  An optimal dynamic treatment regime (DTR) consists of a sequence of decision
rules in maximizing long-term benefits, which is applicable for chronic
diseases such as HIV infection or cancer. In this paper, we develop a novel
angle-based approach to search the optimal DTR under a multicategory treatment
framework for survival data. The proposed method targets maximization the
conditional survival function of patients following a DTR. In contrast to most
existing approaches which are designed to maximize the expected survival time
under a binary treatment framework, the proposed method solves the
multicategory treatment problem given multiple stages for censored data.
Specifically, the proposed method obtains the optimal DTR via integrating
estimations of decision rules at multiple stages into a single multicategory
classification algorithm without imposing additional constraints, which is also
more computationally efficient and robust. In theory, we establish Fisher
consistency of the proposed method under regularity conditions. Our numerical
studies show that the proposed method outperforms competing methods in terms of
maximizing the conditional survival function. We apply the proposed method to
two real datasets: Framingham heart study data and acquired immunodeficiency
syndrome (AIDS) clinical data.
