Covariate Adjustment for Time-Restricted Marginal Win Statistics in Randomized Trials: Assumption-Lean Inference and Guaranteed Efficiency Gain

Abstract

Hierarchical composite endpoints, analyzed through win statistics such as the net benefit (NB), win ratio (WR), and win odds (WO), are increasingly used in randomized trials to prioritize endpoints according to clinical importance. Although covariate-adjustment methods for win statistics have been developed, a unified model-assisted approach for mixed-type, time-restricted HCEs with simultaneous asymptotic no-loss efficiency guarantees remains of interest. We propose a unified, model-assisted covariate-adjustment framework for time-restricted marginal win statistics evaluated at a prespecified post-randomization restriction horizon, a clinically interpretable estimand particularly suited to acute and high-acuity trials with well-defined short-term follow-up windows. The Hoeffding--H'ajek projection of the two-sample win--loss U-statistics yields subject-level influence functions for the marginal win and loss probabilities. We apply treatment-specific linear covariate adjustment to these influence functions and propagate the adjustment to NB, log WR, and log WO. The resulting estimators are assumption-lean, remaining consistent and asymptotically valid without correct specification of the linear working model, and are asymptotically guaranteed efficiency gain over their unadjusted counterparts. Simulations with mixed-type HCEs demonstrate substantial efficiency and power gains with prognostic covariate adjustment. However, including additional non-prognostic covariates can impair finite-sample variance estimation and inflate Type I error, particularly in smaller trials. Bootstrap variance estimation improved inferential calibration in these settings. We illustrate the proposed method using a randomized acute kidney injury alert trial.