Power prior models for treatment effect estimation in a small n, sequential, multiple assignment, randomized trial

TL;DR

This paper introduces and compares power prior models for estimating treatment effects in small sample, two-stage sequential trials, demonstrating their effectiveness and proposing practical methods for analysis.

Contribution

The paper develops new extensions of power prior models specifically for small n, sequential, multiple assignment randomized trials, and compares them to existing methods through simulations.

Findings

Power prior models perform well in small sample settings.

Fisher's exact test and Bhattacharyya's overlap measure are effective for treatment effect estimation.

Proposed methods outperform or match Bayesian joint stage model in simulations.

Abstract

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.