We present a novel Bayesian approach to random effects meta analysis of binary data with excessive zeros in two-arm trials. We discuss the development of likelihood accounting for excessive zeros, the prior, and the posterior distributions of parameters of interest. Dirichlet process prior is used to account for the heterogeneity among studies. A zero inflated binomial model with excessive zero parameters were used to account for excessive zeros in treatment and control arms. We then define a modified unconditional odds ratio accounting for excessive zeros in two arms. The Bayesian inference is carried out using Markov chain Monte Carlo (MCMC) sampling techniques. We illustrate the approach using data available in published literature on myocardial infarction and death from cardiovascular causes. Bayesian approaches presented here use all the data, including the studies with zero events and capture heterogeneity among study effects, and produce interpretable estimates of overall and study-level odds-ratios, over the commonly used frequentist’s approaches. Results from the data analysis and the model selection also indicate that the proposed Bayesian method, while accounting for zero events, adjusts for excessive zeros and provides better fit to the data resulting in the estimates of overall odds-ratio and study-level odds-ratios that are based on the totality of the information.

中文翻译：

---

在两臂试验中对带有过多零的二进制数据进行元分析

我们提出了一种新颖的贝叶斯方法，用于在两臂试验中对具有过多零的二进制数据进行随机效应元分析。我们讨论了考虑零参数，先验和后验分布的可能性的发展。Dirichlet过程先验用于解释研究之间的异质性。使用零参数过多的零膨胀二项式模型来说明治疗和控制臂中的零过多。然后，我们定义了修正的无条件优势比，说明了两个分支中过多的零。贝叶斯推断是使用马尔可夫链蒙特卡洛（MCMC）采样技术进行的。我们使用公开发表的有关心肌梗塞和心血管原因死亡的文献中的数据来说明该方法。这里介绍的贝叶斯方法会使用所有数据，包括零事件的研究，并捕获研究效果之间的异质性，并根据常用的频频主义者的方法得出整体和研究水平比值比的可解释性估计。数据分析和模型选择的结果还表明，提出的贝叶斯方法在考虑零事件的情况下，会针对过多的零点进行调整，并更好地拟合数据，从而估算总体比值比和研究水平的比值比基于全部信息。