Debiased learning of the causal net benefit with censored event time data

Summary Cox regression is the default approach to evaluating the (relative) effect of two treatments on a survival endpoint. This standard framework has nonetheless been criticized for its canonical effect measure, the hazard ratio, having a subtle interpretation, thereby hindering policy-making. This in turn has prompted interest in other effects measures, such as the difference in restricted mean survival time, the net benefit and the win ratio, which have become increasingly popular. Developments in estimation and inference for the net benefit and win ratio proceed either under a semiparametric model, at the risk of bias due to model misspecification, or in a nonparametric model, but without the flexibility to adjust for covariates. In this paper, we overcome these challenges by introducing a scalar, model-free measure of conditional causal net benefit in terms of counterfactuals and developing a debiased estimator based on its efficient influence function. This estimator is root-$ n $ consistent and asymptotically model-free by flexibly enabling data-adaptive learning (e.g., machine learning) of the dependence of treatment, survival and censoring time on baseline covariates. By incorporating such covariates, the proposed estimators can improve the efficiency of randomized trial analyses, as well as correct for confounding and censoring bias in both randomized and observational studies. We also propose variations of the considered estimand (and estimator) that have a more favourable efficiency bound. The proposed method is illustrated by simulation studies and analysis of breast cancer data.