* Epidemiologic Measures of Association
Saeed Akhtar, PhD Associate Professor, Epidemiology Division of Epidemiology and Biostatistics Aga Khan University, Karachi, Pakistan Email* 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* 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* 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* Cohort Study
Cont.* CHD Risk among non-smokers 1-year risk of CHD among non-smokers (CIE-) CHD Yes No Non-smokers 87 4913 5000 CIE-= 87/5000=17.4/1000/yr (1-yr risk of CHD among non-smokers)
Cont.
* Assessment of Excess Risk (Two methods) Ratio RR (Ratio of two risks; Risk Ratio; Relative Risk)CIE+ / CIE- = 28/17.4 = 1.6Interpretation of RR Smokers were 1.6 times as likely to develop CHD as were non-smokersDifferenceDifference of two risks (Risk Difference)* CIE+- CIE-= 28.0 – 17.4 = 10.6* 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.
* 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* 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* 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 = = PD+|E-/1-P D+|E- = c/(c+d) d/(c + d) = c/d Odds ratio a/b : c/d = ad/bc
* 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.
* OR in case-control Study
Probability of case being exposed = Pcase Probability of case being non-exposed =1-Pcase Odds of case being exposed = Pcase/1- Pcase Probability of control being exposed = Pcontrol Probability of case being non-exposed =1-Pcontrol Odds of control being exposed = Pcontrol/ 1-Pcontrol
* 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
* Past surgery HCV status HCV+ HCV- Yes 59 168 No 54 48 113 216
Example OR in case-control Study
* Odds of Past surgery among HCV+ P1 (Surgery among HCV+) = 59/113 1-P1 (No surgery among HCV+) = 54/113 Odds of surgery among HCV+ ) = 59/54 = 1.09 Odds of Past surgery among HCV- P2 (Surgery among HCV-) = 168/216 1-P2 (No surgery among HCV-) = 48/216 Odds of surgery among HCV- = 168/48 = 3.5 OR = 3.50/1.09 = 3.21
* 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)
* 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.
* 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 /ci.e. # of pairs in which cases exposed / # of pairs in which controls were exposed
* 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.
* 8
18
7
38
8 + 1b
Cases
<8 1b
Total
26
45
15
56
71
8+ 1b
<8 1b
Total
Normal Controls
Odds Ratio
18/7 = 2.57 χ2 = 4.00; P = 0.046Interpretation the is same as before Example