Measures of association

Shikur Mohammed

(BSc, MPHE)

1prepared by Shikur Mohammed

(BSc,MPHE)2/2/2015

Measures of Association

� It is a single summarizing numberthat reflects the

strength of a relationship b/n variables

� The relative risk and the odds ratio are appropriate

measures of thestrength of the association b/n

categorical variables

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(BSc,MPHE)22/2/2015

Measures of Association…

� Most of epidemiological data are categorical

(nominal) variables; and presented in two-by-two

tableform. Do not forgetascontinuousvariablescantableform. Do not forgetascontinuousvariablescan

be condensed (transformed) to categorical variable

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Presentation of data in a two-by-two table

Disease status

Yes No Total

Exposure

Yes a+ba bYes a+b

No c+d

Total a+c b+d a+b+c+d

a b

c d

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How strong is the association?

1. Relative risk (Risk ratio)

� Indicate the likelihood of developing the disease in

the exposed group relative to those who are not

exposed

� For a cohort study with count dataFor a cohort study with count data

RR = Ie = CIe =a/(a+b)

Io CIo c/(c+d)

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Example

Table 2: data from a cohort study of oral contraceptive (OC) use and

bacteruria among women aged 16-49 years

Bacteriuria

Yes No Total

Current OC use

Yes 27 455 482

No 77 1831 1908

Total 104 2286 2390

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Example cont…

RR = a/(a+b) =27/482 =1.4

c/(c+d) 77/1908

� Interpretation: OC users had 1.4 times the risk� Interpretation: OC users had 1.4 times the risk

more likely to develop bacteriuria than

nonusers

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Interpretation of risk ratio

RR= 1 indicates no association

RR > 1 indicates a positive association.

RR < 1 indicates negative association

In general the strength of association can be

considered:

In general the strength of association can be

considered:

High - if the RR is >3

Moderate – if the RR is from 1.5 to 2.9

Weak – if the RR is from 1.2 to 1.4

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2. Odds ratio

� 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 = adOR = a/c = ad

b/d bc

� OR indicates the likelihood of having been

exposed among cases relative to controls

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(BSc,MPHE)2/2/2015

ExampleTable 3: Data from a case-control study of current oral

contraceptive (OC) use and MI in pre-menopausal female

nurses

Myocardial infarction

Yes No TotalYes 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)

� Those women with MI are 1.6 times more� Those women with MI are 1.6 times more

likely to be OC user when compare with

women without MI

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Odds Ratio as estimator of Relative RiskOdds Ratio as estimator of Relative Risk

OR is a valid estimator of RR if:

1. Cases are incident and drawn from a known

and defined population (from cohort study)

2. Controls are drawn from the same defined2. Controls are drawn from the same defined

population; Controls are selected in an

unbiased way

3. the disease is rare

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3. Attributable Risk (AR)

What is the excess risk among exposed individuals?

The attributable risk is used to quantify the risk of

disease in the “exposed” group that can be

considered attributable to the exposure byconsidered attributable to the exposure by

removing the risk of disease that would have

occurred anyway due to other causes

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How to calculate

� Attributable risk is defined as the difference between the

incidence rates (or cumulative incidence) in the exposed

and non-exposed.

AR = Ie – Io or AR = CIe-CIo

Where Ie = incidence rate in the exposed

Io = incidence rate in the non-exposed

� AR is used to quantify the risk of disease in the exposed

group

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(BSc,MPHE)14

Interpretation of the AR

� AR=0 - no association

� AR > 0, AR is the number of cases of the disease

among the exposed that could be eliminated if

the exposure were eliminated. Thus, the AR is

useful as a measure of public health impact of anuseful as a measure of public health impact of an

exposure

• AR < 0 the exposure is preventive

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For example

Recall the OC use and bacteriuria example:

AR=27/482 – 77/1908 = 0.01566 = 1566/105

� Thus, the excess occurrence of bacteriuria among OC

users attributable to their OC use is 1566 per

100,000.100,000.

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AR% (Attributable percent or Etiologic fraction)

What proportion of cases is attributed to the actual

exposure among exposed people?

� The proportion of the disease among the exposed

that is attributable to the exposurethat is attributable to the exposure

� It is an estimate of the proportion of the disease

in the exposed group that could be prevented by

eliminating the exposure

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How to calculate

• AR% = ( Ie – Io)/Ie or AR% = (RR-1)/RR*100

Where RR is the risk ratio or relative risk of the

exposure and disease (cohort study)

Preventive fraction:

• When exposure is preventive (AR is less than 0) • When exposure is preventive (AR is less than 0)

then the analogous figure to the AR% is the

preventive fraction (AF/PF):

PF% = Io – Ie/Io*100

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(BSc,MPHE)18

Example

Recall OC use and bacteriuria example:

• AR% = AR X 100= (Ie – Io) X 100

Ie Ie

AR% = 1566/105x 1OO = 27.96%

27/48227/482

� Interpretation: If OC use does cause bacteriuria, about 28% of

bacteriuria 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% in case-control study

� For most case-control studies, the AR cannot be

calculated

� It is, however, possible to calculate the AR% using the

following formula

AR% = (OR – 1) x 100AR% = (OR – 1) x 100

OR

20prepared by Shikur Mohammed

(BSc,MPHE)2/2/2015

Example (recall OC & MI example)

� From the data OR of MI associated with current OC

use was 1.6, yielding AR% of 37.5%.

� Interpretation: If OC use causes MI, nearly 38% of

MIs among young women who used OCs could beMIs among young women who used OCs could be

attributable to that exposure or could be eliminated

if they were to stop using OCs

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