Arcsine-based transformations for meta-analysis of proportions: Pros, cons, and alternatives

Abstract

Meta-analyses have been increasingly used to synthesize proportions (eg, disease prevalence) from multiple studies in recent years. Arcsine-based transformations, especially the Freeman-Tukey double-arcsine transformation, are popular tools for stabilizing the variance of each study's proportion in two-step meta-analysis methods. Although they offer some benefits over the conventional logit transformation, they also suffer from several important limitations (eg, lack of interpretability) and may lead to misleading conclusions. Generalized linear mixed models and Bayesian models are intuitive one-step alternative approaches, and can be readily implemented via many software programs. This article explains various pros and cons of the arcsine-based transformations, and discusses the alternatives that may be generally superior to the currently popular practice.

Keywords: Bayesian model; arcsine‐based transformation; generalized linear mixed model; meta‐analysis; proportion.

Figure 1

Bar plot of the number of research items using the double‐arcsine transformation in meta‐analyses and the corresponding proportion among meta‐analysis publications over the past two decades based on Google Scholar (https://scholar.google.com/). For each year, the left bar, in white, represents the number of research items, and the right bar, in gray, represents the corresponding proportion (in percentage)