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 adverse 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 risk of adverse side effects are quantities commonly present in the clinicians' vocabulary, the hyperparameters of the prior are directly interpretable, thus facilitating the elicitation of prior knowledge and sensitivity analysis; and (iii) we provide 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：我们提出了BREASE框架，用于对二元处理变量和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，我们建议将似然函数参数化为基线风险、治疗效果和不良副作用三个参数，并为这些参数构建灵活、直观且易于处理的独立贝塔先验分布。研究表明，该分布是潜在结果联合分布的狄利克雷先验的推广形式。相较于当前主流方法，本方法具有以下理想特性：(i) 自然引入处理组与对照组期望结果间的先验依赖性；(ii) 由于基线风险、疗效和不良副作用风险均为临床常用术语，先验的超参数具有直接可解释性，便于先验知识获取和敏感性分析；(iii) 在传统MCMC失效的情况下，我们推导出边际似然、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采样。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性。