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Related Experiment Video

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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

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Published on: September 19, 2012

How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis.

Manuela Ott¹, Martyn Plummer², Małgorzata Roos¹

¹Department of Biostatistics at Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Zurich, Switzerland.

Statistics in Medicine

|May 27, 2021

Summary

A new framework quantifies the informativeness of heterogeneity priors in Bayesian meta-analysis. This posterior reference analysis (post-RA) helps researchers understand how prior choices impact results, ensuring more reliable evidence-based medicine.

Keywords:

Bayesian meta-analysis conservative/anticonservative heterogeneity priors normal-normal hierarchical model prior informativeness quantification reference analysis

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Area of Science:

Statistics
Biostatistics
Evidence-based Medicine

Background:

Bayesian meta-analysis, often using a normal-normal hierarchical model (NNHM), synthesizes evidence from multiple studies.
Choosing appropriate prior distributions for between-study heterogeneity in NNHM is crucial but lacks quantification methods.
Existing 'vague' priors for heterogeneity can lead to varied and unquantified impacts on meta-analysis outcomes.

Purpose of the Study:

To develop a principled reference analysis (post-RA) framework for Bayesian NNHM to quantify heterogeneity prior informativeness.
To provide a method for comparing the impact of different heterogeneity priors against minimally informative and highly anticonservative benchmarks.
To implement the post-RA framework in an accessible R package (ra4bayesmeta) for practical application.

Main Methods:

Developed the posterior reference analysis (post-RA) framework operating at the posterior level.
Utilized two posterior benchmarks: one from an improper reference prior and another from a highly anticonservative proper prior.
Employed the Hellinger distance to measure the informativeness of a heterogeneity prior by comparing marginal posteriors to benchmarks.

Main Results:

Anticonservative heterogeneity priors resulted in platykurtic posteriors, shorter 95% credible intervals (CrI), and optimistic inference compared to the reference posterior.
Conservative heterogeneity priors led to leptokurtic posteriors, longer 95% CrI, and cautious inference.
The post-RA framework successfully quantified prior informativeness in two medical case studies.

Conclusions:

The novel post-RA framework offers a robust method for assessing heterogeneity prior informativeness in Bayesian meta-analysis.
Understanding prior influence is critical for interpreting meta-analysis results and ensuring reliable evidence synthesis.
This approach supports informed prior selection across diverse research fields utilizing Bayesian meta-analysis.