Variable selection for estimating optimal treatment regimes with multiple treatments

We propose a penalized classification method for estimating optimal treatment regimes (OTRs) with multiple treatments when the number of covariates is large. Our approach reformulates the OTR estimation problem as a weighted multiclass classification problem and integrates variable selection with doubly robust estimation into a unified framework that simultaneously performs variable selection and regime estimation. By employing a data expansion technique and incorporating Formula: see text-type penalization along with augmented inverse probability weighting (AIPW) estimators, the method effectively identifies the sparse subset of covariates that genuinely drive treatment effect heterogeneity. Extensive simulation studies demonstrate the superior performance of the proposed method in terms of accuracy and double robustness for estimating the optimal treatment regimes. The method's practical utility is further illustrated through an application to a clinical trial for chronic depression.