Variable selection for estimating the optimal treatment regimes in the presence of a large number of covariates

Abstract

Most existing methods for optimal treatment regimes, with few exceptions, focus on estimation and are not designed for variable selection with the objective of optimizing treatment decisions. In clinical trials and observational studies, often numerous baseline variables are collected and variable selection is essential for deriving reliable optimal treatment regimes. Although many variable selection methods exist, they mostly focus on selecting variables that are important for prediction (predictive variables) instead of variables that have a qualitative interaction with treatment (prescriptive variables) and hence are important for making treatment decisions. We propose a variable selection method within a general classification framework to select prescriptive variables and estimate the optimal treatment regime simultaneously. In this framework, an optimal treatment regime is equivalently defined as the one that minimizes a weighted misclassification error rate and the proposed method forward sequentially select prescriptive variables by minimizing this weighted misclassification error. A main advantage of this method is that it specifically targets selection of prescriptive variables and in the meantime is able to exploit predictive variables to improve performance. The method can be applied to both single- and multiple-decision point setting. The performance of the proposed method is evaluated by simulation studies and application to a clinical trial.