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1 Epidemiologic Measures of Association Saeed Akhtar, PhD Associate Professor, Epidemiology Division of Epidemiology and Biostatistics Aga Khan University, Karachi, Pakistan Email

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2 Epidemiologic Measures of Association Session Objectives By the end of session students should be able to: Compute & Interpret Relative risk (RR) & Odds ratio (OR) as a measure of association between exposure and Disease Understand when OR approximates RR

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3 Definitions Association A statistical relationship between two or more variables Risk Probability conditional or unconditional of the occurrence of some event in time Probability of an individual developing a disease or change in health status over a fixed time interval, conditional on the individual not dying during the same time period Absolute risk

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4 Association between exposure & Disease Question: Is there an excess risk associated with a given exposure? Objective: To determine whether certain exposure is associated with a given disease Methodology: Use one of the epidemiologic study designs Cohort Case-control

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5 Cohort Study Assess the cumulative incidence (CI E+ ) of disease in an exposed group (absolute Risk) Assess the cumulative incidence (CI E- ) of disease in unexposed group (absolute Risk) e.g. Coronary Heart Disease (CHD) Risk among Smokers 1-year risk of CHD among smokers (CI E+ )* CHD Yes NoTotal Smokers 84 29163000 CI E+ = 84/3000 = 28/1000/yr (1-risk of CHD among smokers) Cont.

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6 CHD Risk among non-smokers 1-year risk of CHD among non-smokers (CI E- ) CHD Yes No Non-smokers 874913 5000 CI E- = 87/5000=17.4/1000/yr (1-yr risk of CHD among non-smokers) Cont.

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7 Assessment of Excess Risk (Two methods) a.Ratio RR (Ratio of two risks; Risk Ratio; Relative Risk) CI E+ / CI E- = 28/17.4 = 1.6 Interpretation of RR Smokers were 1.6 times as likely to develop CHD as were non-smokers b.Difference Difference of two risks (Risk Difference)* CI E+ - CI E- = 28.0 – 17.4 = 10.6

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8 OR (Odds Ratio, Relative Odds) In case-control study (CCS), we cannot calculate the CI or IR, therefore, cannot calculate the RR “directly ” OR as a measure of association between exposure & disease is used when data are collected in case-control study OR can be obtained however, from a cohort as well as a case-control study and can be used instead of RR.

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9 OR in case-control and cohort studies Cohort study Ratio of the proportion of exposed subjects who developed the disease to the proportion of non- exposed subjects who developed the disease Case-control study Ratio of the proportion of cases who were exposed to the proportion of controls who were non-exposed

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10 Odds Ratio Odds are ratio of two probabilities i.e. Probability that event occurs / 1-Probability that event does not occur Odds refer to single entity If an event has the probability P, then the odds of the same event are P/1-P

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11 Derivation of OR in Cohort study P D + | E + = (exposed developed the disease) = a/(a+b) P D - | E + = (exposed did not develop the disease) = b/(a+b) Odds of developing disease among exposed = D+|E+ /1-P D-|E+ = a/(a+b) b/(a+b) = a/b P D + | E - = (non-exposed developed the disease) = c/(c + d) P D - | E - = (non-exposed did not develop the disease)= d/(c + d) Odds of developing disease among non-exposed = = P D+|E - /1-P D+|E - = c/(c+d) d/(c + d) = c/d Odds ratio a/b : c/d = ad/bc

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12 OR in case-control study In case-control study RR cannot be calculated directly to determine the association between exposure and disease. Don’t know the risk of disease among exposed and un-exposed since we start recruiting cases and controls. Can use OR as measure of association between exposure and disease in a case control study.

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13 OR in case-control Study Probability of case being exposed = P case Probability of case being non-exposed =1-P case Odds of case being exposed = P case /1- P case Probability of control being exposed = P control Probability of case being non-exposed =1-P control Odds of control being exposed = P control / 1-P control

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14 Derivation of OR in case-control Study Probability of being exposed among cases = a /(a + c) Probability of being non-exposed among cases) = c /(a + c) Odds of being exposed among cases = a/c Probability of being exposed among controls = b/(b + d) Probability of being unexposed among controls = d/(b + d) Odds of being exposed among controls = b/d OR = ad/bc

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15 Past surgery HCV status HCV+ HCV- Yes 59 168 No 54 48 » 113 216 Example OR in case-control Study

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16 Odds of Past surgery among HCV + P 1 (Surgery among HCV + ) = 59/113 1-P 1 (No surgery among HCV + ) = 54/113 Odds of surgery among HCV + ) = 59/54 = 1.09 Odds of Past surgery among HCV - P 2 (Surgery among HCV - ) = 168/216 1-P 2 (No surgery among HCV - ) = 48/216 Odds of surgery among HCV - = 168/48 = 3.5 OR = 3.50/1.09 = 3.21

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17 When is the OR a good estimate of RR? In CCS, only OR can be calculated as measure of association In Cohort study, either RR or OR is a valid measure of association When a RR can be calculated from case control study? *When exposure prevalence among studied cases in similar and nearly similar to that of disease subjects in the population from which cases are taken. *Prevalence of exposure among studied controls is similar to that of non-diseased population from cases were drawn. *Rare disease (CI < 0.1)

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18 Matched case-control study Matching: In a matched case-control study each case is matched to a control according to variables that are known to be related to disease risk i.e. age, sex, race Data are analyzed in terms of case- control pairs rather than for individual subjects Four types of case-control combinations are possible in regard to exposure history.

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19 Concordant pairs are ignored since they don’t contribute in calculation of effect estimate (i.e. OR) Disconcordant pairs of cases and controls are used to calculate the matched OR. Matched OR = Ratio of discordant pairs = b /c i.e. # of pairs in which cases exposed / # of pairs in which controls were exposed

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20 Example: Risk factors for brain tumors in children. Hypothesis = children with higher birth weights are at increased risk for certain childhood cancers. Cases = Children with brain tumors Controls = Normal children Exposure = Birth weight > 8 lbs.

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21 818 738 8 + 1b Cases<8 1b Total 26 45 1556 71 8+ 1b<8 1b Total Normal Controls Odds Ratio18/7 = 2.57 χ 2 = 4.00; P = 0.046 Interpretation the is same as before Example

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