A simple method to estimate prediction intervals and predictive distributions: Summarizing meta-analyses beyond means and confidence intervals

Abstract

A systematic review and meta-analysis is an important step in evidence synthesis. The current paradigm for meta-analyses requires a presentation of the means under a random-effects model; however, a mean with a confidence interval provides an incomplete summary of the underlying heterogeneity in meta-analysis. Prediction intervals show the range of true effects in future studies and have been advocated to be regularly presented. Most commonly, prediction intervals are estimated assuming that the underlying heterogeneity follows a normal distribution, which is not necessarily appropriate. In this article, we provide a simple method with a ready-to-use spreadsheet file to estimate prediction intervals and predictive distributions nonparametrically. Simulation studies show that this new method can provide approximately unbiased estimates compared with the conventional method. We also illustrate the advantage and real-world significance of this approach with a meta-analysis evaluating the protective effect of vaccination against tuberculosis. The nonparametric predictive distribution provides more information about the shape of the underlying distribution than does the conventional method.

Keywords: meta-analysis; normality assumption; prediction interval; predictive distribution.