As alternatives to the time-to-first-event analysis of composite endpoints, the {\it net benefit} (NB) and the {\it win ratio} (WR) -- which assess treatment effects using prioritized component outcomes based on clinical importance -- have been proposed. However, statistical inference of NB and WR relies on a large-sample assumptions, which can lead to an invalid test statistic and inadequate, unsatisfactory confidence intervals, especially when the sample size is small or the proportion of wins is near 0 or 1.
In this paper, we develop a systematic approach to address these limitations in a paired-sample design. We first introduce a new test statistic under the null hypothesis of no treatment difference. Then, we present the formula to calculate the sample size. Finally, we develop the confidence interval estimations of these two estimators. To estimate the confidence intervals, we use the {\it method of variance estimates recovery} (MOVER), that combines two separate individual-proportion confidence intervals into a hybrid interval for the estimand of interest. We assess the performance of the proposed test statistic and MOVER confidence interval estimations through simulation studies.
We demonstrate that the MOVER confidence intervals are as good as the large-sample confidence intervals when the sample is large and when the proportions of wins is bounded away from 0 and 1. Moreover, the MOVER intervals outperform their competitors when the sample is small or the proportions are at or near the boundaries 0 and 1. We illustrate the method (and its competitors) using three examples from randomized clinical studies.
Win-Ratio Regression for Prioritized Composite Outcomes in Observational Studies: Doubly Robust and Efficient Estimation with Future-Score Correction
University of Florida（佛罗里达大学）；University of California San Diego（加州大学圣地亚哥分校）；Stanford University School of Medicine（斯坦福大学医学院）；University of Rochester Medical Center（罗切斯特大学医学中心）
Win Time In Favor of Treatment (WINFT) for Hierarchical Endpoints
North Carolina State University（北卡罗来纳州立大学）；Duke Clinical Research Institute, Duke University（杜克大学杜克临床研究所）；Department of Biostatistics and Bioinformatics, Duke University（杜大学生统计与生物信息系）；Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin, Madison（威斯康星大学麦迪逊分校医学院公共卫生学院生物统计与医学信息系）
Estimation and Inference of the Win Ratio for Two Hierarchical Endpoints Subject to Censoring and Missing Data
Duke Clinical Research Institute（杜克临床研究所）；Department of Biostatistics and Bioinformatics, Duke University（杜克大学生物统计与生物信息学系）；Department of Statistics, North Carolina State University（北卡罗来纳州立大学统计学系）
