MEASURES OF ASSOCIATION

1. MEASURES OF ASSOCIATION Dr Santosh K Yatnatti

2. ASSOCIATION • An association is present if probability of occurrence of a variable depends upon one or more variable. • (A dictionary of Epidemiology by John M. Last) • Concurrence of two variables more often than would be expected • (park)

3. ASSOCIATION • If two attributes say A and B are found to co-exit more often than an ordinary chance. • It is useful to consider the concept of correlation. • Correlation indicates the degree of association between two variables.

4. Types Of Association • 1. Spurious association • 2. Indirect association • 3. Direct association • One-to-one causal association • Multifactorial causation

5. Spurious Association • This is an association which appears due to improper comparison. • Observed association between a disease and suspected factor may not be real. E.g.; Neonatal mortality was observed to be more in the newborns born in a hospital than those born at home. This is likely to lead to a conclusion that home delivery is better for the health of newborn. However, this conclusion was not drawn in the study because the proportion of “high risk” deliveries was found to be higher in the hospital than in home.

6. Indirect Association • It is a statistical association between a characteristic of interest and a disease due to the presence of another factor i.e. common factor (confounding variable). E.g.: Neonatal mortality (A) was found to be associated with maternal age above 30 years (B) and with birth order 4 and above (c). It was also shown that the attribute B and C were associated with each other. Salt intake  Hypertension CAD

7. Direct Association • The association between the two attributes is not through the third attributes. • When the study reveals it is not a spurious association. • When the disease is present, the factor must also be present.

8. Direct Association Is Classified Into Two Types One-to-one Casual Relationship: • The variables are stated to be casual related (AB) if a change in A is followed by a change in B. • When the disease is present, the factor must also be present. • A single factor or cause may lead to more than one outcome. • Salt intake-------------- Hypertension.

9. Direct Association Is Classified Into Two Types Multifactorial causation: • Alternative causal factors each acting independently. E.g. In lung cancer more than one factor (e.g. air pollution, smoking, heredity) can produce the disease independently.

10. Absolute differences(Syn: Difference measures) • It is often an absolute reduction in the risk of an undesirable outcome. • When outcome of interest is continuous, the assessment of mean absolute differences between exposed and unexposed individuals may be an appropriate method for the determination of association. • Preferred by public health or preventive activist.

11. Relative differences (Syn:Ratio measures) • Can be assessed for discrete outcomes. • To assess causal associations.

12. Measures of association used in analytic epidemiologic studies. • Relative risk • Odds ratio • Attributable risk

13. Cohort Study • Assess the cumulative incidence (CIE+) of disease in an exposed group (absolute Risk) Assess the cumulative incidence (CIE-) of disease in unexposed group (absolute Risk) e.g. Coronary Heart Disease (CHD) Risk among Smokers 1-year risk of CHD among smokers (CIE+)* CHD Yes No Total Smokers 84 2916 3000  CIE+ = 84/3000 = 28/1000/yr(1-risk of CHD among smokers) Cont.

14. 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.

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

16. Interpreting Relative risk of a disease.

17. 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 in case-control study and can be used instead of RR.

18. 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

19. 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

20. 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 ratioa/b : c/d = ad/bc

21. 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.

22. 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

23. 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

24. ExampleOR in case-control Study • Past surgery HCV status HCV+ HCV- • Yes 59 168 • No 5448 113 216

25. 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

26. 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)

27. 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.

28. 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

29. Calculation of the odds ratio is based on discordant pairs. Odds ratio (matched pairs) = b/c

30. 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.

31. Example Normal Controls 8+ 1b <8 1b Total 8 + 1b 26 45 Cases <8 1b Total 15 56 71 Odds Ratio 18/7 = 2.57

32. ATTRIBUTABLE RISK (AR) • How much of the disease that occurs can be attributed to a certain exposure? • AR is defined as the amount of proportion of disease incidence (or disease risk) that can be attributed to a specific exposure. • AR in exposed persons(eg. AR of lung cancer in smokers) • AR for the population includes both exposed and unexposed persons(AR of lung cancer in population which consists of both smokers and non-smokers)

33. AR is a measure of association based on the absolute difference between two risk estimates. • It is often used to imply a cause-effect relationship and should be interpreted as a true etiologic fraction only when there is a reasonable certainty of a causal connection between exposure and outcome. • When causality has not been firmly established then the AR is termed as excess fraction.

34. AR in exposed individuals • It is merely a difference between the risk estimates of different exposure levels and a reference exposure level. • If q+ = risk in exposed individual. q- = risk in unexposed individual. • ARexp = q+ - q- • It measures the excess risk for a given exposure category associated with the exposure

35. Example: MI and HT • Cumulative incidence of MI among hypertensive indivs. q+ = 0.018 (1.8%). • Cumulative incidence of MI among normotensives (reference or unexposed category) q- = 0.003(0.3%). • Excess risk associated with exposure to hypertension = (0.018-0.003) = 0.015(1.5%). Interpretation: if the excess incidence were completely reversible, the cessation of the exposure(severe HT) would lower the risk in the exposed group from 0.018 to 0.003. That is the absolute excess incidence that would be prevented by eliminating hypertension is 1.5%

36. Percent ARexp: When AR is expressed as a percentage. %AR exp Interpretation: The percentage of the total risk in the exposed attributable to the exposure. The percentage of the MI attributable to the severe HT= 83.3%

37. Measures of association • Qualitative data • Chi-square test • Yates correction • Fishers test • Quantitative data • Correlation