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Abstract:
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Pocock et al. (2012) following Finkelstein and Schoenfeld (1999) popularized the win ratio for analysis of controlled clinical trials with multiple types of outcome event. The approach uses pairwise comparisons between patients in the treatment and control groups using a primary outcome, say time to death, with indeterminacies resolved where possible using a secondary outcome, say time to hospitalization. Preferences assigned by this method may not be transitive. Intransitivity occurs when potential follow-up time varies between patients and rankings based on primary events differ from those based on secondary events. We derive some general properties of win-ratio preferences and provide numerical illustrations under some simple models. Unless all follow-up times are equal, see Oakes (2016), intransitivities are certain to occur in sufficiently large samples, but their overall frequency is low and there is no simple remediation of the problem.
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