Learning Robust Treatment Rules for Censored Data

Abstract: There is a fast-growing literature on estimating optimal treatment rules directly by maximizing the expected outcome. In biomedical studies and operations applications, censored survival outcome is frequently observed, in which case the restricted mean survival time and survival probability are of great interest. In this paper, we propose two robust criteria for learning optimal treatment rules with censored survival outcomes; the former one targets at an optimal treatment rule maximizing the restricted mean survival time, where the restriction is specified by a given quantile such as median; the latter one targets at an optimal treatment rule maximizing buffered survival probabilities, where the predetermined threshold is adjusted to account the restricted mean survival time. We provide theoretical justifications for the proposed optimal treatment rules and develop a sampling-based difference-of-convex algorithm for learning them. In simulation studies, our estimators show improved performance compared to existing methods. We also demonstrate the proposed method using AIDS clinical trial data.