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：整群随机试验常采用多个终点指标。当需要跨终点汇总处理效应的单一指标时，全局假设检验/效应估计方法构成常用分析策略。然而，这些方法所需的联合分布设定具有较大难度，尤其是在各终点性质存在差异时。本研究针对被称为"全局获胜概率"（即治疗组个体平均而言优于对照组个体的概率）的全局处理效应，开发了基于秩的区间估计方法。基于合并样本及组内各终点排序，将每个个体观测值转化为"获胜分数"，用以量化该个体在对照组所有观测值中的获胜比例。随后将个体在多个终点上的观测值替换为单一"全局获胜分数"，该分数通过对各终点获胜分数取均值构建。直接对全局获胜分数应用线性混合模型，可恢复经整群调整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，且可通过标准软件简便实现。本文配套提供基于公开数据的案例研究及相应R与SAS代码。