Exposure-time-varying hazard function ratios in case-control studies of drug effects

Abstract

For many adverse effects of drugs, the instantaneous risk of an incident event per day of therapy (i.e., the hazard function) varies by duration of therapy and by prior exposure. In cohort studies of adverse drug effects time-varying hazard functions are easily modeled using standard statistical software packages. Tests of the hypothesis of a constant proportional hazard function ratio are also available. In case control studies, the need to consider time-varying hazard functions seems to be somewhat less well-recognized than in cohort studies. When the hazard function ratio for an adverse drug event is not constant over time, an overall single odds ratio (OR) estimated in a case control study not accounting for the time variation in the hazard function is a weighted average of duration-specific ORs with weights reflecting the distribution of exposure time in the study population. The resulting estimate depends not only on the drug but also on the exposure time distribution in the study population. This can lead to misleading conclusions when comparing the risks of two drugs within the same population and when comparing risks of the same drug in different populations. Analytic approaches for addressing time-varying hazard functions in case-control studies have been published but seem to be less used than in cohort studies. This article discusses adverse drug effects with time-varying hazard functions and methods for addressing these in case-control studies during study design, data collection, and analysis.