Sample size estimation for stratified cluster randomization trial with survival endpoint

Cluster randomization trials with survival endpoint are predominantly used in drug development and clinical care research when drug treatments or interventions are delivered at a group level. Unlike conventional cluster randomization design, stratified cluster randomization design is generally considered more effective in reducing the impacts of imbalanced baseline prognostic factors and varying cluster sizes between groups when these stratification factors are adopted in the design. Failure to account for stratification and cluster size variability may lead to underpowered analysis and inaccurate sample size estimation. Apart from the sample size estimation in unstratified cluster randomization trials, there are no development of an explicit sample size formula for survival endpoint when a stratified cluster randomization design is employed. In this article, we present a closed-form sample size formula based on the stratified cluster log-rank statistics for stratified cluster randomization trials with survival endpoint. It provides an integrated solution for sample size estimation that account for cluster size variation, baseline hazard heterogeneity, and the estimated intracluster correlation coefficient based on the preliminary data. Simulation studies show that the proposed formula provides the appropriate sample size for achieving the desired statistical power under various parameter configurations. A real example of a stratified cluster randomization trial in the population with stable coronary heart disease is presented to illustrate our method.