Assessing the properties of the prediction interval in random-effects meta-analysis

TL;DR

This paper evaluates the performance of various frequentist prediction interval methods in random-effects meta-analysis, highlighting issues with coverage probability reliability especially with few studies and heterogeneity.

Contribution

It provides an extensive simulation study analyzing the distribution of coverage probabilities of prediction intervals, emphasizing the importance of considering their variability rather than just mean coverage.

Findings

Coverage probabilities vary significantly with heterogeneity and number of studies.

Small sample sizes lead to unreliable prediction interval coverage.

Interval length and robustness are affected by non-normal effects.

Abstract

Random effects meta-analysis is a widely applied methodology to synthetize research findings of studies in a specific scientific question. Besides estimating the mean effect, an important aim of the meta-analysis is to summarize the heterogeneity, i.e. the variation in the underlying effects caused by the differences in study circumstances. The prediction interval is frequently used for this purpose: a 95% prediction interval contains the true effect of a similar new study in 95% of the cases when it is constructed, or in other words, it covers 95% of the true effects distribution on average. In this article, after providing a clear mathematical background, we present an extensive simulation investigating the performance of all frequentist prediction interval methods published to date. The work focuses on the distribution of the coverage probabilities and how these distributions change depending on the amount of heterogeneity and the number of involved studies. Although the single requirement that a prediction interval has to fulfill is to keep a nominal coverage probability on average, we demonstrate why the distribution of coverages cannot be disregarded, and that for small number of studies no reliable conclusion can be drawn from the prediction interval. We argue that assessing only the mean coverage can easily lead to misunderstanding and misinterpretation. The length of the intervals and the robustness of the methods concerning non-normality of the true effects are also investigated.