  A treatment regime is a deterministic function that dictates personalized
treatment based on patients' individual prognostic information. There is a
fast-growing interest in finding optimal treatment regimes to maximize expected
long-term clinical outcomes of patients for complex diseases, such as cancer
and AIDS. For many clinical studies with survival time as a primary endpoint, a
main goal is to maximize patients' survival probabilities given treatments. In
this article, we first propose two nonparametric estimators for survival
function of patients following a given treatment regime. Then, we derive the
estimation of the optimal treatment regime based on a value-based searching
algorithm within a set of treatment regimes indexed by parameters. The
asymptotic properties of the proposed estimators for survival probabilities
under derived optimal treatment regimes are established under suitable
regularity conditions. Simulations are conducted to evaluate the numerical
performance of the proposed estimators under various scenarios. An application
to an AIDS clinical trial data is also given to illustrate the methods.
