Blinded sample size re-estimation for comparing over-dispersed count data incorporating follow-up lengths

Blinded sample size re-estimation (BSSR) is an adaptive design to prevent the power reduction caused by misspecifications of the nuisance parameters in the sample size calculation of comparative clinical trials. However, conventional BSSR methods used for overdispersed count data may not recover the power as expected under the misspecification of the working variance function introduced by the specified analysis model. In this article, we propose a BSSR method that is robust to the misspecification of the working variance function. A weighted estimator of the dispersion parameter for the BSSR is derived, where the weights are introduced to incorporate the difference in the distribution of follow-up length between the interim analysis with BSSR and the final analysis. Simulation studies demonstrated the power of the proposed BSSR method was relatively stable under misspecifications of the working variance function. An application to a hypothetical randomized clinical trial of a treatment to reduce exacerbation rate in patients with chronic obstructive pulmonary disease is provided.