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 baselinerisk, 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 an exact posterior sampling algorithm and an accurate and fast data-augmented Gibbs sampler 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，用于对具有二元处理和二元结果的随机对照试验进行贝叶斯分析。从因果推断的角度出发，我们建议以治疗的基线风险、疗效和不良副作用作为似然函数的参数化基础，并结合一个灵活、直观且易于处理的联合独立贝塔先验分布。我们证明该先验是潜在结果联合分布的狄利克雷先验的推广形式。与当前主流方法相比，我们的方法具有以下优势：(i) 它自然地诱导了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是临床医学常用术语，先验的超参数具有直接可解释性，便于先验知识的提取和敏感性分析；(iii) 我们提供了边际似然、贝叶斯因子及其他后验量的解析公式，并给出了精确后验采样算法，以及在传统MCMC方法失效时使用的精确高效数据增强吉布斯采样器。实证案例表明，我们的方法在治疗效果估计、假设检验和敏感性分析方面具有实用价值。