Network meta-analysis (NMA) is gaining popularity in evidence synthesis and network meta-regression allows us to incorporate potentially important covariates into network meta-analysis. In this article, we propose a Bayesian network meta-regression hierarchical model and assume a general multivariate t distribution for the random treatment effects. The multivariate t distribution is desired for heavy-tailed random effects and converges to the multivariate normal distribution when the degrees of freedom go to infinity. Moreover, in NMA, some treatments are compared only in a single study. To overcome such sparsity, we propose a log-linear regression model for the variances of the random effects and incorporate aggregate covariates into modeling the variance components. We develop a Markov chain Monte Carlo sampling algorithm to sample from the posterior distribution via the collapsed Gibbs technique. We further use the deviance information criterion and the logarithm of the pseudo-marginal likelihood for model comparison. A simulation study is conducted and a detailed analysis from our motivating case study is carried out to further demonstrate the proposed methodology.

中文翻译：

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贝叶斯网络元回归分层模型使用具有协变量相关方差的重尾多元随机效应

网络元分析 (NMA) 在证据合成中越来越受欢迎，网络元回归允许我们将潜在的重要协变量纳入网络元分析。在本文中，我们提出了贝叶斯网络元回归层次模型，并假设随机处理效果的一般多元t 分布。多元t重尾随机效应需要分布，当自由度趋于无穷大时，它会收敛到多元正态分布。此外，在 NMA 中，某些治疗仅在一项研究中进行比较。为了克服这种稀疏性，我们提出了随机效应方差的对数线性回归模型，并将聚合协变量纳入方差分量的建模中。我们开发了一种马尔可夫链蒙特卡罗采样算法，通过折叠吉布斯技术从后验分布中采样。我们进一步使用偏差信息准则和伪边际似然的对数进行模型比较。进行了一项模拟研究，并对我们的激励案例研究进行了详细分析，以进一步证明所提出的方法。