Robust Learning for Optimal Treatment Strategy with Survival Data

The personalized medicine has received exponentially increasing attention recently. Different people may respond differently to the same treatment. Also, the same person may respond differently to different treatments. Compared to the traditional one-size-fits all strategy, personalization may provide more accurate and more effective treatments to patients. People are interested in tailoring the treatment strategy for each patient particularly to his or her characteristics, genomic information and financial budget through all aspects of health care from diagnosis and medical product to follow-up. People are also interested in adapting the medical decisions along with the disease progression and changes in health status. A treatment regime is a function that dictates personalized treatment based on patients individual information. Our objective is to use data-driven methods to identify the optimal treatment regime among all feasible ones, which can provide guidance to physicians and patients to achieve the most favorable clinical outcome at the population level. In this thesis work, we focus on the estimation of the optimal treatment regime when the primary outcome is subject to censoring.;In Chapter 2, we propose two nonparametric estimators for the t-year survival probability of patients following a given treatment regime involving one or more decisions, i.e., the value function. 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 are conducted to evaluate the finite-sample performance of the proposed regime estimators. The methods are illustrated by an application to a dataset from an AIDS clinical trial.;In Chapter 3, we extend the proposed methods in Chapter 2 to a general class of value functions, which can be expressed as a function of the regime-specific survival function. The extension is meaningful and helpful, since the t-year survival probability may not be informative without the ability to balance the short-term and long-term benefits. Two commonly used examples of the value functions are the restricted mean survival time and the median survival time. We study the asymptotic properties of the proposed estimates and investigate their numerical performance via simulation studies. We also illustrate the proposed methods to an AIDS data from the UNC Center of AIDS Research to identify the regime that maximize the restricted mean duration time of the initial treatment.