Burke Danielle L, Bujkiewicz Sylwia, Riley Richard D
1 Research Institute for Primary Care and Health Sciences, Keele University, Staffordshire, UK.
2 Biostatistics Group, Department of Health Sciences, University of Leicester, Leicester, UK.
Stat Methods Med Res. 2018 Feb;27(2):428-450. doi: 10.1177/0962280216631361. Epub 2016 Mar 17.
Multivariate random-effects meta-analysis allows the joint synthesis of correlated results from multiple studies, for example, for multiple outcomes or multiple treatment groups. In a Bayesian univariate meta-analysis of one endpoint, the importance of specifying a sensible prior distribution for the between-study variance is well understood. However, in multivariate meta-analysis, there is little guidance about the choice of prior distributions for the variances or, crucially, the between-study correlation, ρ; for the latter, researchers often use a Uniform(-1,1) distribution assuming it is vague. In this paper, an extensive simulation study and a real illustrative example is used to examine the impact of various (realistically) vague prior distributions for ρ and the between-study variances within a Bayesian bivariate random-effects meta-analysis of two correlated treatment effects. A range of diverse scenarios are considered, including complete and missing data, to examine the impact of the prior distributions on posterior results (for treatment effect and between-study correlation), amount of borrowing of strength, and joint predictive distributions of treatment effectiveness in new studies. Two key recommendations are identified to improve the robustness of multivariate meta-analysis results. First, the routine use of a Uniform(-1,1) prior distribution for ρ should be avoided, if possible, as it is not necessarily vague. Instead, researchers should identify a sensible prior distribution, for example, by restricting values to be positive or negative as indicated by prior knowledge. Second, it remains critical to use sensible (e.g. empirically based) prior distributions for the between-study variances, as an inappropriate choice can adversely impact the posterior distribution for ρ, which may then adversely affect inferences such as joint predictive probabilities. These recommendations are especially important with a small number of studies and missing data.
多变量随机效应荟萃分析允许联合综合来自多项研究的相关结果，例如，针对多个结局或多个治疗组。在对一个终点进行的贝叶斯单变量荟萃分析中，为研究间方差指定一个合理的先验分布的重要性已得到充分理解。然而，在多变量荟萃分析中，对于方差的先验分布选择，或者至关重要的是研究间相关性ρ的先验分布选择，几乎没有指导意见；对于后者，研究人员通常使用均匀分布（-1,1），认为它是模糊的。在本文中，通过一项广泛的模拟研究和一个实际示例，来检验在对两个相关治疗效果进行的贝叶斯双变量随机效应荟萃分析中，各种（实际）模糊的先验分布对ρ以及研究间方差的影响。考虑了一系列不同的场景，包括完整数据和缺失数据，以检验先验分布对后验结果（治疗效果和研究间相关性）、强度借用量以及新研究中治疗效果的联合预测分布的影响。确定了两条关键建议以提高多变量荟萃分析结果的稳健性。首先，如果可能，应避免常规使用均匀分布（-1,1）作为ρ的先验分布，因为它不一定是模糊的。相反，研究人员应确定一个合理的先验分布，例如，根据先验知识将值限制为正或负。其次，为研究间方差使用合理的（例如基于经验的）先验分布仍然至关重要，因为不恰当的选择可能会对ρ的后验分布产生不利影响，进而可能对诸如联合预测概率等推断产生不利影响。这些建议在研究数量较少和存在缺失数据的情况下尤为重要。
