The Freeman–Tukey double arcsine transformation for the meta-analysis of proportions: Recent criticisms were seriously misleading

Abstract

Pooling of proportions in meta-analysis are used to get better and more precise estimates of disease frequency, including cumulative incidence or prevalence. Meta-analysis is of course only useful when there are a limited number of studies, and the latter are estimating (conceptually) the same underlying parameter of interest. This means that meta-analysis may be inappropriate for global burden of disease studies where other (risk adjustment or standardization related) weights are more appropriate than meta-analytic (error) weights.1

Recently, Schwarzer et al.2 generated some controversy regarding the pooling of proportions in meta-analyses. The authors undertook a burden of disease meta-analysis to illustrate issues with the Freeman–Tukey double-arcsine square root transformation (FTT) when back-transformed using the harmonic mean of study sample sizes.3 Their conclusion was that the FTT method can be misleading and should be used only with caution. However, the authors did not fully investigate alternative expressions for the back-transform; in particular, they were apparently unaware of our previous work on this topic from 2013.4 We will therefore use the same five studies on burden of disease used by Schwarzer et al.2 as an example and ignore the point of the inappropriateness1 of pooling burden of disease via meta-analysis. We start by first discussing the specific issues raised by the authors and then follow this up with a simulation study to demonstrate the properties of the FTT5 as a valuable option to deal with instability of the variance of a proportion in meta-analysis.