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

Yifan Cui,Ruoqing Zhu,Michael Kosorok

doi:10.1214/17-ejs1305

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.

Highlights

An individualized treatment regime provides a personalized treatment strategy for each patient in the population based on their individual characteristics
While each of these approaches has strengths and weaknesses, we highlight the approach in [25] because of its robustness to model misspecification combined with its ability to incorporate support vector machines through the recognition that optimizing the treatment rule can be recast as a weighted classification problem
Adapting outcome weighted learning to the censored setting, [26] proposed two new approaches, inverse censoring weighted outcome weighted learning and doubly robust outcome weighted learning, both of which require semiparametric estimation of the conditional censoring probability given the patient characteristics and treatment choice

Summary

Introduction

An individualized treatment regime provides a personalized treatment strategy for each patient in the population based on their individual characteristics. A significant amount of work has been devoted to estimating optimal treatment rules [17, 18, 23, 24, 25] While each of these approaches has strengths and weaknesses, we highlight the approach in [25] because of its robustness to model misspecification (this is true of the approach in [23]) combined with its ability to incorporate support vector machines through the recognition that optimizing the treatment rule can be recast as a weighted classification problem. This approach is commonly referred to as outcome weighted learning. Potential drawbacks of these methods are that either or both models may be misspecified and inverse censoring weighting estimation can be unstable numerically [18, 29]

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