“Predictive Distributions for Between-Study Heterogeneity and Simple Methods for Their Application in Bayesian Meta-Analysis”, 2014-12-05 ():
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 2 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 2 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 2 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.
The distribution of tau across all the meta-analyses in Cochrane with a binary outcome has been estimated by et al 2014.
They estimated the distribution of log(τ2) as normal with mean −2.56 and standard deviation 1.74. I’ve estimated the distribution of μ across Cochrane as a generalized t-distribution with mean=0, scale=0.52 and 3.4 degrees of freedom.
These estimated priors usually don’t make a very big difference compared to flat priors. That’s just because the signal-to-noise ratio of most meta-analyses is reasonably good. For most meta-analyses, finding an honest set of reliable studies seems to be a much bigger problem than sampling error.]