Robust outcome weighted learning for optimal individualized treatment rules

Personalized medicine has received increasing attentions among scientific communities in recent years. Because patients often have heterogenous responses to treatments, discovering individualized treatment rules (ITR) is an important component of precision medicine. To that end, one needs to develop a proper decision rule using patient-specific characteristics to maximize the expected clinical outcome, i.e. the optimal ITR. Recently, outcome weighted learning (OWL) has been proposed to estimate optimal ITR under a weighted classification framework. Since most of commonly used loss functions are unbounded, the resulting ITR may suffer similar effects of outliers as the corresponding classifiers. In this paper, we propose robust OWL (ROWL) to build more stable ITRs using a new family of bounded and non-convex loss functions. Moreover, we extend the proposed ROWL method to the multiple treatment setting under the angle-based classification structure. Our theoretical results show that ROWL is Fisher consistent, and can provide the estimation of rewards' ratios for the resulting ITRs. We develop an efficient difference of convex functions algorithm (DCA) to solve the corresponding nonconvex optimization problem. Through analysis of simulated examples and a real medical dataset, we demonstrate that the proposed ROWL method yields more competitive performance in terms of the empirical value function and the misclassification error than several existing methods.