A Class of Proportional Win-Fractions Regression Models for Composite Outcomes
The win ratio is gaining traction as a simple and intuitive approach to analysis of prioritized composite endpoints. To extend it from two-sample comparison to regression, we propose a general class of semiparametric models that includes as special cases both the two-sample win ratio and the traditional Cox proportional hazards model on time to the first event. Under the assumption that the covariate-specific win and loss fractions are proportional over time, the regression parameter is free from influence by the censoring distribution and can be interpreted as the log win ratio associated with one-unit increase in the covariate. A class of U-statistic weighted estimating equations, with the familiar partial likelihood score equation as a special case, is constructed to obtain consistent estimators for the regression parameter, whose asymptotic variances are derived and estimated using $U$-process theory. Visual inspection of a “score” process provides useful clues as to the plausibility of the proportionality assumption. Extensive numerical studies using both simulated data and real data from a major cardiovascular trial suggest that the regression models perform well in practice. The proposed methodology is implemented in the R-package “WR” available from CRAN.