Sample size determination for win statistics in cluster-randomized trials

TL;DR

This paper develops a comprehensive framework for calculating the power and sample size needed when using win statistics in cluster-randomized trials with composite time-to-event outcomes, addressing a gap in methodology.

Contribution

It introduces analytical variance formulas for win statistics in cluster trials, extending existing methods to complex composite endpoints and enabling more accurate study planning.

Findings

Variance expressions accurately predict finite-sample performance.

Framework accounts for intracluster correlation, cluster size, and tie probability.

Simulation studies validate the method's accuracy.

Abstract

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.