Abstract: Owing to the heterogeneity exhibited by many chronic diseases, precise personalized medicine, also known as precision medicine, has garnered increased attention in the scientific community. One main goal of precision medicine is to develop the most effective tailored therapy for each individual patient. To this end, one needs to incorporate individual characteristics to determine a proper individual treatment rule (ITR), which is used to make suitable decisions on treatment assignments that optimize patients’ clinical outcomes. For binary treatment settings, outcome-weighted learning (OWL) and several of its variations have been proposed to estimate an ITR by optimizing the conditional expected outcome, given patients’ information. However, for multiple treatment scenarios, it remains unclear how to use OWL effectively. It can be shown that some direct extensions of OWL for multiple treatments, such as the one-versus-one and one-versus-rest methods, can yield suboptimal performance. In this paper, we propose a new learning method, called multicategory outcome-weighted margin-based learning (MOML), for estimating an ITR with multiple treatments. Our proposed method is very general and covers OWL as a special case. We show the Fisher consistency of the estimated ITR, and establish its convergence rate properties. Variable selection using the sparse l₁ penalty is also considered. Simulations and a type-2 diabetes mellitus observational study are used to demonstrate the competitive performance of the proposed method.

Key words and phrases: Angle-based classifier, large-margin, multiple treatments, outcome weighted learning, precision medicine, support vector machine.