Study specific prediction intervals for random-effects meta-analysis
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Description: The pooled estimate of the average effect is of primary interest when fit- ting 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. Here we present the case for estimating the true study specific effects using so called ‘Empirical Bayes estimates’ or ‘Best Unbiased Linear Predic- tions’ 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 evaluate the methodology using real examples and simulation studies. These simulation studies reveal that coverage probability of study specific prediction inter- vals are substantially too low if the between-study variance is small but not negligible. Researchers need to be aware of this defect when interpreting pre- diction intervals. We also show how Empirical Bayes estimates, accompanied with study specific prediction intervals, can embellish forest plots. We hope that this paper will serve to provide a clear theoretical underpinning for this methodology and encourage its widespread adoption.