1908 = 316/105/year
o
• 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.
What proportion of cases is attributed to
the actual exposure among the general
population?
Population Attributable Risk Percent (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
Example
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
PAR%…
• For example: in the cohort study of OC use and
bacteruria (Table 1)
• PAR% = 316/105 x 100 = 7.3%
4351.5/105
• 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.
