An individualized treatment rule is often employed to maximize a certain patient-specific clinical outcome based on his/her clinical or genomic characteristics as well as heterogeneous response to treatments. Although developing such a rule is conceptually important to personalized medicine, existing methods such as the partial least squares Qian and Murphy (2011) suffers from the difficulty of indirect maximization of a patient's clinical outcome, while the outcome weighted learning Y. Zhao, Zeng, Rush, and Kosorok (2012) is not robust against any perturbation of the outcome. In this article, we propose a weighted ψ-learning method to optimize an individualized treatment rule, which is robust against any data perturbation near the decision boundary by seeking the maximum separation. To solve nonconvex minimization, we employ a difference convex algorithm to relax the non-convex minimization iteratively based on a decomposition of the cost function into a difference of two convex functions. On this ground, we also introduce a variable selection method for further removing redundant variables for a higher performance. Finally, we illustrate the proposed method by simulations and a lung health study and demonstrate that it yields higher performances in terms of accuracy of prediction of individualized treatment.
Keywords: Lung cancer treatments; Personalized medicine; Regularization; Variable selection.