Abstract
The pooled estimate of the average effect is of primary interest when fitting the random-effects model for meta-analysis. However estimates of study specific effects, for example those displayed on forest plots, are also often of interest. In this tutorial, we present the case, with the accompanying statistical theory, for estimating the study specific true effects using so called 'empirical Bayes estimates' or 'Best Unbiased Linear Predictions' under the random-effects model. These estimates can be accompanied by prediction intervals that indicate a plausible range of study specific true effects. We coalesce and elucidate the available literature and illustrate the methodology using two published meta-analyses as examples. We also perform a simulation study that reveals that coverage probability of study specific prediction intervals are substantially too low if the between-study variance is small but not negligible. Researchers need to be aware of this defect when interpreting prediction intervals. We also show how empirical Bayes estimates, accompanied with study specific prediction intervals, can embellish forest plots. We hope that this tutorial will serve to provide a clear theoretical underpinning for this methodology and encourage its widespread adoption.