Estimating Individualized Treatment Rules Using Outcome Weighted Learning

Abstract

There is increasing interest in discovering individualized treatment rules for patients who have heterogeneous responses to treatment. In particular, one aims to find an optimal individualized treatment rule which is a deterministic function of patient specific characteristics maximizing expected clinical outcome. In this paper, we first show that estimating such an optimal treatment rule is equivalent to a classification problem where each subject is weighted proportional to his or her clinical outcome. We then propose an outcome weighted learning approach based on the support vector machine framework. We show that the resulting estimator of the treatment rule is consistent. We further obtain a finite sample bound for the difference between the expected outcome using the estimated individualized treatment rule and that of the optimal treatment rule. The performance of the proposed approach is demonstrated via simulation studies and an analysis of chronic depression data.

Keywords: Bayes Classifier; Cross Validation; Dynamic Treatment Regime; Individualized Treatment Rule; RKHS; Risk Bound; Weighted Support Vector Machine.

Figures

Figure 1

Contour Plots of Value Function for Example 1 with λn ∈ (0, 10) and σn ∈ (0, 10)

Figure 2

MSE for Value Functions of Individualized Treatment Rules

Figure 3

MSE for Misclassification Rates of Individualized Treatment Rules