The win ratio is gaining traction as a simple and intuitive approach to analysis of prioritized composite endpoints in clinical trials. To extend it from two-sample comparison to regression, we propose a novel class of semiparametric models that includes as special cases both the two-sample win ratio and the traditional Cox proportional hazards model on time to the first event. Under the assumption that the covariate-specific win and loss fractions are proportional over time, the regression coefficient is unrelated to the censoring distribution and can be interpreted as the log win ratio resulting from one-unit increase in the covariate. U-statistic estimating functions, in the form of an arbitrary covariate-specific weight process integrated by a pairwise residual process, are constructed to obtain consistent estimators for the regression parameter. The asymptotic properties of the estimators are derived using uniform weak convergence theory for U-processes. Visual inspection of a “score” process provides useful clues as to the plausibility of the proportionality assumption. Extensive numerical studies using both simulated and real data from a major cardiovascular trial show that the regression methods provide valid inference on covariate effects and outperform the two-sample win ratio in both efficiency and robustness. The proposed methodology is implemented in the R-package WR, publicly available from the Comprehensive R Archive Network (CRAN).

中文翻译：

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一类复合结果的比例获胜分数回归模型

作为在临床试验中分析优先复合终点的一种简单直观的方法，胜率越来越受到关注。为了将其从双样本比较扩展到回归，我们提出了一类新的半参数模型，其中包括作为特例的双样本获胜率和传统的 Cox 比例风险模型按时间到第一个事件。假设协变量特定的获胜和损失分数随时间成正比，回归系数与审查分布无关，可以解释为协变量增加一个单位所产生的对数获胜比率。ü-统计估计函数，以由成对残差过程集成的任意协变量特定权重过程的形式，被构建以获得回归参数的一致估计量。估计器的渐近特性是使用U过程的均匀弱收敛理论导出的。对“评分”过程的目视检查为比例假设的合理性提供了有用的线索。使用主要心血管试验的模拟和真实数据进行的广泛数值研究表明，回归方法提供了对协变量效应的有效推断，并且在效率和稳健性方面优于双样本胜率。建议的方法在 R 包WR中实现，可从 Comprehensive R Archive Network (CRAN) 公开获得。