Bias and estimation under misspecification of the risk period in self-controlled case series studies

The self-controlled case series (SCCS) method is useful for estimating the relative incidence (RI) of acute events, such as adverse events (AEs) during a specified risk period following an exposure (e.g., 6-week period after vaccinations or 30-day period after infection-related hospitalizations). In practice, the "optimal" risk period is unknown and must be specified. To date, two approaches are available to guide the specification of the risk period. Both methods do not fully utilize the nature of the bias due to misspecification, which to date has not been characterized. Thus, we elucidate the bias of SCCS estimate of the RI when the risk period is misspecified. We then propose a novel method that more effectively estimates the optimal risk period and the associated RI of AEs. The new method incorporates information on the functional form of the bias. Efficacy of the proposed approach is illustrated with substantial reduction in bias and variance in simulation studies. The proposed method is illustrated with two SCCS studies to determine the (1) risk of idiopathic thrombocytopenic purpura after measles-mumps-rubella vaccination in children and (2) risk of cardiovascular events after infection-related hospitalizations in older patients on dialysis.