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 | INTRODUCTIONA systematic review and meta-analysis can integrate the information from many studies and is becoming more important in a diverse range of fields including biomedical, ecological, social, and behavioral sciences. [1][2][3] The fixed-effect model in meta-analyses assumes a common underlying effect, while the random-effects model allows for heterogeneity across the included studies. The random-effects model is usually preferred, because the included studies often differ in various ways. The current standard of meta-analysis therefore includes the quantification of heterogeneity with b τ 2 or I 2 . 4 A test of homogeneity such as the Q statistic 5 had been previously used but was considered not providing a relevant summary of heterogeneity. 4,6-8 If heterogeneity is present, a randomeffects model is recommended. An estimate of the mean of the underlying random-effects distribution is routinely

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Reducing meat consumption by appealing to animal welfare: protocol for a meta-analysis and theoretical review

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