The win ratio (WR) is a widely used metric to compare treatments in randomized clinical trials with hierarchically ordered endpoints. Counting-based approaches, such as Pocock's algorithm, are the standard for WR estimation. However, this algorithm treats participants with censored or missing data inadequately, which may lead to biased and inefficient estimates, particularly in the presence of heterogeneous censoring or missing data between treatment groups. Although recent extensions have addressed some of these limitations for hierarchical time-to-event endpoints, no existing methods -- aside from the computationally intensive multiple imputation approach -- can accommodate settings that include non-survival endpoints that are subject to missing data. In this paper, we propose a simple nonparametric maximum likelihood estimator (NPMLE) of WR for two hierarchical endpoints that are subject to censoring and missing data. Our method uses all observed data, avoids strong parametric assumptions, and comes with a closed-form asymptotic variance estimator. We demonstrate its performance using simulation studies and two data examples, based on the HEART-FID and ISCHEMIA trials. The proposed method provides a consistent estimator, improves estimation efficiency, and is robust under non-informative censoring and missing at random (MAR) assumptions, offering a flexible alternative to existing WR estimation methods. A user-friendly R package, WinRS, is available to facilitate implementation.

翻译：胜率（WR）是随机临床试验中比较分层排序终点治疗效果时广泛使用的指标。基于计数的Pocock算法是WR估计的标准方法。然而，该算法对存在删失或缺失数据的参与者处理不当，可能导致有偏且低效的估计，尤其在治疗组间存在异质性删失或缺失数据时更为明显。尽管近期扩展方法已针对分层时间-事件终点的部分局限性进行了改进，但除计算密集的多重插补法外，现有方法均无法处理包含缺失数据的非生存终点情形。本文针对存在删失与缺失数据的两个分层终点，提出了一种简单的非参数极大似然估计量（NPMLE）。该方法充分利用所有观测数据，避免强参数假设，并具有闭式渐近方差估计量。我们基于HEART-FID和ISCHEMIA试验数据，通过模拟研究和两个实例验证了其性能。所提方法提供了一致估计量，提升了估计效率，在无信息删失与随机缺失（MAR）假设下具有稳健性，为现有WR估计方法提供了灵活的替代方案。用户友好的R软件包WinRS可用于便捷实现。