Bayesian approaches to random-effects meta-analysis: a comparative study

TLDR: It is described how a full Bayesian analysis can deal with unresolved issues, such as the choice between fixed- and random-effects models, the choice of population distribution in a random- effects analysis, the treatment of small studies and extreme results, and incorporation of study-specific covariates.

Abstract: Current methods for meta-analysis still leave a number of unresolved issues, such as the choice between fixed- and random-effects models, the choice of population distribution in a random-effects analysis, the treatment of small studies and extreme results, and incorporation of study-specific covariates. We describe how a full Bayesian analysis can deal with these and other issues in a natural way, illustrated by a recent published example that displays a number of problems. Such analyses are now generally available using the BUGS implementation of Markov chain Monte Carlo numerical integration techniques. Appropriate proper prior distributions are derived, and sensitivity analysis to a variety of prior assumptions carried out. Current methods are briefly summarized and compared to the full Bayes analysis.