  Dynamic treatment regimens (DTRs) aim at tailoring individualized sequential
treatment rules that maximize cumulative beneficial outcomes by accommodating
patients' heterogeneity in decision-making. For many chronic diseases including
type 2 diabetes mellitus (T2D), treatments are usually multifaceted in the
sense that aggressive treatments with a higher expected reward are also likely
to elevate the risk of acute adverse events. In this paper, we propose a new
weighted learning framework, namely benefit-risk dynamic treatment regimens
(BR-DTRs), to address the benefit-risk trade-off. The new framework relies on a
backward learning procedure by restricting the induced risk of the treatment
rule to be no larger than a pre-specified risk constraint at each treatment
stage. Computationally, the estimated treatment rule solves a weighted support
vector machine problem with a modified smooth constraint. Theoretically, we
show that the proposed DTRs are Fisher consistent, and we further obtain the
convergence rates for both the value and risk functions. Finally, the
performance of the proposed method is demonstrated via extensive simulation
studies and application to a real study for T2D patients.
