Cluster randomization trials commonly employ multiple endpoints. When a single summary of treatment effects across endpoints is of primary interest, global hypothesis testing/effect estimation methods represent a common analysis strategy. However, specification of the joint distribution required by these methods is non-trivial, particularly when endpoint properties differ. We develop rank-based interval estimators for a global treatment effect referred to as the "global win probability," or the probability that a treatment individual responds better than a control individual on average. Using endpoint-specific ranks among the combined sample and within each arm, each individual-level observation is converted to a "win fraction" which quantifies the proportion of wins experienced over every observation in the comparison arm. An individual's multiple observations are then replaced by a single "global win fraction," constructed by averaging win fractions across endpoints. A linear mixed model is applied directly to the global win fractions to recover point, variance, and interval estimates of the global win probability adjusted for clustering. Simulation demonstrates our approach performs well concerning coverage and type I error, and methods are easily implemented using standard software. A case study using publicly available data is provided with corresponding R and SAS code.

翻译：簇随机试验常采用多个结局指标。当需跨结局汇总处理效应时，全局假设检验/效应估计方法是一种常用分析策略。但此类方法所需联合分布的设定具有挑战性，尤其是在不同结局性质存在差异的情况下。本研究针对名为"全局获胜概率"的全局处理效应——即处理组个体平均优于对照组个体的概率——开发了基于秩的区间估计方法。通过利用合并样本及各组内部按结局特异性排序的秩次，将每个个体观测值转换为"获胜分数"，该分数量化了该个体在对照组的每次观测中获胜的比例。随后通过跨结局平均获胜分数的方式，将个体的多结局观测值替换为单一"全局获胜分数"。直接对全局获胜分数应用线性混合模型，可恢复经聚类调整后的全局获胜概率的点估计、方差估计及区间估计。模拟实验表明该方法在覆盖率和第一类错误方面表现良好，且可通过标准软件轻松实现。本文使用公开数据提供案例研究，并附有相应的R和SAS代码。