Stabilized direct learning for efficient estimation of individualized treatment rules

In recent years, the field of precision medicine has seen many advancements. Significant focus has been placed on creating algorithms to estimate individualized treatment rules (ITRs), which map from patient covariates to the space of available treatments with the goal of maximizing patient outcome. Direct learning (D-Learning) is a recent one-step method which estimates the ITR by directly modeling the treatment-covariate interaction. However, when the variance of the outcome is heterogeneous with respect to treatment and covariates, D-Learning does not leverage this structure. Stabilized direct learning (SD-Learning), proposed in this paper, utilizes potential heteroscedasticity in the error term through a residual reweighting which models the residual variance via flexible machine learning algorithms such as XGBoost and random forests. We also develop an internal cross-validation scheme which determines the best residual model among competing models. SD-Learning improves the efficiency of D-Learning estimates in binary and multi-arm treatment scenarios. The method is simple to implement and an easy way to improve existing algorithms within the D-Learning family, including original D-Learning, Angle-based D-Learning (AD-Learning), and Robust D-learning (RD-Learning). We provide theoretical properties and justification of the optimality of SD-Learning. Head-to-head performance comparisons with D-Learning methods are provided through simulations, which demonstrate improvement in terms of average prediction error (APE), misclassification rate, and empirical value, along with a data analysis of an acquired immunodeficiency syndrome (AIDS) randomized clinical trial.