Win Ratio as an Effect Size Measure Under Non-Proportional Hazards: A Comparison With Difference in Restricted Mean...

When the proportional hazards assumption does not hold, the hazard ratio can misrepresent treatment effects in survival analysis. We evaluate the win ratio, originally proposed for prioritizing multiple outcomes, as an effect size measure for a single survival outcome under non-proportional hazards, and compare it with the difference in restricted mean survival time (RMST). We perform bootstrap-based inference for the win ratio under both right- and interval-censoring using plug-in estimators based on nonparametric maximum likelihood estimators or spline-based sieve maximum likelihood estimators of the survival functions. We also study stratified win ratio to mitigate confounding. Extensive simulations are conducted to assess and compare the performances of the win ratio and the difference in RMST under various types of alternatives encountered in practice. The simulation results show that the win ratio-based tests outperform RMST-based tests when treatment benefits arise early, whereas RMST is more sensitive to late-onset effects, and stratified win ratio maintains nominal type I error in the presence of confounding, unlike unstratified win ratio. As an illustration, we analyze right-censored and interval-censored progression-free survival in patients with multiple myeloma treated with two different regimens. The results of this article support reporting the win ratio, along with the difference in RMST, when the proportional hazards assumption is doubtful, offering complementary clinical interpretability and robustness across censoring mechanisms and treatment effect patterns.