We introduce the BREASE framework for the Bayesian analysis of randomized controlled trials with a binary treatment and a binary outcome. Approaching the problem from a causal inference perspective, we propose parameterizing the likelihood in terms of the baseline risk, efficacy, and side effects of the treatment, along with a flexible, yet intuitive and tractable jointly independent beta prior distribution on these parameters, which we show to be a generalization of the Dirichlet prior for the joint distribution of potential outcomes. Our approach has a number of desirable characteristics when compared to current mainstream alternatives: (i) it naturally induces prior dependence between expected outcomes in the treatment and control groups; (ii) as the baseline risk, efficacy and side effects are quantities inherently familiar to clinicians, the hyperparameters of the prior are directly interpretable, thus facilitating the elicitation of prior knowledge and sensitivity analysis; and (iii) it admits analytical formulae for the marginal likelihood, Bayes factor, and other posterior quantities, as well as exact posterior sampling via simulation, in cases where traditional MCMC fails. Empirical examples demonstrate the utility of our methods for estimation, hypothesis testing, and sensitivity analysis of treatment effects.

翻译：我们引入BREASE框架，用于对二元处理变量与二元结果变量的随机对照试验进行贝叶斯分析。从因果推断视角出发，我们提出以基线风险、疗效和治疗副作用参数化似然函数，并为这些参数设计了一种灵活、直观且易于处理的联合独立贝塔先验分布——我们证明该分布是潜在结果联合分布的狄利克雷先验的推广形式。与当前主流替代方法相比，我们的方法具有以下理想特性：(i) 自然地在处理组与对照组的预期结果之间引入先验依赖性；(ii) 由于基线风险、疗效和副作用是临床医生固有的熟悉指标，先验的超参数具有直接可解释性，便于先验知识提取与敏感性分析；(iii) 在传统MCMC失效的情况下，可推导出边缘似然、贝叶斯因子及其他后验量的解析表达式，并通过模拟实现精确后验抽样。实证案例展示了该方法在治疗效果估计、假设检验及敏感性分析中的实用价值。