Robust statistical inference for matched win statistics

As alternatives to the time-to-first-event analysis of composite endpoints, the win statistics, that is, the net benefit, the win ratio, and the win odds have been proposed to assess treatment effects, using a hierarchy of prioritized component outcomes based on clinical relevance or severity. Whether we are using paired organs of a human body or pair-matching patients by risk profiles or propensity scores, we can leverage the level of granularity of matched win statistics to assess the treatment effect. However, inference for the matched win statistics (net benefit, win ratio, and win odds)-quantities related to proportions-is either not available or unsatisfactory, especially in samples of small to moderate size or when the proportion of wins (or losses) is near 0 or 1. In this paper, we present methods to address these limitations. First, we introduce a different statistic to test for the null hypothesis of no treatment effect and provided a sample size formula. Then, we use the method of variance estimates recovery to derive reliable, boundary-respecting confidence intervals for the matched net benefit, win ratio, and win odds. Finally, a simulation study demonstrates the performance of the proposed methods. We illustrate the proposed methods with two data examples.