Sample size calculation for cluster randomization trials with a time-to-event endpoint

Cluster randomization trials randomize groups (called clusters) of subjects (called subunits) between intervention arms, and observations are collected from each subject. In this case, subunits within each cluster share common frailties, so that the observations from subunits of each cluster tend to be correlated. Oftentimes, the outcome of a cluster randomization trial is a time-to-event endpoint with censoring. In this article, we propose a closed form sample size formula for weighted rank tests to compare the marginal survival distributions between intervention arms under cluster randomization with possibly variable cluster sizes. Extensive simulation studies are conducted to evaluate the performance of our sample size formula under various design settings. Real study examples are taken to demonstrate our method.