In Bayesian meta-analysis, the specification of prior probabilities for the between-study heterogeneity is commonly required, and is of particular benefit in situations where only few studies are included. Among the considerations in the set-up of such prior distributions, the consultation of available empirical data on a set of relevant past analyses sometimes plays a role. How exactly to summarize historical data sensibly is not immediately obvious; in particular, the investigation of an empirical collection of heterogeneity estimates will not target the actual problem and will usually only be of limited use. The commonly used normal-normal hierarchical model for random-effects meta-analysis is extended to infer a heterogeneity prior. Using an example data set, we demonstrate how to fit a distribution to empirically observed heterogeneity data from a set of meta-analyses. Considerations also include the choice of a parametric distribution family. Here, we focus on simple and readily applicable approaches to then translate these into (prior) probability distributions.
翻译:在Bayesian元分析中,通常需要说明研究间差异的先前概率,在只包括少数研究的情况下特别有益。在这种先前分布的设置中,对一套相关过去分析的现有经验数据的协商有时会起到一定的作用。如何准确地对历史数据进行感知性总结并不立即明显;特别是,对实证的异质性估计的收集调查不会针对实际问题,通常只是有限地使用。对随机效应元分析通常使用的正常等级模型将扩大至推断先前的异质性。我们使用一组示例数据,表明如何将分布与一套元分析中经验观测到的异质性数据相匹配。考虑还包括选择一个参数分布型。在这里,我们侧重于简单和易于应用的方法,然后将这些方法转化为(原始)概率分布。