Variable Selection in Regression-based Estimation of Dynamic Treatment Regimes

Abstract: Dynamic treatment regimes (DTRs) consist of a sequence of decision rules, one per stage of intervention, that finds effective treatments for individual patients according to patient information history. DTRs can be estimated from models which include the interaction between treatment and a small number of covariates which are often chosen a priori. However, with increasingly large and complex data being collected, it is difficult to know which prognostic factors might be relevant in the treatment rule. Therefore, a more data-driven approach of selecting these covariates might improve the estimated decision rules and simplify models to make them easier to interpret. We propose a variable selection method for DTR estimation using penalized dynamic weighted least squares. Our method has the strong heredity property, that is, an interaction term can be included in the model only if the corresponding main terms have also been selected. Through simulations, we show our method has both the double robustness property and the oracle property, and the newly proposed methods compare favorably with other variable selection approaches.