Bayesian analysis for pretest-posttest binary outcomes with adaptive significance levels

TL;DR

This paper introduces a Bayesian methodology for analyzing binary pretest-posttest data, incorporating adaptive significance levels and the Full Bayesian Significance Test, validated through simulations and applied to a real clinical dataset.

Contribution

It develops a novel Bayesian approach with adaptive significance levels for paired binary outcomes, filling a gap in existing methods for simple pretest-posttest scenarios.

Findings

Validated through simulation studies

Applied successfully to real clinical data

Demonstrated effectiveness of adaptive significance levels

Abstract

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be taken into account. However, in more straightforward scenarios, where only two stages of an experiment are observed (pre-treatment vs. post-treatment), there are only a few tools available, mainly for continuous outcomes. Thus, this work introduces a Bayesian statistical methodology for comparing paired samples in binary pretest-posttest scenarios. We establish a Bayesian probabilistic model for the inferential analysis of the unknown quantities, which is validated and refined through simulation analyses, and present an application to a dataset taken from the Television School and Family Smoking Prevention and Cessation Project (TVSFP) (Flay et al., 1995). The application of the Full Bayesian Significance Test (FBST) for precise hypothesis testing, along with the implementation of adaptive significance levels in the decision-making process, is included.