Evaluation and Comparison of Dynamic Treatment Regimes: Methods and Challenges.

Abstract

Dynamic treatment regimes (DTRs) are sequences of decision rules that link the patient history with treatment recommendations. Clinical scientists have become increasingly interested in the development of DTRs in various fields including substance abuse, mental health and cancer. The Sequential Multiple Assignment Randomized Trial (SMART) is a multi-stage trial design that explicitly targets the development of high-quality DTRs. In this dissertation, we develop statistical methodologies, which can be applied to SMART data, that either address novel research questions regarding the construction of a high-quality DTR, or exhibit better performance than existing statistical methods.

In Chapter 2, we develop an assisted estimator that can be used to compare the mean outcomes of a pair of competing DTRs. The term “assisted” refers to the fact that estimators from the structural nested mean model, a parametric model for the intermediate causal effect at each time point, are used in the process of estimating the mean outcome. In Chapter 3, we compare a pre-determined set of DTRs in terms of a repeated-measures outcome that spans across multiple treatment stages in a SMART. We illustrate the repeated-measures modeling considerations, that are particular to SMART studies, by discussing three case studies in autism, child ADHD and adult alcoholism. In Chapter 4, we focus on the well developed and widely used weighted-and-replicated (WR) estimator that is used to compare a pre-determined set of DTRs in terms of an end-of-study outcome. The typically used sandwich estimator for the variance of the WR estimator can be biased for the true variance when the sample size is small; therefore, we derive a small-sample adjusted estimator for the variance of WR estimator. In Chapter 5, we introduce the ongoing work regarding the search for the optimal treatment decision rule within a pre-specified parametrized class, with the additional aim to make inference about the usefulness of including one particular variable as a tailoring variable. We consider a regularized estimator for the optimal policy, with two components of regularization motivated by two issues of the original unregularized estimator.