Study specific prediction intervals for random-effects meta-analysis

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.

在构建随机效应模型进行荟萃分析时，对平均效应的汇总估计尤为关注。然而，对于特定研究效果的估计，例如在森林图中展示的效果，亦常引起兴趣。本研究旨在探讨在随机效应模型下，利用所谓的‘经验贝叶斯估计’或‘最佳无偏线性预测’来估算真实的研究特定效果。此类估计可伴随预测区间，以指示研究特定真实效果的合理范围。本研究综合并阐释了现有文献，并通过实际案例和模拟研究对方法论进行评估。模拟研究表明，若研究间方差较小但非可忽略不计，则特定研究预测区间的覆盖概率将显著偏低。研究人员在解读预测区间时需注意此缺陷。此外，本研究还展示了如何将经验贝叶斯估计与特定研究的预测区间相结合，以丰富森林图。我们期望本文能为该方法提供清晰的理论基础，并促进其广泛应用。