The Multitime Case-control Design for Time-varying Exposures

BACKGROUND: The conventional approach to improve precision of the odds ratio in a case-control study is to increase the number of controls per case. With time-varying exposures, an alternative is to increase the number of observations per control. METHOD: We present the multitime case-control design, which uses multiple control person-moments of exposure within each control subject. The point and variance estimators of the odds ratio are corrected for within-subject correlation. We illustrate this approach using case-control data from studies of the effects of respiratory medications. RESULTS: Simulations show that, with uncorrelated exposures, it is possible to reduce the variance of the odds ratio by around 30% by increasing the number of control person-moments per subject. With correlated exposures, an accurate variance can be obtained by correcting for within-subject correlation. The corrected variance increases with increasing correlation, depending on the number of control person-moments. The first illustration shows that the rate ratio (RR) of cardiac death associated with β-agonist use, not estimable with 1 control per case (30 cases) and 1 control person-moment, was 4.2 (95% confidence interval = 0.4-49) with 12 control person-moments. The second example finds a rate ratio of acute myocardial infarction associated with antibiotics of 2.00 (1.16-3.44) with 1 control per case, which improves in precision with 10 control subjects per case (RR = 2.13 [1.48-3.05]) but also with 1 control per case and 10 control person-moments per control subject (1.99 [1.36-2.90]). CONCLUSION: When dealing with time-varying exposures, the multitime case-control design can increase the efficiency of conventional case-control studies without additional control subjects.