On the intransitivity of the win ratio

David Oakes

Statistics & Probability Letters, 2025, vol. 216, issue C

Abstract: The win-ratio analysis of controlled clinical trials uses pairwise comparisons between patients in the treatment and control group based on a primary outcome, say time to death, with indeterminacies resolved where possible by a secondary outcome, say time to hospitalization. The resulting preferences may not be transitive. Intransitivity occurs when potential follow-up times vary between patients and rankings from the primary events differ from those from secondary events. We characterize the structure of closed loops, derive some general properties of win-ratio preferences and provide simple numerical illustrations. Under realistic assumptions, unless all potential follow-up times are equal, intransitivities are certain to occur in sufficiently large samples, but their overall frequency is low.

Keywords: Censored data; Clinical trials; Composite outcome; Prioritized analyses; Survival analysis (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110267

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