In recent years, Bayesian meta-analysis expressed by a normal–normal hierarchical model (NNHM) has been widely used for combining evidence from multiple studies. Data provided for the NNHM are frequently based on a small number of studies and on uncertain within-study standard deviation values. Despite the widespread use of Bayesian NNHM, it has always been unclear to what extent the posterior inference is impacted by the heterogeneity prior (sensitivity ) and by the uncertainty in the within-study standard deviation values (identification ). Thus, to answer this question, we developed a unified method to simultaneously quantify both sensitivity and identification (-) for all model parameters in a Bayesian NNHM, based on derivatives of the Bhattacharyya coefficient with respect to relative latent model complexity (RLMC) perturbations. Three case studies exemplify the applicability of the method proposed: historical data for a conventional therapy, data from which one large study is first included and then excluded, and two subgroup meta-analyses specified by their randomization status. We analyzed six scenarios, crossing three RLMC targets with two heterogeneity priors (half-normal, half-Cauchy). The results show that - explicitly reveals which parameters are affected by the heterogeneity prior and by the uncertainty in the within-study standard deviation values. In addition, we compare the impact of both heterogeneity priors and quantify how - values are affected by omitting one large study and by the randomization status. Finally, the range of applicability of - is extended to Bayesian NtHM. A dedicated R package facilitates automatic - quantification in applied Bayesian meta-analyses.

中文翻译：

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贝叶斯荟萃分析中相对潜在模型复杂度扰动的敏感性和识别量化

近年来，由正态-正态层次模型（NNHM）表示的贝叶斯荟萃分析已被广泛用于结合多项研究的证据。为 NNHM 提供的数据通常基于少量研究和不确定的研究内标准偏差值。尽管贝叶斯 NNHM 得到广泛使用，但一直不清楚后验推断在多大程度上受到先验异质性（敏感性）和研究内标准差值的不确定性（识别）的影响。因此，为了回答这个问题，我们开发了一种统一的方法来同时量化灵敏度和识别（-) 对于贝叶斯 NNHM 中的所有模型参数，基于 Bhattacharyya 系数相对于相对潜在模型复杂度 (RLMC) 扰动的导数。三个案例研究举例说明了所提出方法的适用性：常规治疗的历史数据，首先包含一项大型研究然后排除的数据，以及由其随机化状态指定的两个亚组荟萃分析。我们分析了六种情景，将三个 RLMC 目标与两个异质性先验（半正常，半柯西）交叉。结果表明-明确揭示了哪些参数受先验异质性和研究内标准偏差值的不确定性影响。此外，我们比较了异质性先验的影响并量化了如何-值受到省略一项大型研究和随机化状态的影响。最后，将-的适用范围扩展到贝叶斯 NtHM。专用的R包有助于在应用贝叶斯元分析中进行自动量化。