Maximin Projection Learning for Optimal Treatment Decision with Heterogeneous Individualized Treatment Effects

A saline feature of data from clinical trials and medical studies is inhomogeneity. Patients not only differ in baseline characteristics, but also the way they respond to treatment. Optimal individualized treatment regimes are developed to select effective treatments based on patient's heterogeneity. However, the optimal treatment regime might also vary for patients across different subgroups. In this paper, we mainly consider patient's heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups. We propose a new maximin-projection learning for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation. Based on estimated optimal treatment regimes for all subgroups, the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming (QCLP) problem, which can be efficiently computed by interior-point methods. Consistency and asymptotic normality of the estimator is established. Numerical examples show the reliability of the proposed methodology.