Sample size determination for win statistics in cluster-randomized trials

Composite endpoints are increasingly used in clinical trials to capture treatment effects across multiple or hierarchically ordered outcomes. Although inference procedures based on win statistics, such as the win ratio, win odds, and net benefit, have gained traction in individually randomized trials, their methodological development for cluster-randomized trials remains limited. In particular, there is no formal framework for power and sample size determination when using win statistics with composite time-to-event outcomes. We develop a unified framework for power and sample size calculation for win statistics under cluster randomization. Analytical variance expressions are derived for a broad class of win statistics, yielding closed-form variance expressions and power procedures that avoid computationally intensive simulations. The variance expressions explicitly characterize the roles of the rank intracluster correlation coefficient, cluster size, tie probability, and outcome prioritization for study planning purposes. Importantly, our variances nest existing formulas for univariate outcomes as special cases while extending them to complex, hierarchically ordered composite endpoints. Simulation studies confirm accurate finite-sample performance, and we supply a case study to illustrate the use of our method to re-design a real-world cluster-randomized trial.