Sample size estimation for case-crossover studies

Case-crossover study designs are observational studies used to assess postmarket safety of medical products (eg, vaccines or drugs). As a case-crossover study is self-controlled, its advantages include better control for confounding because the design controls for any time-invariant measured and unmeasured confounding and potentially greater feasibility as only data from those experiencing an event (or cases) are required. However, self-matching also introduces correlation between case and control periods within a subject or matched unit. To estimate sample size in a case-crossover study, investigators currently use Dupont's formula (Biometrics 1988; 43:1157-1168), which was originally developed for a matched case-control study. This formula is relevant as it takes into account correlation in exposure between controls and cases, which are expected to be high in self-controlled studies. However, in our study, we show that Dupont's formula and other currently used methods to determine sample size for case-crossover studies may be inadequate. Specifically, these formulas tend to underestimate the true required sample size, determined through simulations, for a range of values in the parameter space. We present mathematical derivations to explain where some currently used methods fail and propose two new sample size estimation methods that provide a more accurate estimate of the true required sample size.