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.

In a meta-analysis of clinical trials, an important issue is whether the treatment benefit varies according to the underlying risk of the patients in the different trials. The usual naive analyses employed to investigate this question use either the observed risk of events in the control groups, or the average risk in the control and treatment groups, as a measure of underlying risk. These analyses are flawed and can produce seriously misleading results. We show how their biases depend on three components of variability, the within-trial and between-trial variances of the control group risks, and the between-trial variance of the treatment effects. We propose a Bayesian solution to the problem which can be carried out using the BUGS implementation of Gibbs sampling. The analysis is illustrated for a meta-analysis of bleeding and mortality data in trials of sclerotherapy for patients with cirrhosis, and the results contrasted with those from the naive approaches. Comparisons with other methods recently proposed for this problem are also made. We conclude that the Bayesian solution presented in this paper is not only more appropriate than other proposed methods, but is also sufficiently easy to implement that it can be used by applied researchers undertaking meta-analyses.

No abstract