Efficient Estimation of Mann–Whitney-Type Effect Measures for Right-Censored Survival Outcomes in Randomized Clinical Trials

Mann–Whitney-type effect measures are clinically relevant, easy to interpret, and readily applicable to a wide range of study settings. This article considers estimation of such effect measures in randomized clinical trials where the outcome variable is a survival time subject to independent censoring (within each treatment group). In this setting, a plug-in estimator based on Kaplan–Meier estimates of survival functions is readily available, and can be used to generate a class of augmented estimators that incorporate baseline covariate information. The optimal augmentation, which leads to the most efficient non-parametric estimator, can be estimated by minimizing an empirical version of the asymptotic variance of an augmented estimator using machine learning methods. Implementing this approach requires estimating the influence function of the initial plug-in estimator, for which we propose to use the empirical influence function available in the jackknife method. Sample splitting can be used to strengthen the theoretical validity of this non-parametric augmentation approach by removing a previously assumed Donsker’s condition. The proposed methods are evaluated and compared in simulation experiments, and applied to real data from a colon cancer trial.