On estimation of optimal treatment regimes for maximizing t-year survival probability

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 to maximize expected long-term clinical outcomes, where larger outcomes are preferred. For chronic diseases such as cancer or human immunodeficiency virus infection, survival time is often the outcome of interest, and the goal is to select treatment to maximize survival probability. We propose two non-parametric estimators for the survival function of patients following a given treatment regime involving one or more decisions, i.e. the so-called value. On the basis of 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 simulation studies evaluate the finite sample performance of the regime estimators. The methods are illustrated by application to data from an acquired immune deficiency syndrome clinical trial.