Group sequential procedures for repeated events data with frailty

In this article we consider the design aspects of group sequential trials with recurrent study endpoints, where the subjects are from a heterogeneous population. The usual procedures of sequential analysis based on the "independent increments" property are no longer valid due to the heterogeneity of the study subjects, as pointed out by Cook and Lawless. We focus on the aspect of study planning and consider a special model (Poisson process with frailty) to investigate the effects of frailty (or subject heterogeneity). We prescribe the valid procedures and provide convenient tables for computing stopping boundaries and sample sizes. The methodology is illustrated through an example of an animal experiment with recurrent tumors, using procedures such as group sequential tests and repeated confidence intervals. Minimal cost analysis is considered for determining the optimal combination of study duration and sample size.