Variable Selection for Individualized Treatment Rules with Discrete Outcomes

Abstract: An individualized treatment rule (ITR) is a decision rule that aims to improve individual patients health outcomes by recommending optimal treatments according to patients specific information. In observational studies, collected data may contain many variables that are irrelevant for making treatment decisions. Including all available variables in the statistical model for the ITR could yield a loss of efficiency and an unnecessarily complicated treatment rule, which is difficult for physicians to interpret or implement. Thus, a data-driven approach to select important tailoring variables with the aim of improving the estimated decision rules is crucial. While there is a growing body of literature on selecting variables in ITRs with continuous outcomes, relatively few methods exist for discrete outcomes, which pose additional computational challenges even in the absence of variable selection. In this paper, we propose a variable selection method for ITRs with discrete outcomes. We show theoretically and empirically that our approach has the double robustness property, and that it compares favorably with other competing approaches. We illustrate the proposed method on data from a study of an adaptive web-based stress management tool to identify which variables are relevant for tailoring treatment.