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How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Statistics in Medicine. 2021; 1– 17. https://doi.org/10.1002/sim.9076, , .
Meta-analysis provides important insights for evidence-based medicine by synthesizing evidence from multiple studies which address the same research question. Within the Bayesian framework, meta-analysis is frequently expressed by a Bayesian normal-normal hierarchical model (NNHM).
For the widely used Bayesian NNHM, the prior distribution for the between-study heterogeneity parameter is particularly difficult to choose and to justify. Acknowledging that all priors contribute some information, the popular concepts of “vague” and “weakly informative” heterogeneity priors are rather elusive. In fact, a practical and accessible methodology is needed to assess the informativeness of a chosen heterogeneity prior in a Bayesian NNHM. Therefore, the authors developed a posterior reference analysis (post-RA) for the Bayesian NNHM, which aims to establish how informative an actual heterogeneity prior is for the data at hand, as compared to the minimally informative reference prior.
The post-RA is based on two posterior benchmarks: one induced by the Jeffreys reference prior, which is minimally informative for the data, and the other induced by a highly anticonservative prior, which is concentrated on very small heterogeneity values. The informativeness of a heterogeneity prior of interest is quantified by the Hellinger distance between the corresponding marginal posteriors and both posterior benchmarks. The post-RA is implemented in the freely accessible R package ra4bayesmeta.
For medical case studies, the post-RA determined the informativeness of several heterogeneity priors used in the literature. The authors found that the informativeness depends on the number of studies, the heterogeneity prior, and the parameter under consideration. Moreover, this principled assessment of “vagueness” and “weak informativeness” can support a better understanding of the validity of posterior inference in evidence-based medicine and many other research fields.More Details