Estimating individualized treatment rules with risk constraint.

Individualized treatment rules (ITRs) recommend treatments based on patient-specific characteristics in order to maximize the expected clinical outcome. At the same time, the risks caused by various adverse events cannot be ignored. In this paper, we propose a method to estimate an optimal ITR that maximizes clinical benefit while having the overall risk controlled at a desired level. Our method works for a general setting of multi-category treatment. The proposed procedure employs two shifted ramp losses to approximate the 0-1 loss in the objective function and constraint, respectively, and transforms the estimation problem into a difference of convex functions (DC) programming problem. A relaxed DC algorithm is used to solve the nonconvex constrained optimization problem. Simulations and a real data example are used to demonstrate the finite sample performance of the proposed method.