Doubly Robust Learning for Estimating Individualized Treatment with Censored Data

Abstract

Individualized treatment rules recommend treatments based on individual patient characteristics in order to maximize clinical benefit. When the clinical outcome of interest is survival time, estimation is often complicated by censoring. We develop nonparametric methods for estimating an optimal individualized treatment rule in the presence of censored data. To adjust for censoring, we propose a doubly robust estimator which requires correct specification of either the censoring model or survival model, but not both; the method is shown to be Fisher consistent when either model is correct. Furthermore, we establish the convergence rate of the expected survival under the estimated optimal individualized treatment rule to the expected survival under the optimal individualized treatment rule. We illustrate the proposed methods using simulation study and data from a Phase III clinical trial on non-small cell lung cancer.

Keywords: Censored data; Doubly robust estimator; Individualized treatment rule; Risk bound; Support vector machine.

Fig. 1

Boxplots of values of estimated rules using different methods, representing the logarithm of the survival time with higher values being more preferable. Cox, Cox model; Q, inverse censoring weighted Q-learning; L2Q, inverse censoring weighted L₂ Q-learning; ICO, inverse censoring weighted outcome weighted learning with linear kernel; DRO, doubly robust outcome weighted learning with linear kernel.