Title: Design and Analysis of Sequential Multiple Assignment Randomized Trial for Comparing Multiple Adaptive Interventions
Description: The research of my dissertation studies the methods of designing and analyzing sequential multiple assignment randomized trial (SMART) for comparing multiple adaptive interventions. As a SMART typically consists of numerous adaptive interventions, inferential procedures based on pairwise comparisons of all interventions may suffer substantial loss in power after accounting for multiplicity. I address this problem using two approaches. First, I propose a likelihood-based Wald test, study the asymptotic distribution of its test statistics, and apply it as a gate-keeping test for making an adaptive intervention selection. Second, I consider a multiple comparison with the best approach by constructing simultaneous confidence intervals that compare the interventions of interest with the truly best intervention, which is assumed to be unknown in inference; an adaptive intervention with the proposed interval excluding zero will be declared as inferior to the truly best with a pre-specified confidence level.

Simulation studies show that both methods outperform the corresponding multiple comparison procedures based on Bonferroni's correction in terms of the power of test and the average width of confidence intervals for estimation. Simulations also suggest desirable properties of the proposed methods. I apply these methods to analyze two real data sets. As part of the dissertation, I also develop a user-friendly R software package that covers many statistical work related to SMART, including study design, data analysis and visualization. Both proposed methods can be implemented by using this R package. In the end of the dissertation, I show an application of designing a SMART to compare multiple patient care strategies for depression management based on one of the proposed methods.