  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 treatment effect of interest in an snSMART is the first-stage
response rate, 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 applies power prior models, in which first stage outcomes from an
snSMART are regarded as the primary data and second stage outcomes are regarded
as supplemental. 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 treatment
effect 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.
