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 in clinical trials. To extend it from two‐sample comparison to regression, we propose a novel 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 coefficient is unrelated to the censoring distribution and can be interpreted as the log win ratio resulting from one‐unit increase in the covariate. U‐statistic estimating functions, in the form of an arbitrary covariate‐specific weight process integrated by a pairwise residual process, are constructed to obtain consistent estimators for the regression parameter. The asymptotic properties of the estimators are derived using uniform weak convergence theory for U‐processes. Visual inspection of a “score” process provides useful clues as to the plausibility of the proportionality assumption. Extensive numerical studies using both simulated and real data from a major cardiovascular trial show that the regression methods provide valid inference on covariate effects and outperform the two‐sample win ratio in both efficiency and robustness. The proposed methodology is implemented in the R‐package WR, publicly available from the Comprehensive R Archive Network (CRAN).