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

Abstract

Estimating individualized treatment rules is a central task for personalized medicine. [23] and [22] 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 inverse probability of censoring weighting or semiparametric modeling of the censoring and failure times as done in [26]. To accomplish this, we take advantage of the tree based approach proposed in [28] 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.

Precision Medicine

“…In addition, computation of error bounds can be a useful assessment of performance which is more precise than the presence or absence of consistency but not precise enough to obtain first order inference. These have been developed for many machine learning tools used in precision medicine, as in (Qian and Murphy 2011; Goldberg and Kosorok 2012;Zhao et al 2012;Cui et al 2017), and, more recently, have been improved for some settings in (Athey and Wager 2017). We also note the sample size formulas for the single-decision setting have been developed based on the value function (Laber et al 2016).…”

The change-plane Cox model

“…As for the recursively imputed survival tree estimate of α , Theorem 1 of Cui et al (2017) addresses the consistency of estimating the underlying hazard function using a similar survival tree-based method. In both cases, a single tree is partitioned enough so that the failure and censoring observations in the terminal nodes are approximately independent while maintaining a sufficient number of observations.…”

A nonparametric method for value function guided subgroup identification via gradient tree boosting for censored survival data

“…Zhao et al 24 and Zhang et al 25 transformed the value function optimization to a weighted classification problem known as outcome weighted learning. Numerous methods have been proposed under this framework, [26][27][28][29][30][31][32][33][34][35][36][37][38] with developments in the areas of robust estimation, variable selection, and sparse or interpretable treatment regime using tree-based methods. Among the clinical endpoints considered by ITR methods, the time-to-event or survival endpoints deserve some special attention.…”