Meta-analysis has been widely applied to rare adverse event data because it is very difficult to reliably detect the effect of a treatment on such events in an individual clinical study. However, it is known that standard meta-analysis methods are often biased, especially when the background incidence rate is very low. A recent work by Bhaumik et al. proposed new moment-based approaches under a natural random effects model, to improve estimation and testing of the treatment effect and the between-study heterogeneity parameter. It has been demonstrated that for rare binary events, their methods have superior performance to commonly used meta-analysis methods. However, their comparison does not include any Bayesian methods, although Bayesian approaches are a natural and attractive choice under the random-effects model. In this article, we study a Bayesian hierarchical approach to estimation and testing in meta-analysis of rare binary events using the random effects model in Bhaumik et al. We develop Bayesian estimators of the treatment effect and the heterogeneity parameter, as well as hypothesis testing methods based on Bayesian model selection procedures. We compare them with the existing methods through simulation. A data example is provided to illustrate the Bayesian approach as well.

荟萃分析已广泛应用于罕见不良事件数据，因为在个体临床研究中很难可靠地检测治疗对此类事件的影响。然而，众所周知，标准荟萃分析方法常常存在偏差，特别是当背景发生率非常低时。 Bhaumik 等人最近的一项工作。在自然随机效应模型下提出了新的基于矩的方法，以改进治疗效果和研究间异质性参数的估计和测试。事实证明，对于罕见的二元事件，他们的方法比常用的荟萃分析方法具有优越的性能。然而，他们的比较不包括任何贝叶斯方法，尽管贝叶斯方法在随机效应模型下是一个自然且有吸引力的选择。在本文中，我们使用 Bhaumik 等人的随机效应模型研究了一种贝叶斯分层方法，用于估计和测试罕见二元事件的荟萃分析。我们开发了治疗效果和异质性参数的贝叶斯估计量，以及基于贝叶斯模型选择程序的假设检验方法。我们通过模拟将它们与现有方法进行比较。还提供了一个数据示例来说明贝叶斯方法。