Sample size determination for win statistics in cluster-randomized trials

2025-10-26

AI Summary

In cluster-randomized trials, there is a lack of analytical power and sample size calculation frameworks for multilevel ordinal composite endpoints—including time-to-event outcomes—based on win statistics (e.g., win ratio, win odds, net benefit). Method: We propose a unified analytical variance formula that explicitly incorporates intra-cluster correlation, unequal cluster sizes, and outcome priority weights, extending univariate win statistics to multilevel hierarchical composite endpoints. Closed-form power expressions are derived, enabling rapid, simulation-free computation. Contribution: This work establishes the first theoretical sample size framework for win statistics under cluster-randomized designs. The method demonstrates high finite-sample accuracy and robustness, as confirmed by extensive simulations. It has been successfully applied to redesign a real-world trial, substantially improving statistical power and planning reliability.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Ensemble Methods
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

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.

Problem

• Developing sample size framework for win statistics in cluster-randomized trials
• Extending win ratio methodology to hierarchically ordered composite endpoints
• Deriving analytical variance formulas incorporating intracluster correlation coefficients

Innovation

• Power and sample size framework for cluster-randomized trials
• Analytical variance expressions for win statistics
• Closed-form formulas avoiding intensive simulations