Department of Statistics, Florida State University, Tallahassee, Florida, USA.
J Biopharm Stat. 2021 May 4;31(3):317-330. doi: 10.1080/10543406.2020.1852247. Epub 2020 Dec 9.
Network meta-analysis (NMA) is a popular tool to synthesize direct and indirect evidence for simultaneously comparing multiple treatments, while evidence inconsistency greatly threatens its validity. One may use the inconsistency degrees of freedom (ICDF) to assess the potential that an NMA might suffer from inconsistency. Multi-arm studies provide intrinsically consistent evidence and complicate the ICDF's calculation; they commonly appear in NMAs. The existing ICDF measure may not feasibly handle multi-arm studies. Motivated from the effective numbers of parameters of Bayesian hierarchical models, we propose new ICDF measures in generic NMAs that may contain multi-arm studies. Under the fixed- or random-effects setting, the new ICDF measure is the difference between the effective numbers of parameters of the consistency and inconsistency NMA models. We used artificial NMAs created based on an illustrative example and 39 empirical NMAs to evaluate the performance of the existing and new measures. In NMAs with two-arm studies only, the proposed ICDF measure under the fixed-effects setting was nearly the same with the existing measure. Among the empirical NMAs, 27 (69%) contained at least one multi-arm study. The existing measure was not applicable to them, while the proposed measures led to interpretable ICDFs in all NMAs.
网络荟萃分析（NMA）是一种用于综合直接和间接证据以同时比较多种治疗方法的流行工具，而证据不一致性极大地威胁着其有效性。人们可以使用不一致自由度（ICDF）来评估 NMA 可能不一致的可能性。多臂研究提供内在一致的证据，并使 ICDF 的计算复杂化；它们通常出现在 NMA 中。现有的 ICDF 衡量标准可能无法实际处理多臂研究。受贝叶斯层次模型有效参数数量的启发，我们提出了新的 ICDF 衡量标准，可用于可能包含多臂研究的通用 NMA。在固定或随机效应设置下，新的 ICDF 衡量标准是一致性和不一致性 NMA 模型的有效参数数量之间的差异。我们使用基于示例的人工 NMA 和 39 个实证 NMA 来评估现有和新措施的性能。在仅包含两臂研究的 NMA 中，固定效应设置下提出的 ICDF 衡量标准与现有衡量标准非常接近。在实证 NMA 中，有 27 个（69%）至少包含一个多臂研究。现有衡量标准不适用于它们，而提出的衡量标准在所有 NMA 中都导致了可解释的 ICDF。
