A Study of Non-regularity in Dynamic Treatment Regimes and Some Design Considerations for Multicomponent Interventions.

This dissertation investigates two methodological problems. The first problem concerns developing and optimizing multicomponent interventions. The traditional approach to this problem is to conduct a two-group randomized trial of a "likelybest" intervention vs. control, followed by observational analyses. In this approach, all inferences about individual components and their interactions are typically based on observational analyses, and hence are subject to confounding bias. An emerging approach called the Multiphase Optimization Strategy (MOST) addresses the aboveproblem by including two evidentiary phases of randomized experiments to precede and inform a confirmatory two-group randomized trial. Full and fractional factorial designs are useful tools in this approach. However there exists a lot of criticism in the clinical and behavioral intervention trials literature regarding their use. In this dissertation, we address these criticisms in the context of the MOST framework.Furthermore, we provide an operationalization of the screening phase of MOST using fractional factorial designs. Also to strengthen the case for MOST as the "gold standard" for designing multicomponent intervention trials, we provide an illustrative simulation study comparing MOST with the traditional approach. The second problem investigated in this dissertation is that of non-regularity thatarises in the estimation of the optimal dynamic treatment regimes (DTR). DTRs are multistage, individualized treatment rules that are useful for treating chronic disorders. In the estimation of the optimal DTRs, the treatment effect parameters at any stage prior to the last can be non-regular under certain distributions of the data. This results in biased estimates and invalid confidence intervals for the treatmenteffect parameters. To address the problem of non-regularity, we propose a shrinkage estimator called the soft-threshold estimator. We derive this as an empirical Bayes estimator under a hierarchical Bayesian model. We also provide an extensive simulation study to compare the soft-threshold estimator with other available estimators that attempt to address non-regularity. Analysis of data from a smoking cessation trial is provided as an illustration.