Title: Tree based weighted learning for estimating individualized treatment rules with censored data,
Abstract: 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.