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Power and sample size calculation incorporating misspecifications of the variance function in comparative clinical trials with over‐dispersed count data

Over‐dispersed count data are frequently observed in clinical trials where the primary endpoint is occurrence of clinical events. Sample sizes of comparative clinical trials with these data are typically calculated under negative binomial models or quasi–Poisson models with specified variance functions, or under the assumption that the specified “working” variance functions are correctly specified. In this article, we propose a sample size formula anticipating misspecifications of the working variance function. We derived a method based on the asymptotic distribution of a Wald test statistic with a sandwich‐type robust variance estimator under quasi–Poisson models. Under misspecifications of the working variance function, the asymptotic variance of the estimator of the treatment effect is expressed as a form involving both true and working variance functions. Our sample size formula includes several existing formulas as special cases when the working variance function is correctly specified as the true variance function. We also consider a sensitivity analysis for possible misspecifications of the “true” variance function when estimating sample sizes using our formula. A simulation study demonstrated the adequacy of our formulas in finite sample size settings. An application to a clinical trial to evaluate the treatment effect on prevention of COPD exacerbation is provided.