Power prior models for estimating response rates in a small n, sequential, multiple assignment, randomized trial

A small n, sequential, multiple assignment, randomized trial (snSMART) is a small sample, two-stage design where participants receive up to two treatments sequentially, but the second treatment depends on response to the first treatment. The parameters of interest in an snSMART are the first-stage response rates of the treatments, but outcomes from both stages can be used to obtain more information from a small sample. A novel way to incorporate the outcomes from both stages uses power prior models, in which first stage outcomes from an snSMART are regarded as the primary (internal) data and second stage outcomes are regarded as supplemental data (co-data). We apply existing power prior models to snSMART data, and we also 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 response rates in an snSMART, which both have performance mostly as good or better than the BJSM. We describe the situations where each of these suggested approaches is preferred.