Bridging Balancing Weights and Augmentation in Covariate-adjusted Analyses with Time-to-Event Endpoints: Theory and Practical Recommendations

2026-08-06

AI Summary

This study addresses the challenge of efficiently and accurately adjusting for covariates in randomized clinical trials with time-to-event endpoints while simultaneously preserving the validity of the log-rank test and improving marginal hazard ratio estimation. The authors establish, for the first time, a first-order asymptotic equivalence between balancing weighting methods—such as stabilized balancing weights and entropy balancing—and augmentation approaches in time-to-event analysis, demonstrating that calibrated weighting achieves estimation efficiency comparable to augmentation without requiring outcome modeling. By integrating propensity score weighting with augmented log-rank scores, they propose a variance estimator that controls finite-sample type I error inflation. Theoretical and simulation results show substantial efficiency gains when covariates are strongly prognostic, and the method’s practical utility is confirmed through application to the REWIND cardiovascular trial.

Abstract

Covariate adjustment improves the efficiency of treatment-effect analyses in randomized clinical trials, provided the adjustment targets the correct quantity. For time-to-event endpoints, two marginal targets are of primary interest: the log-rank test for the presence of a treatment effect and the marginal hazard ratio for its magnitude. Existing covariate adjustment approaches reach these targets by different ways. Augmentation adjusts the log-rank score by regressing derived outcomes on the baseline covariates within each arm. Weighting instead reweights the two arms to balance the covariates before the survival comparison is formed: inverse probability weighting does so through a fitted propensity model, while calibration weighting solves directly for weights that match covariate means. In this manuscript, we first develop balancing weighting for time-to-event endpoints, covering both calibration weights (stable balancing weights and entropy balancing) and propensity score weights, and prove that any balancing-regular weighting is first-order equivalent to the augmented log-rank score and to the root of the marginal Cox score. All three routes therefore deliver the same estimator to first order, and calibration reaches it without fitting any model. The weighted procedures thereby inherit the validity and guaranteed efficiency gain of the augmentation approach. In addition, we show that the efficiency gain grows with the prognostic strength of the adjustment covariates, while the practical caveat lies in variance estimation, for which we give recommendations to guard against finite-sample Type I error inflation. We further confirm our results through simulation studies and an analysis of the REWIND cardiovascular trial.

Problem

• covariate adjustment
• time-to-event endpoints
• balancing weights
• augmentation
• marginal hazard ratio

Innovation

• balancing weights
• covariate adjustment
• time-to-event endpoints
• augmentation
• calibration weighting