Predictive distributions for between‐study heterogeneity and simple methods for their application in Bayesian meta‐analysis
Open accessAbstract
Numerous meta‐analyses in healthcare research combine results from only a small number of studies, for which the variance representing between‐study heterogeneity is estimated imprecisely. A Bayesian approach to estimation allows external evidence on the expected magnitude of heterogeneity to be incorporated. The aim of this paper is to provide tools that improve the accessibility of Bayesian meta‐analysis. We present two methods for implementing Bayesian meta‐analysis, using numerical integration and importance sampling techniques. Based on 14 886 binary outcome meta‐analyses in the Cochrane Database of Systematic Reviews , we derive a novel set of predictive distributions for the degree of heterogeneity expected in 80 settings depending on the outcomes assessed and comparisons made. These can be used as prior distributions for heterogeneity in future meta‐analyses. The two methods are implemented in R, for which code is provided. Both methods produce equivalent results to standard but more complex Markov chain Monte Carlo approaches. The priors are derived as log‐normal distributions for the between‐study variance, applicable to meta‐analyses of binary outcomes on the log odds‐ratio scale. The methods are applied to two example meta‐analyses, incorporating the relevant predictive distributions as prior distributions for between‐study heterogeneity. We have provided resources to facilitate Bayesian meta‐analysis, in a form accessible to applied researchers, which allow relevant prior information on the degree of heterogeneity to be incorporated. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.
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A Bayesian estimation framework more naturally accounts for all parameter uncertainty in the derivation of credibility and probability intervals.
“which more naturally accounts for all parameter uncertainty in the derivation of credibility and probability intervals.”
From A framework for meta-analysis of prediction model studies with binary and time-to-event outcomes (2019) · cites this paper as [53]
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- Authors
- Turner, R. M., Jackson, D., Wei, Y., Thompson, S. G., & Higgins, J. P. T.
- Affiliations
- MRC Biostatistics Unit (GB)
- University of Plymouth (GB)
- University of Cambridge (GB)
- University of Bristol (GB)
- Corresponding author
- Turner, Rebecca M.
- Venue
- Statistics in Medicine
- Publisher
- Wiley
- Published
- 2014-12-05
- Volume
- 34
- Issue
- 6
- Pages
- 984-998
- ISSN
- 0277-6715 (ISSN-L)
- 1097-0258
- PMC
- PMC4383649
- OpenAlex
- W1857542727
- Cited by
- 410
- References
- 26
- Citations by year
- 2026: 56 · 2025: 34 · 2024: 51 · 2023: 34 · 2022: 51 · 2021: 70 · 2020: 36 · 2019: 25 · 2018: 17 · 2017: 12 · 2016: 19 · 2015: 4 · 2014: 1
- FWCI
- 12.03
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Statistics in Medicine (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- PEARL (University of Plymouth) (submittedVersion)
- Bristol Research (University of Bristol) (submittedVersion)
- Funders
- Medical Research Council (U105260558)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- study heterogeneity, predictive distribution, Bayesian meta-analysis, prior distributions, between-study variance, binary outcomes, odds ratio, numerical integration, importance sampling, external evidence
- MeSH terms
- Bayes Theorem, Data Interpretation, Statistical, Humans, Review Literature as Topic, Meta-Analysis as Topic, Logistic Models, Databases, Bibliographic
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