Department of Biostatistics, Waterhouse Building, University of Liverpool, Liverpool, UK.
School of Social and Community Medicine, University of Bristol, Bristol, UK.
Res Synth Methods. 2019 Jun;10(2):207-224. doi: 10.1002/jrsm.1327. Epub 2018 Nov 12.
When numerous treatments exist for a disease (Treatments 1, 2, 3, etc), network meta-regression (NMR) examines whether each relative treatment effect (eg, mean difference for 2 vs 1, 3 vs 1, and 3 vs 2) differs according to a covariate (eg, disease severity). Two consistency assumptions underlie NMR: consistency of the treatment effects at the covariate value 0 and consistency of the regression coefficients for the treatment by covariate interaction. The NMR results may be unreliable when the assumptions do not hold. Furthermore, interactions may exist but are not found because inconsistency of the coefficients is masking them, for example, when the treatment effect increases as the covariate increases using direct evidence but the effect decreases with the increasing covariate using indirect evidence. We outline existing NMR models that incorporate different types of treatment by covariate interaction. We then introduce models that can be used to assess the consistency assumptions underlying NMR for aggregate data. We extend existing node-splitting models, the unrelated mean effects inconsistency model, and the design by treatment inconsistency model to incorporate covariate interactions. We propose models for assessing both consistency assumptions simultaneously and models for assessing each of the assumptions in turn to gain a more thorough understanding of consistency. We apply the methods in a Bayesian framework to trial-level data comparing antimalarial treatments using the covariate average age and to four fabricated data sets to demonstrate key scenarios. We discuss the pros and cons of the methods and important considerations when applying models to aggregated data.
当一种疾病存在多种治疗方法（治疗方法 1、2、3 等）时，网络荟萃回归（NMR）会检查每种相对治疗效果（例如，2 与 1、3 与 1 和 3 与 2 的平均值差异）是否根据协变量（例如，疾病严重程度）而有所不同。NMR 有两个一致性假设：在协变量值为 0 时治疗效果的一致性和治疗与协变量交互作用的回归系数的一致性。当假设不成立时，NMR 结果可能不可靠。此外，可能存在交互作用，但由于不一致的系数掩盖了它们，例如，当直接证据表明随着协变量的增加治疗效果增加，但间接证据表明随着协变量的增加治疗效果降低时，交互作用可能存在但未被发现。我们概述了现有的包含不同类型治疗与协变量相互作用的 NMR 模型。然后，我们介绍了可用于评估汇总数据中 NMR 基础一致性假设的模型。我们扩展了现有的节点分裂模型、无关平均效应不一致模型和治疗不一致设计模型，以纳入协变量相互作用。我们提出了同时评估两个一致性假设的模型和逐个评估每个假设的模型，以更全面地了解一致性。我们在贝叶斯框架中应用这些方法对使用协变量平均年龄比较抗疟治疗的试验水平数据进行了比较，并对四个伪造数据集进行了演示，以说明关键情况。我们讨论了这些方法的优缺点以及在将模型应用于汇总数据时的重要注意事项。
