Statistics in Medicine

Sample size estimation for case‐crossover studies

Journal Article

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.

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