As an extension of pairwise meta-analysis of two treatments, network meta-analysis has recently attracted many researchers in evidence-based medicine because it simultaneously synthesizes both direct and indirect evidence from multiple treatments and thus facilitates better decision making. The Bayesian hierarchical model is a popular method to implement network meta-analysis, and it is generally considered more powerful than conventional pairwise meta-analysis, leading to more precise effect estimates with narrower credible intervals. However, the improvement of effect estimates produced by Bayesian network meta-analysis has never been studied theoretically. This article shows that such improvement depends highly on evidence cycles in the treatment network. When all treatment comparisons are assumed to have different heterogeneity variances, a network meta-analysis produces posterior distributions identical to separate pairwise meta-analyses for treatment comparisons that are not contained in any evidence cycles. However, this equivalence does not hold under the commonly-used assumption of a common heterogeneity variance for all comparisons. Simulations and a case study are used to illustrate the equivalence of the Bayesian network and pairwise meta-analyses in certain networks.

中文翻译：

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网络荟萃分析中的证据循环

作为两种治疗成对荟萃分析的延伸，网络荟萃分析最近吸引了许多循证医学研究人员，因为它同时综合了多种治疗的直接和间接证据，从而促进了更好的决策。贝叶斯分层模型是实现网络元分析的一种流行方法，它通常被认为比传统的成对元分析更强大，导致更精确的效果估计和更窄的可信区间。然而，从未在理论上研究过贝叶斯网络荟萃分析产生的效果估计的改进。本文表明，这种改进在很大程度上取决于治疗网络中的证据周期。当假设所有处理比较具有不同的异质性方差时，网络荟萃分析产生的后验分布与单独的成对荟萃分析相同，用于不包含在任何证据周期中的治疗比较。然而，这种等价性在所有比较的共同异质性方差的常用假设下并不成立。模拟和案例研究用于说明贝叶斯网络和某些网络中成对元分析的等效性。