A treatment regime is a deterministic function that dictates personalized treatment based on patients' individual prognostic information. There is increasing interest in finding optimal treatment regimes, which determine treatment at one or more treatment decision points so as to maximize expected long-term clinical outcome, where larger outcomes are preferred. For chronic diseases such as cancer or HIV infection, survival time is often the outcome of interest, and the goal is to select treatment to maximize survival probability. We propose two nonparametric estimators for the survival function of patients following a given treatment regime involving one or more decisions, i.e., the so-called value. Based on data from a clinical or observational study, we estimate an optimal regime by maximizing these estimators for the value over a prespecified class of regimes. Because the value function is very jagged, we introduce kernel smoothing within the estimator to improve performance. Asymptotic properties of the proposed estimators of value functions are established under suitable regularity conditions, and simulations studies evaluate the finite-sample performance of the proposed regime estimators. The methods are illustrated by application to data from an AIDS clinical trial.
Keywords: Inverse probability weighted estimation; Kaplan-Meier estimator; optimal treatment regime; personalized medicine; survival probability; value function.