Law Martin, Jackson Dan, Turner Rebecca, Rhodes Kirsty, Viechtbauer Wolfgang
MRC Biostatistics Unit, Cambridge, UK.
BMC Med Res Methodol. 2016 Jul 28;16:87. doi: 10.1186/s12874-016-0184-5.
Meta-analysis is a valuable tool for combining evidence from multiple studies. Network meta-analysis is becoming more widely used as a means to compare multiple treatments in the same analysis. However, a network meta-analysis may exhibit inconsistency, whereby the treatment effect estimates do not agree across all trial designs, even after taking between-study heterogeneity into account. We propose two new estimation methods for network meta-analysis models with random inconsistency effects.
The model we consider is an extension of the conventional random-effects model for meta-analysis to the network meta-analysis setting and allows for potential inconsistency using random inconsistency effects. Our first new estimation method uses a Bayesian framework with empirically-based prior distributions for both the heterogeneity and the inconsistency variances. We fit the model using importance sampling and thereby avoid some of the difficulties that might be associated with using Markov Chain Monte Carlo (MCMC). However, we confirm the accuracy of our importance sampling method by comparing the results to those obtained using MCMC as the gold standard. The second new estimation method we describe uses a likelihood-based approach, implemented in the metafor package, which can be used to obtain (restricted) maximum-likelihood estimates of the model parameters and profile likelihood confidence intervals of the variance components.
We illustrate the application of the methods using two contrasting examples. The first uses all-cause mortality as an outcome, and shows little evidence of between-study heterogeneity or inconsistency. The second uses "ear discharge" as an outcome, and exhibits substantial between-study heterogeneity and inconsistency. Both new estimation methods give results similar to those obtained using MCMC.
The extent of heterogeneity and inconsistency should be assessed and reported in any network meta-analysis. Our two new methods can be used to fit models for network meta-analysis with random inconsistency effects. They are easily implemented using the accompanying R code in the Additional file 1. Using these estimation methods, the extent of inconsistency can be assessed and reported.
荟萃分析是整合多项研究证据的重要工具。网状荟萃分析作为在同一分析中比较多种治疗方法的手段，正得到越来越广泛的应用。然而，网状荟萃分析可能会出现不一致性，即即便考虑了研究间的异质性，治疗效果估计在所有试验设计中仍不一致。我们针对具有随机不一致效应的网状荟萃分析模型提出了两种新的估计方法。
我们考虑的模型是将传统荟萃分析的随机效应模型扩展到网状荟萃分析情境，并通过随机不一致效应考虑潜在的不一致性。我们的第一种新估计方法使用贝叶斯框架，对异质性和不一致性方差采用基于经验的先验分布。我们使用重要性抽样来拟合模型，从而避免了一些可能与使用马尔可夫链蒙特卡罗（MCMC）相关的困难。不过，我们通过将结果与以MCMC作为金标准所获得的结果进行比较，确认了我们重要性抽样方法的准确性。我们描述的第二种新估计方法使用基于似然的方法，在metafor软件包中实现，可用于获得模型参数的（受限）最大似然估计以及方差成分的轮廓似然置信区间。
我们通过两个对比示例说明了这些方法的应用。第一个示例将全因死亡率作为结局，几乎没有显示出研究间异质性或不一致性的证据。第二个示例将“耳溢液”作为结局，呈现出显著的研究间异质性和不一致性。两种新估计方法给出的结果与使用MCMC所获得的结果相似。
在任何网状荟萃分析中都应评估并报告异质性和不一致性的程度。我们的两种新方法可用于拟合具有随机不一致效应的网状荟萃分析模型。使用随附在补充文件1中的R代码可轻松实现这些方法。使用这些估计方法，可以评估并报告不一致性的程度。
