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Stat Med. 2015 Mar 15;34(6):984-98. doi: 10.1002/sim.6381. Epub 2014 Dec 5.

Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis.

Author information

1
MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge, U.K.

Abstract

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.

KEYWORDS:

Bayesian methods; heterogeneity; meta-analysis; prior distributions

PMID:
25475839
PMCID:
PMC4383649
DOI:
10.1002/sim.6381
[Indexed for MEDLINE]
Free PMC Article

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