MRC Clinical Trials Unit at UCL, Institute of Clinical Trials and Methodology, London, UK.
MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge, UK.
Stat Med. 2019 Apr 15;38(8):1321-1335. doi: 10.1002/sim.8044. Epub 2018 Nov 28.
In a network meta-analysis, between-study heterogeneity variances are often very imprecisely estimated because data are sparse, so standard errors of treatment differences can be highly unstable. External evidence can provide informative prior distributions for heterogeneity and, hence, improve inferences. We explore approaches for specifying informative priors for multiple heterogeneity variances in a network meta-analysis. First, we assume equal heterogeneity variances across all pairwise intervention comparisons (approach 1); incorporating an informative prior for the common variance is then straightforward. Models allowing unequal heterogeneity variances are more realistic; however, care must be taken to ensure implied variance-covariance matrices remain valid. We consider three strategies for specifying informative priors for multiple unequal heterogeneity variances. Initially, we choose different informative priors according to intervention comparison type and assume heterogeneity to be proportional across comparison types and equal within comparison type (approach 2). Next, we allow all heterogeneity variances in the network to differ, while specifying a common informative prior for each. We explore two different approaches to this: placing priors on variances and correlations separately (approach 3) or using an informative inverse Wishart distribution (approach 4). Our methods are exemplified through application to two network metaanalyses. Appropriate informative priors are obtained from previously published evidence-based distributions for heterogeneity. Relevant prior information on between-study heterogeneity can be incorporated into network meta-analyses, without needing to assume equal heterogeneity across treatment comparisons. The approaches proposed will be beneficial in sparse data sets and provide more appropriate intervals for treatment differences than those based on imprecise heterogeneity estimates.
在网状荟萃分析中，由于数据稀疏，研究间异质性方差往往估计得非常不准确，因此治疗效果差异的标准误差可能非常不稳定。外部证据可以为异质性提供信息性先验分布，从而改善推断。我们探讨了在网状荟萃分析中为多个异质性方差指定信息性先验分布的方法。首先，我们假设所有成对干预比较的异质性方差相等（方法 1）；然后，为共同方差指定信息性先验分布是很简单的。允许异质性方差不等的模型更符合实际情况；然而，必须注意确保隐含的方差-协方差矩阵仍然有效。我们考虑了为多个不等异质性方差指定信息性先验分布的三种策略。最初，我们根据干预比较类型选择不同的信息性先验分布，并假设异质性在比较类型之间成比例，且在同一比较类型内相等（方法 2）。接下来，我们允许网络中的所有异质性方差都不同，同时为每个方差指定一个共同的信息性先验分布。我们探讨了两种不同的方法：分别对方差和相关系数进行先验分布（方法 3）或使用信息性逆 Wishart 分布（方法 4）。我们通过对两个网状荟萃分析的应用来举例说明我们的方法。适当的信息性先验分布可以从先前发表的基于证据的异质性分布中获得。关于研究间异质性的相关先验信息可以纳入网状荟萃分析，而无需假设治疗效果差异的异质性在各比较中相等。与基于不精确异质性估计的方法相比，所提出的方法将在数据稀疏的情况下受益，并为治疗效果差异提供更合适的区间。
