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How vague is vague? How informative is informative? Reference analysis for Bayesian meta‐analysis


Ott, Manuela; Plummer, Martyn; Roos, Małgorzata (2021). How vague is vague? How informative is informative? Reference analysis for Bayesian meta‐analysis. Statistics in Medicine, 40(20):4505-4521.

Abstract

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). Recently, several publications have discussed the choice of the prior distribution for the between-study heterogeneity in the Bayesian NNHM and used several “vague” priors. However, no approach exists to quantify the informativeness of such priors, and thus, we develop a principled reference analysis framework for the Bayesian NNHM acting at the posterior level. The posterior reference analysis (post-RA) is based on two posterior benchmarks: one induced by the improper reference prior, which is minimally informative for the data, and the other induced by a highly anticonservative proper prior. This approach applies the Hellinger distance to quantify the informativeness of a heterogeneity prior of interest by comparing the corresponding marginal posteriors with both posterior benchmarks. The post-RA is implemented in the freely accessible R package ra4bayesmeta and is applied to two medical case studies. Our findings show that anticonservative heterogeneity priors produce platykurtic posteriors compared with the reference posterior, and they produce shorter 95% credible intervals (CrI) and optimistic inference compared with the reference prior. Conservative heterogeneity priors produce leptokurtic posteriors, longer 95% CrI and cautious inference. The novel post-RA framework could support numerous Bayesian meta-analyses in many research fields, as it determines how informative a heterogeneity prior is for the actual data as compared with the minimally informative reference prior.

Abstract

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). Recently, several publications have discussed the choice of the prior distribution for the between-study heterogeneity in the Bayesian NNHM and used several “vague” priors. However, no approach exists to quantify the informativeness of such priors, and thus, we develop a principled reference analysis framework for the Bayesian NNHM acting at the posterior level. The posterior reference analysis (post-RA) is based on two posterior benchmarks: one induced by the improper reference prior, which is minimally informative for the data, and the other induced by a highly anticonservative proper prior. This approach applies the Hellinger distance to quantify the informativeness of a heterogeneity prior of interest by comparing the corresponding marginal posteriors with both posterior benchmarks. The post-RA is implemented in the freely accessible R package ra4bayesmeta and is applied to two medical case studies. Our findings show that anticonservative heterogeneity priors produce platykurtic posteriors compared with the reference posterior, and they produce shorter 95% credible intervals (CrI) and optimistic inference compared with the reference prior. Conservative heterogeneity priors produce leptokurtic posteriors, longer 95% CrI and cautious inference. The novel post-RA framework could support numerous Bayesian meta-analyses in many research fields, as it determines how informative a heterogeneity prior is for the actual data as compared with the minimally informative reference prior.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Health Sciences > Epidemiology
Physical Sciences > Statistics and Probability
Uncontrolled Keywords:Statistics and Probability, Epidemiology
Language:English
Date:10 September 2021
Deposited On:29 Dec 2021 13:42
Last Modified:26 Jun 2024 01:47
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0277-6715
OA Status:Hybrid
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1002/sim.9076
PubMed ID:34041768
Project Information:
  • : FunderSNSF
  • : Grant ID200021_175933
  • : Project TitleSEDA: Sensitivity diagnostics for Bayesian hierarchical models
  • Content: Published Version
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)