1

MEASURE OF ASSOCIATION

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 Measures of associations
2

At the end of this section, you are expected to be able to

 Define different measures of associations

 Calculate and interpret associations using relevant

formulae
 Describe different impact measures and discuss their

importance
 Calculate and interpret impacts using relevant

formulae.

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3

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 Measures of associations…
4

 The key to epidemiologic analysis is comparison.

 A measure of association quantifies the relationship
between exposure and disease among the two groups.
 Exposure is used loosely to mean not only exposure to
foods, mosquitoes, a partner with STI, or a toxic waste
dump, but
 Also, inherent characteristics of persons (age, race, sex),
or (socioeconomic status or access to medical care)...
 Reference group is the unexposed

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 Exposure
5

Exposure in usual sense

e.g., ingestion of contaminated food
Behaviors
e.g., sharing needles, drinking alcohol etc
Treatment
e.g., intervention - education program
Trait
e.g., genotype

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 Outcome
6

Outcome
Disease
– X e.g., malaria, TB
– X e.g., diabetes
Event
– X e.g., injury from land mine,
– car accident
Condition
– X e.g., blindness
Death
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 Exposure and outcome variables
7

▪ The hypothesis to be tested in a study usually defines

which variable is assumed to be cause and which
variable is the effect (outcome)
▪ The definition of a variable therefore depends on the
study hypothesis:
▪ A variable may be exposure in one hypothesis, a
confounder in another, and outcome in a third
hypothesis
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8 3/25/2025
 MEASURES OF STRENGTH OF ASSOCIATION
9

▪ Association : occurrence of statistical relationship

between the disease and the risk factor
▪ Exposure / risk factor Outcome
▪ Is there a relationship between the exposure and
outcome of interest?
▪ The occurrence of disease in a group of people
exposed to a risk factor is compared to those un
exposed to a risk factor.

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 Description of Relationships
10

„ Variables can be related or unrelated to one

another
„ 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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 Related or unrelated?
11

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 Statistically Significant or Not?
12

„ Statistically significant
 association is unlikely to be due to chance

But remember:

 Statistically significant means that the association is

not likely due to chance

 It is dependent on the strength of the association

and sample size

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Testing and measuring the association b/n risk factor and diseases
13

 Epidemiologic data are often presented in the form

of two-by-two (contingency) table
 2X2 table contains 4 cells → A, B, C, D

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14

 Statistical tests like Chi-square show mainly the

presence or absence of association….CI too
 The strength of association is assessed by calculating
Relative Risk (RR), Odds Ratio (OR) or other
measures of association.

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 Measurement of risk:
15

 A number N of subjects exposed to a factor of risk for a period

of time T. The risk of becoming ill is the proportion of people
in this cohort of N people, becoming ill (new cases) during the
period T.
Risk (R) = number with the event or
Number observed
= The chances of something happening
The chances of all things happening
The risk is therefore a proportion, its minimum value is zero and
its maximum value is 1.

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 Risk Vs Rate
16

 Risk is a probability, lying between 0 and 1 that gives the

likelihood of a change in health status for an individual
over a specified period of follow-up.
 Rate describes how rapidly new events are occurring in
a population.
 A rate is not a probability, is always non-negative, has
no upper bound (i.e. 0 < Rate < ∞+ ) and is defined in
units of time, such as years, months, or days.

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 Relative Risk (RR)
17

▪ Risk: The probability of an event occurring over time

▪ Risk Ratio: The ratio of two risks or relative risk

▪ Relative risk .It is defined as the ratio of the incidence of

disease in exposed group divided by the incidence of disease in

non exposed group
Example:-
▪ Comparison between the incidence of HIV among people

having contact with CSW and incidence of HIV among people

having no contact with CSW.

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18
Relative Risk (RR) or Risk Ratio
 It is a direct measurement of a risk
 It is usually used in Cohort and experimental study design

 RR = Incidence among exposed (Ie)

Incidence among non-exposed (Io)

RR = a/a+b = CIe/Cio, or
c/c+d
 Relative Risk (RR) or Risk Ratio
19

 The Relative risk estimates the magnitude of an

association between exposure and disease and indicates
the likelihood of developing the disease in the exposed
group relative to those who are not exposed.

 When the risk in the exposed and the risk in the non
exposed is known, the ratio of these risks can be
calculated and represent the relative risk.

Relative Risk (RR) =Risk in the exposed

Risk in the non exposed

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 Calculation of the relative risk
Disease

Referring the prototype two-by- Yes No

two table presented above a b a+b

yes
Exposed
c d c+d

No
risk in exposed =a/a+b
a+c b+d a+b+c+d

Risk in non-exposed=c/c+d

Therefore, RR= a/a+b

c/c+d
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20
 Example
21

Table 1: Data from a cohort study of oral

contraceptive (OC) use and bacteruria among
women aged 16-49 years

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 Example cont…
22

▪ 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

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 Example cont.…
23

Table 2: Data from a cohort study of

postmenopausal hormone use and coronary heart
disease among female nurses

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 Example cont.…
24

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 Odds Ratio (OR)
25

▪ 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
▪ Indicates the likelihood of having been exposed among
cases relative to controls
▪ It is possible to calculate either exposure or disease odds
ratio, which are exactly the same
Exposure OR =odds of disease in exposed
odds of disease in non-exposed
Disease OR=odds of disease in exposed
odds of disease in non-exposed

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 Odds Ratio…
26

▪ It is an indirect measure of a risk in a disease of rare

occurrence
▪ It is usually used in a case-control and cross-sectional
studies
▪ Cases and controls are predetermined and we are
calculating to determine whether cases or controls are
more exposed to a postulated risk factors

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 Odds ratio…
27

 The risk of becoming ill cannot be calculated in a case

control study, the odds of being ill can be.
 The ratio of the odds in the exposed over the odds in the non
exposed is called the Odds Ratio and can be calculated.
Calculation of the Odds Ratio
 Odds of being ill in exposed=__a__
b
 Odds of being ill in non exposed = __ c__
d
 Odds ratio (OR) =_Odds in exposed
Odds in non exposed
Odds Ratio = ad/ bc 3/25/2025
28

 In case control studies, RR can be estimated by

calculating the ratio of the odds of exposure among the
cases to that among the controls i.e

In case-control studies, the OR is given by the exposure

odds for the cases divided by the exposure odds for
controls. (derivate from 2*2 table)

RR= OR = a/c = ad
b/d bc
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 Odds Ratio…
29

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 Example:

30

 Table 6: This table shows data from case control study of oral
contraceptive (OC) use & myocardial infarction in pre-
menopausal female nurses
Myocardial infarction
yes No Total
Yes 23 304 327

Current No 133 2816 2949

OC use total 156 3120 3276
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 Odds ratio cont…
31

Calculate OR
OR = ad = (23) (2816) = 1.6
bc (304) (133)

Interpretation: Women who were current OC users had 1.6 times higher
risk of developing myocardial infarction when compared to non-users
of OC

RR can be estimated by OR if the following conditions are fulfilled:

 The controls are representative of the general population

 The selected cases are representative of all cases

 The disease is rare

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 Interpretation
32

 OR=1 There is no association between exposure and

disease. That means the odds of developing disease in the
exposed and non-exposed groups are identical.
 OR>1 There is an association between exposure and
disease and the exposure is associated with an increase of
the odds of the disease.
 OR<1 There is an association between exposure and
disease and the exposure is associated with a decrease of
the odds of the disease.

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 Strength of association
33

➢ In general strength of association can be considered

as:

 High if RR>3
 Moderate if RR is between 1.5 & 2.9
 Weak if RR is between 1.2 & 1.4
34

 An odds ratio of 0.75 means that in one group the

outcome is 25% less likely or
 An odds ratio of 1.33 means that in one group the
outcome is 33% more likely.“
 The odds of outcome among exposed is 1.33 times
higher than among non exposed.
 The odds that a case exposed is about 1.33 times
the odds that a control subjects exposed.

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 Odds Ratio…
35

➢ Odds ratio could be used as a valid estimate of the relative

risk, when:
 The outcome is rare event
 The cases and controls were drown from representative
population
 Cases are incident and drawn from a known and defined
population
 Controls are drawn from the same defined population and
would have been in the case group if they had the disease
 Controls are selected in an unbiased way

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 Impact Measures
36

 Attributable Risk (AR)

 Attributable Risk Percent (ARP)
 Population Attributable Risk (PAR)
 Population Attributable Risk Percent (PARP)

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Measures of potential impact
Measures of potential impact among the exposed:
 AR: Attributable risk = (Ie – Io)
 AR%: Attributable risk % = (Ie – Io) / Ie = AR / Ie = (RR-1) / RR

Measures of potential impact in the whole population:

 PAR: Population attributable risk = It – Io
 PAR%: Population attributable risk % = PAR / It
◼ Alternative formula: Pexp (RR–1) * 100
Pexp (RR–1) + 1
Where Pexp = Prevalence of exposure in the population
37
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41 3/25/2025
 Exercise:
42

Mortality rates per 100,000 person-years

from Lung ca and coronary artery disease:
(person year calculated in cohort study)

Smokers Nonsmokers Ratio Difference

RR AR
Lung Ca 48.3 4.5 10.8 44

CAD 294.7 169.5 1.7 125

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 Exercise
43

 Which disease mortality is more strongly associated

with cigarette smoking? Why?
 If the number of deaths attributable to smoking is
used as an index of public health importance which
disease has more significance?

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 Answer
44

 Which disease mortality is more strongly associated

with cigarette smoking? Lung ca Why? RR=10.8
 If the number of deaths attributable to smoking is
used as an index of public health importance which
disease has more significance? CAD b/c AR=125

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Attributable risk vs. Relative Risk

 Relative risk
◼ Provides a measure of the strength of an association between an
exposure and a disease
◼ Helps to evaluate the causal relationship between an exposure and
a disease
◼ Magnitude of relative risk does not predict magnitude of
attributable risk
 Attributable risk
◼ Provides a measure of the public health impact of an exposure on
the exposed group: if the exposure where removed, how
much of the disease burden will be reduced?
◼ Assumes the exposure is causal
◼ Attributable risks for different risk factors do not add up to 100%
(because multiple causes interact to cause disease – see 4
later) 5
 I. Attributable Risk (AR)
46

▪ Risk difference (RD) indicates how much of the risk is

due to ( attributable to) the exposure alone
▪ Quantify the excess risk in the exposed that can be
attributable to the exposure
▪ Is the difference between the disease rate in
exposed groups and the disease rate in non-exposed
groups
▪ AR provides information about the absolute effect of
the exposure or the excess risk of disease in those
exposed

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 Attributable Risk (AR)
47

 AR provides information about the absolute effect of

the exposure or the excess risk of disease in those
exposed.

 AR = Incidence among exposed (Ie) _

Incidence among non-exposed (Io)

 AR quantifies the risk of disease in the exposed group

that is attributable to the exposure by removing the
risk of disease that occurs due to other causes.
 Attributable Risk…
48

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49 3/25/2025
Attributable Risk in Cohort Studies

 Attributable risk (AR)

◼ Synonym (and conceptually): AR = risk difference (RD)
◼ Provides information about absolute effect of an exposure
removal
 The excess risk of disease in the exposed
AR = Iexposed – Inonexposed
= Ie – Io
The incidence measure can be either CI (cumulative incidence)
or ID (incidence density)

5
0
Example: measures of effect in case-control studies

Overall, 57.4% (27/47) of all infants

who died of SIDS usually slept in the
prone position as opposed to 24.6%
(35/142) of control infants
5
1
 Attributable Risk example (Cohort data)
SIDS No SIDS Column Cumulative incidence among exposed
total (prone) = 1.06% [10.6 per 1000]
Prone 9 837 846
Cumulative incidence among unexposed =
0.34% [3.4 per 1000]
Non- 6 1755 1761
prone
Risk difference or attributable risk or
Row total 15 2592 2607 excess risk (AR) = 0.7% or 7 per
1000

AR has same units as the incidence measure

used (dimensionless if CI; time-1 if ID)
Interpretation: Among every 1000 babies that
sleep prone, there are 7 excess cases of
SIDS attributable to prone sleeping.
Note: the interpretation of the AR is dependent
upon the assumption that the risk factor
(in this case prone sleeping position) is
 Presence of Association
53

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 II. Attributable Risk Percent (AR %)
54

▪ The attributable proportion, also known as the

attributable risk percent, is a measure of the public
health impact of a causative factors
▪ It is the proportion of additional case observed
because of the exposure
▪ It represents the expected reduction in disease if the
exposure could be eliminated

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 Attributable Risk Percent
55

 Estimates the proportion of the disease among the

exposed that is attributable to the exposure, or

the proportion of the disease in the exposed group

that could be prevented by eliminating the exposure
AR % = (Ie - Io) X 100
Ie
 Attributable Risk Percent…
56

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 Attributable Risk Percent (AR%)
57

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AR% in a cohort study

 Suppose you wish to estimate, among exposed babies (prone), what

proportion of cases of SIDS are due to prone posture?
 In other words, among all of the cases among the exposed, what proportion
is represented by the excess cases?
 The appropriate measure is the attributable risk % (AR%)
AR% = (AR) / Ie x 100 AR% = (Ie – Io) / Ie x 100
 Alternative formulation (very helpful when incidence measures are not
available – e.g. case-control study):
AR% = (RR – 1) / RR x 100

AR% is also known as “Attributable Fraction (Exposed)” – defined as “the

proportion by which the incidence rate of the outcome among those
exposed would be reduced if the exposure were eliminated” [Porta, 2008]

5
8
Attributable Risk Percent in a cohort study

 Suppose you wish to estimate, among exposed babies

(prone), what proportion of cases of SIDS are due to prone
posture?
 The appropriate measure is the attributable risk % (AR%)
AR% = (AR) / Ie x 100
= {(Ie – Io) / Ie} x 100
= (0.7%) / (1.06%) x 100
= 66%
 Interpretation: Among the prone sleeping babies, 66% of the
cases of SIDS are attributable to the prone sleeping posture
[so, not all SIDS is due to prone posture; in about a third of
the cases, something other than prone posture is responsible]
 Alternative formulation:
AR% = (RR – 1) / RR x 100
= {(3.12 – 1) / 3.12} x 100 = 67% 32
Attributable Risk Percent in a case-control
study
 In case control studies, it is (generally) not possible to estimate incidence
rates.
 Therefore, it is not possible to directly estimate attributable risk (AR) in
case control studies.
 However…it is possible to estimate attributable risk percent (AR%) using
the following alternative expression for AR% (Note: this formula may
also be used in cohort or in case control studies).
AR% = (RR – 1) / (RR) x 100
 In a case control study [previous example on SIDS], it will be:
 (OR – 1) / (OR) x 100
AR% = (4.13 – 1) / (4.13) x 100 = 76%
 Interpretation: Among babies that sleep prone, 76% of cases of SIDS are
due to prone sleeping posture. [note 76% is higher than the estimate in
the cohort study (66%) – because the case-control study reported a
stronger association (OR = 4.13) than the cohort study (RR =3.12)]
 Question: why did the case-control study report a stronger effect?? 60
 III. Population attributable risk
61

 We want to study health related problem in a

community
 But we do the study in a sample of a population
 We should conclude our result to the population
where the sample come from.
 When we discuss about population attributable risk,
we are trying to generalize what we found in our
sample

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 Population attributable risk (PAR)
62

▪ Excess risk of disease in total population attributable to

exposure to risk factors
▪ Reduction in risk factors achieved if total population was
entirely unexposed

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63 3/25/2025
Measures of effect: Population attributable risk

 Population attributable risk (PAR): basic goal is to

estimate the burden of disease due to the exposure on
the entire population (not just among the exposed as
is done with “attributable risk”)
PAR = Itotal – Iunexposed = It – Io
 Another formulation:
PAR = (AR)(Pe)
Utility of the measure: to determine which exposures have the
most relevance to the health of a community: if the exposure
was removed from the population, then how much of the
disease in the population will be averted?

6
4
 Measures of effect: Population attributable
risk

SIDS No SIDS Column Cumulative incidence among exposed

(prone) = 10.6 per 1000
total
Prone 9 837 846 Cumulative incidence among unexposed =
3.4 per 1000
Non- 6 1755 1761
prone Cumulative incidence in the population =
15/2607 = 5.8 per 1000
Row total 15 2592 2607
Risk difference or attributable risk or
excess risk (AR) = 7 per 1000

PAR = It – I0 = 5.8 – 3.4 = 2.4 per 1000

▪Interpretation: Among every 1000 babies in a population,

there are 2 excess cases of SIDS attributable to prone
sleeping: if all babies in a population were made to sleep
on their backs, then 2 SIDS cases can be averted for every 1000 babies 36

▪ Note: PAR will always be less thanAR. Why?

 Answer
66

 Because PAR accounts for the fact that not

everyone in the population is exposed to the risk
factor
 PAR depends on the prevalence of the exposure in
the population
 If the exposure is rare PAR will be much smaller
than AR and if everyone is exposed ,PAR= AR
 Prevalence of exposure always between o and 1

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 Example
67

 Suppose in exposed group = 20%

 Risk in unexposed group= 10%
 Prevalence of exposure in the population = 50%
 AR= 20%_10% = 10%
 Risk in total population = (20%x50%)+(10%x50%)
= 15%
 PAR= 15%_10%= 5%

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 Population Attributable Risk (PAR)
68

 PAR shows the effect of eliminating the exposure on

the population as a whole,
 PAR takes into account not only the actual incidence rate
of the outcome but also the prevalence rate of the
exposure

 PAR = Incidence rate in total population minus

incidence rate in non-exposed population
 PAR = AR X prevalence rate of the exposure

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 IV. Population Attributable Risk Percent (PAR %)
69

▪ PAR% estimates the proportion of disease in the

study population that is attributable to the exposure
and thus could be eliminated if the exposure were
eliminated
▪ Population attributable risk percent is the proportion
of the risk in the population that is related to the
exposure to the postulated risk factor

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 Population Attributable Risk Percent
70

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 Population Attributable Risk Percent…
71

▪ Proportion of cases in the population attributable to

the exposure to the risk factor
▪ PAR expressed as a percentage of total risk in
population

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 Measures of effect: Population attributable risk percent

▪ Population attributable risk percent (PAR%)

– Definition: the proportion of disease in the study population that is attributable
to the exposure and that, theoretically, would be eliminated if the exposure were
removed.
– PAR% = (PAR / It) x 100
– PAR% is also known as “Attributable Fraction (Population)” – defined as “the proportion
by which the incidence rate of the outcome in the entire population would be reduced if
the exposure were eliminated” [Porta, 2008]
▪ SIDS example
▪ PAR = 2.4 per 1000
▪ PAR% = 2.4 / 5.8 x 100 = 41%
– Interpretation: Making all babies sleep on their back would eliminate 41% of
all cases of SIDS in the population.
– Recall that the AR% was 66% (earlier slides)—obviously, the impact on the
exposed group (measured by AR%) is greater than on the whole population
37
(PAR%). Why?
 Example
73

 Because PAR% accounts not everyone in the population is exposed

 Suppose in exposed group = 20%
 Risk in unexposed group= 10%
 Prevalence of exposure in the population = 50%
 Prevalence of exposure in case 66.7%
 AR%= 20%_10% x 100= 50%
10% (50%od disease risk in exposed group is due to the
exposure)
 Risk in total population = (20%x50%)+(10%x50%) = 15%
 PAR%= 15% _ 10% x 100=33.3%
15%

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 Example
74

Table 1: data from a cohort study of oral

contraceptive (OC) use and bacteruria among
women aged 16-49 year

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 Calculate
75

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 Cont.…,
76

3. The PAR of bacteruria associated with OC use is:

PAR = IT - Io = 104/2390 –77/1908 = 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.
4. PAR% = PAR x 100
IT
= 316/105 x 100 = 7.3%
351.5/105
- 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.

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 Interpretation of measure of association
77

RR/ OR:
1. RR/ OR > 1, the exposure is risk
2. RR/ OR = 1, there is no association
3. RR/ OR < 1, the exposure is preventive
4. If confidence interval of RR/ OR includes the null
(1), then there is no statistical significant association
5. If confidence interval of RR/ OR is far from the null
(1), it is a sign of presence of statistical significant
association between exposure and outcome
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 Relative risk vs. population attributable risk

▪ Relative risk
– Provides a measure of the strength of an association between an
exposure and a disease
– Helps to evaluate the causal relationship between an exposure and a
disease
– Magnitude of relative risk does not predict magnitude of attributable
risk
– PAR%
– Provides a measure of the public health impact of an exposure on the
entire population
– Assumes the exposure is causal
– A strong RR may not translate to a large PAR% if the exposure is not
widely prevalent in the population
– Conversely, a weak RR may have a big PAR% if the exposure is very 38
common (e.g. smoking, obesity, air pollution)
 Self-Exercise
79

▪ Suppose that a cohort study of 400 smokers and 600 non-

smokers documented the incidence of hypertension over a
period of 10 years.
 The following table summarizes the data at the end of the
study period:

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 Cont..,
80

▪ Based on the above information, calculate and

interpret the following measures of association:
1.Relative risk (RR)=6
2. Attributable risk (AR) and/or preventive fraction
(PF)=0.25
3. Attributable risk percent (AR%)=83%
4. Population attributable risk (PAR)=0.1
5. Population attributable risk percent (PAR%)=67%

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 References
81

 Hennekens CH, Buring JE. Epidemiology in Medicine

 Woldemichael K et al. Epidemiology for health
science students.
 Leon Gordis. Epidemiology. 3rd edition.

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82

Thanks
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