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On the intransitivity of the win ratio

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  • Oakes, David

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.

Suggested Citation

  • Oakes, David, 2025. "On the intransitivity of the win ratio," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002360
    DOI: 10.1016/j.spl.2024.110267
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    References listed on IDEAS

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    1. Xiaodong Luo & Hong Tian & Surya Mohanty & Wei Yann Tsai, 2015. "An alternative approach to confidence interval estimation for the win ratio statistic," Biometrics, The International Biometric Society, vol. 71(1), pages 139-145, March.
    2. D. Oakes, 2016. "On the win-ratio statistic in clinical trials with multiple types of event," Biometrika, Biometrika Trust, vol. 103(3), pages 742-745.
    3. Lu Mao & KyungMann Kim & Xinran Miao, 2022. "Sample size formula for general win ratio analysis," Biometrics, The International Biometric Society, vol. 78(3), pages 1257-1268, September.
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