The Win Ratio: On Interpretation and Handling of Ties

Abstract

To handle composite endpoints, the win ratio has been applied to data analysis and design of clinical trials. Its interpretation, however, is not always clear, and it could handle ties differently. We address these two aspects. First, we express the win ratio as a ratio of two proportions, namely, the proportion of patient-level comparisons in which the experimental treatment “wins” over the control divided by the proportion of “wins” for the control, taking into account the priority order of the components. This equivalent form, the ratio of proportions, can ease communication to clinical trial stakeholders—especially when the win proportions themselves are reported. We recommend such presentations. In some simple cases, we connect the win ratio to the odds ratio, the hazard ratio, the Mann–Whitney U, and the mean difference. In exploring the role of ties, we introduce the win odds, as an extension of the Mann–Whitney odds under the framework of prioritized pairwise comparisons. Finally, we discuss some practical aspects of the win ratio, including rules for defining winners (or losers) and ties, dependence on censoring, win ratio estimands, and benefit-risk assessments, as well as applications to two clinical studies.

Keywords:

• Benefit-risk
• Estimand
• Mann–Whitney U
• Net benefit
• Win odds
• Win proportion
• Win ratio

Acknowledgments

The authors would like to thank Weichung Joe Shih, Geraldine Rauch, Xiaodong Luo, Ionut Bebu, H. M. James Hung, and Duolao Wang for their comments and review of an early version; Stuart J. Pocock for his suggestions; and Dong Xi for his review of a later version. They would like to also thank the editor, the associate editor, and the reviewers for their insightful and constructive comments, which greatly improved this article.