Design and Monitoring of Clinical Trials with Clustered Time-to-Event Endpoint

Many clinical trials are involved with clustered data that consists of groups (called clusters) of nested subjects (called subunits). Observations from subunits within each cluster tend to be positively correlated due to shared characteristics. Therefore, analysis of such data needs to account for the dependency between subunits. For clustered time-to-event endpoints, there are only few methods proposed for sample size calculation, especially when the cluster sizes are variable. In this dissertation, we aim to derive sample size formula for clustered survival endpoint based on nonparametric weighted rank tests. First, we propose closed form sample size formulas for cluster randomization trials and subunit randomization trials; accordingly, we derive the intracluster correlation coefficient for clustered time-to-event endpoint. We find that the required number of clusters is affected not only by the mean cluster size, but also by the variance of cluster size distribution. In addition, we prove that in group sequentially monitored cluster randomization studies, the log-rank statistics does not have independent increment property, which is different from the result for independent survival data. We further derive the limiting distribution of sequentially computed log-rank statistics, and develop a group sequential testing procedure based on alpha spending approach, as well as a corresponding sample size calculation method.