Estimation Methods and Clinical Trial Design in Small n, Sequential, Multiple-Assignment, Randomized Trials

Abstract

The application of a small n, sequential, multiple-assignment randomized trial (snSMART) to rare disease studies remains an active research area. In this dissertation, we present methods that estimate dynamic treatment regimens (DTRs), or tailored sequences of treatments, for rare diseases, such as focal segmental glomerulosclerosis. We also develop an snSMART design that allows for removing an inferior treatment arm. Moreover, we summarize methods and develop new approaches to incorporate data from both stages in this estimation of the first stage treatment effect in an snSMART through the use of power priors.

Following an introduction of an snSMART and its potential application in Chapter 1, in Chapter 2, we propose a Bayesian joint stage model and a joint stage regression model, first developed by Wei et al. (2018). These models can be applied to estimate DTRs by combining information across stages. We show that the estimates from these two methods are more efficient than that of a standard SMART analysis of weighted and replicated regression (Nahum-Shani et al., 2012). In addition, we introduce a sample size calculation method for our snSMART design when implementing the joint stage regression model with Dunnett's correction.

In Chapter 3, we are motivated by an ongoing snSMART, ARAMIS (NCT02939573), focusing on the evaluation of three drugs for isolated skin vasculitis. We propose an alternative design by formulating an interim decision rule for removing one of the treatments, using Bayesian modelling and the resulting posterior distributions to provide sufficient evidence that one treatment is inferior to the other treatments. By doing so, we can remove the worst performing treatment at an interim analysis and prevent subsequent participants from receiving the removed treatment. In addition, by adjusting the decision rule criteria for the posterior probabilities, we can control the probability of incorrectly removing a treatment, a Bayesian counterpart of Type I or Type II error rate used in frequentist methods.

In Chapter 4, we develop a novel method to incorporate outcomes from both stages in an snSMART to estimate the first stage treatment effects using power prior models. Here, we consider the first stage outcomes from an snSMART as the primary, or current, data and second stage outcomes as supplemental, or historical. We apply existing power prior models to snSMART data, and develop new extensions of power prior models. All methods are compared to each other and to the Bayesian joint stage model (BJSM) via simulation studies. By comparing the biases and the efficiency of the response rate estimates among all proposed power prior methods, we suggest application of Fisher's exact test or the Bhattacharyya's overlap measure to an snSMART to estimate the treatment effect in an snSMART, which both have performance mostly as good or better than the BJSM.