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.

翻译：纵向研究中的计数结果在临床与工程研究中十分常见。在频率学派与贝叶斯统计分析中，混合线性模型等方法能够考虑个体内的变异性或相关性。然而，在更简单的实验场景中——仅观测实验的两个阶段（处理前与处理后）——可用的分析工具较少，且主要针对连续型结果。因此，本研究提出了一种贝叶斯统计方法，用于在二元前测-后测场景中比较配对样本。我们建立了一个贝叶斯概率模型，用于对未知量进行推断分析，该模型通过模拟分析得到验证与改进，并以电视学校与家庭吸烟预防和戒断项目（TVSFP）（Flay等人，1995）的数据集为例进行了应用。研究包含了使用全贝叶斯显著性检验（FBST）进行精确假设检验，以及在决策过程中实施自适应显著性水平的方法。