A re-evaluation of random-effects meta-analysis

Abstract

Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to a priori judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of 'set shifting' ability in people with eating disorders.

Fig. 1

Estimates with 95% confidence intervals for (a) a genuine meta-analysis and (b) an artificially constructed meta-analysis with identical results for the mean of a random-effects distribution

Fig. 3

(a) Predictive distribution for θ_new and (b) cumulative distribution function of the random-effects distribution (with 95% interval) estimated from a Bayesian normal random-effects meta-analysis of set shifting studies

Fig. 2

Bayesian normal random-effects meta-analysis of the set shifting data: for each study the estimated effect size with 95% confidence interval (Table 1) and a posterior median with 95% credible interval are illustrated; 95% credible intervals for μ and for the predicted effect in a new trial, θ_new, are given