Prioritized time-to-event outcomes arise frequently in clinical studies, where treatment comparisons may be based on a prespecified hierarchy of clinically important outcomes. The win ratio provides a natural summary of treatment benefit for such prioritized outcomes. However, methods for characterizing heterogeneous treatment effects by estimating how the win ratio varies with baseline covariates remain limited in this setting. We develop a flexible local inverse probability of censoring weighted estimator of the win ratio as a function of baseline covariates, without imposing the parametric shape or proportional win-fractions structure assumed by existing regression approaches. We use best linear projections to summarize the estimated log win ratio and develop formal tests of log-linearity of the win ratio function. We also propose a complementary model-based estimator of the covariate-specific win ratio assuming proportional hazards models for the marginal distributions, copula dependence between the margins, and Bernstein-polynomial sieves for the baseline hazards. Large-sample properties and bootstrap validity are established for both approaches. Simulations show that the local estimator is robust, while the model-based procedure can provide substantial efficiency and power gains under correct specification, and proportional win-fractions regression may lead to bias when its structural assumptions fail. The methods are illustrated by analyzing data from CALGB 9633, a randomized lung cancer trial.

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