Predicting Win-Loss Probabilities for Composite Time-to-Event Outcomes Under The Proportional Win-Fractions Regression Model.

For composite time-to-event outcomes, the win ratio as a relative measure ignores ties resulting from non-occurrence of events, which can obscure important context in regression settings where event rates-and hence the proportion of ties-vary over time and across covariate values. To gain a more complete understanding of covariate effects, we propose coupling the proportional win-fractions (PW) model, which specifies only the win ratio, with a time-to-first-event model (e.g., Cox model), from which the tie probability can be inferred. This combination enables prediction of time-dependent win and loss probabilities on an absolute scale for any given pair of covariate profiles, with uncertainty quantified through robust variance estimation, and facilitates inference on tie-adjusted measures such as the net benefit and win odds to complement the win ratio in evaluating effect size. Residual-based diagnostics further allow refinement of model fit through appropriate covariate specification or stratification to address potential violations of proportionality assumptions. Through simulation studies and an application to the landmark HF-ACTION trial, we demonstrate that the proposed approach provides accurate and clinically interpretable predictions when model assumptions are approximately satisfied. These predictions reveal a pattern of diminishing returns on absolute win-loss probabilities as a key baseline biomarker increases across the population despite a constant win ratio. We also show that violations of the proportional win-fractions assumption can lead to biased predictions, underscoring the importance of model diagnostics. When the primary objective is to characterize time-varying covariate effects on win-loss probabilities, more flexible modeling approaches may be warranted. In addition to a small code example in the paper, the full methodology is implemented in the WR package, available on GitHub ( https://lmaowisc.github.io/WR/) and the Comprehensive R Archive Network (CRAN).