1.Case control study - Part 2Dr. Rizwan S A, M.D.,

2. Outline Basic Concepts in the Assessment of Risk Sample Size Basic Method of Analysis Multivariate Analysis Nested Case-Control 3. Basic Concepts in the Assessment of Risk Disease Occurrence Relative Measures of Disease Occurrence Cohort and Case-Control Sampling Schemes Risk of Disease Attributable to Exposure Exposure Interpretation of Relative Risk Cumulative Risk of Disease Association and Testing for Significance Relative Risk as a measure of the Strength Of Association Confounding Interaction Summary 4. Disease Occurrence Cumulative Incidence Number of persons with disease onset during a specified period Number of persons at risk in the beginning of the period Incidence Rate Number of new disease events in a specified period The sum of the subjects disease free time of follow up during this period Prevalence Number of persons with a disease at a certain point intime Number of persons in the population at that point in time 5. Relative Measures of Disease Occurrence Relative Risk: the ratio of the risk of disease in exposed individuals to the risk of disease in non exposed individuals.Odds Ratio The odds of an event can be defined as the ratio of the number of ways the event can occur to the number of ways the event cannot occur Case Control study cant determine IR of disease ass. with +/- study exposure ,it can estimate the ratio of IR (RR) in terms of Odds Ratio 6. Figure A, Odds ratio (OR) in a cohort study. B Odds ratio (OR) in a case-control study. 7. When Odds ratio a good estimate of RR? 1. When the cases studied are representative, with regard to history of exposure, of all people with the disease in the population from which the cases were drawn. 2. When the controls studied are representative, with regard to history of exposure, of all people without the disease in the population from which the cases were drawn. 3. When the disease being studied does not occur frequently. 8. The odds ratio is a good estimate of the relative risk when a disease is infrequent.The odds ratio is not a good estimate of relative risk when a disease is not infrequent. 9. Table 10. Cohort Sampling-Table The incidence rates/relative risk/odds of dis. among exposed /non exposed estimated from sample agree with the values in target population but odds of exposure are different in both. 11. Case-Control sampling-Table The proportion of incident cases among exposed /non exposed individual in sample is different from target population , but odds of exposure are same 12. Risk of Disease Attributable to Exposure Q.How much of the disease that occurs can be attributed to a certain exposure? A.The attributable risk,defined as the amount or proportion of disease incidence (or disease risk) that can be attributed to a specific exposure() OR =p1-p2 =(R-1)p2(-1)p2 13. Exposure-Specific Risk IR for entire populations (p) are a weighted avg. of ExposureSpecific rates p1 and p2, pe=M1/N p=N1/N p=p1pe +p2(1-pe) p1=Rp2 p2=p/{Rpe+(1-pe)} p2 = p/{ pe+(1-pe)} P1= p2 P(D/Ei)=P(Ei/D)P(D)/ P(Ei/D)P(D)+P(Ei/D)P(D) The exp-sp prob of dis. can be determined given estimate of overall probability of dis and proportion of cases and controls in ith exp category. 14. Etiologic Fraction Table1 =proportion of all cases in the target population attributable to exposure. =N1-Np2/N1 = pe(R-1)/[pe(R-1)+1] eg-Table p2=p(1- ); p1= Rp(1- ) 15. Exposure-table Intensity dimension Time dimension Estimation of Population Exposure Rate From Control Series Control series must be representative of individual without dis. In target population Dis. must be rare.Unconditional prob of ex in target population=weighted avg of cond.prob of ex among dis. and non-dis. P(E)= P(E/D)P(D)+P(E/D)P(D) If P(D) 0,P(D) 1; P(E)=P(E/D) ,(rare- pe , ) = pe ( -1)/[pe ( -1)+1] 16. Interpretation of Relative Risk-table 17. Relative risk as a measure of strength of association If X uncontrolled var. which doesnt interact with E accounts for all the risk due to E;R>1 X must be R times more common among E/NE; P(X/E)>RP(X/E) X must be as strong a risk facto as the EPresence of multiple real causes reduces the apparent relative risk for any one of them 18. Interaction-Table Effect modification tells us that the association between exposure and disease is modified by a third factor. When IR of a dis. in presence of 2 or > risk factors differs from IR resulting from combination of their individual effects-Interaction Synergism or Antagonism special case of Positive and Negative Interaction . Additive (p11-p00)=(p10-p00)+(p01-p00) (Rxy-1)=(Rx-1)+(Ry-1) Multiplicative p11/p00=(p10/p00)(p01/p00) Rxy=RxRy 19. Sample Size Sample Size and Power for Unmatched Studies Sample Size and Power with Multiple Control per Case Smallest detectable Relative Risk Optimal Allocation Adjustment for Confounding Sample Size and Power for Pair-Matched Studies Sequential Case-Control Studies Summary 20. Sample size-Inroduction Study should be large to avoid: Claiming that E is associated with D when it is not- E is not associated with D when it is- Probability of finding the sampling estimate of RR(OR) differs sig. from unity=1- =PowerHow many subjects for case control study(matched/unmatched)? Relative frequency of E among controls in target population-p0 Hypothesized RR associated with E of public health imp-R Desired level of Significance- Desired study power, 1- 21. Sample Size and Power for Unmatched Studies 22. Sample Size and Power for Unmatched Studies 23. Sample Size and Power for Unmatched Studies 24. Sample Size and Power with Multiple Control per Case-With unequal controls per case 25. Sample Size and Power with Multiple Control per Case-With unequal controls per case 26. Sample Size and Power with Multiple Control per Case-With unequal controls per case 27. Smallest detectable Relative Risk Given fixed n,a,p0;what is smallest R can be detected with specified power? 28. Optimal Allocation Equal Case-control cost 29. Optimal Allocation Unequal cost: Max power for fixed total cost 30. Unequal cost: Max power for fixed total cost 31. Optimal Allocation Minimum cost for Fixed Power 32. Adjustment for Confounding Sample size for Case control study that use stratified analysis to adjust for confounding must specify RR Estimated exposure rate among controls in each of k strata po1,p02 etc Estimated proportion of cases in each strata f1,f2 Significance- power, 1- Eg- 33. Adjustment for Confounding 34. Adjustment for Confounding 35. Sample Size and Power for Pair-Matched Studies Exposed (+) ,Unexposed (-) Case, control(++)(+-)(--)(-+) For specified , no. of discordant pairs required for RR 36. Sample Size and Power for Pair-Matched Studies 37. Sample Size and Power for Pair-Matched Studies 38. Sequential Case-Control Studies Rather than waiting until a predetermined no. of cases and controls have accumulated it proceeds as data become available over time. Sample size