Tree based weighted learning for estimating individualized treatment rules with censored data

Estimating individualized treatment rules is a central task for personalized medicine. [zhao2012estimating] and [zhang2012robust] proposed outcome weighted learning to estimate individualized treatment rules directly through maximizing the expected outcome without modeling the response directly. In this paper, we extend the outcome weighted learning to right censored survival data without requiring either an inverse probability of censoring weighting or a semiparametric modeling of the censoring and failure times as done in [zhao2015doubly]. To accomplish this, we take advantage of the tree based approach proposed in [zhu2012recursively] to nonparametrically impute the survival time in two different ways. The first approach replaces the reward of each individual by the expected survival time, while in the second approach only the censored observations are imputed by their conditional expected failure times. We establish consistency and convergence rates for both estimators. In simulation studies, our estimators demonstrate improved performance compared to existing methods. We also illustrate the proposed method on a phase III clinical trial of non-small cell lung cancer.