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. 2019 Sep;10(3):476-483.
doi: 10.1002/jrsm.1348. Epub 2019 Apr 23.

Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions

Guido Schwarzer  1 , Hiam Chemaitelly  2 , Laith J Abu-Raddad  2   3 , Gerta Rücker  1
Affiliations

Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions

Guido Schwarzer et al. Res Synth Methods. 2019 Sep.

Abstract

Standard generic inverse variance methods for the combination of single proportions are based on transformed proportions using the logit, arcsine, and Freeman-Tukey double arcsine transformations. Generalized linear mixed models are another more elaborate approach. Irrespective of the approach, meta-analysis results are typically back-transformed to the original scale in order to ease interpretation. Whereas the back-transformation of meta-analysis results is straightforward for most transformations, this is not the case for the Freeman-Tukey double arcsine transformation, albeit possible. In this case study with five studies, we demonstrate how seriously misleading the back-transformation of the Freeman-Tukey double arcsine transformation can be. We conclude that this transformation should only be used with special caution for the meta-analysis of single proportions due to potential problems with the back-transformation. Generalized linear mixed models seem to be a promising alternative.

Keywords: back-transformation; generalized linear mixed model; harmonic mean; random intercept logistic regression; variance stabilization.

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Conflict of interest statement

The author reported no conflict of interest.

Figures

Figure 1
Figure 1
Forest plot of hepatitis C virus (HCV) meta‐analysis with Freeman‐Tukey double arcsine transformation and without back‐transformation of results. PFT, Freeman‐Tukey double arcsine transformed proportion
Figure 2
Figure 2
Forest plot of hepatitis C virus (HCV) meta‐analysis with Freeman‐Tukey double arcsine transformation and back‐transformation according to Miller11
Figure 3
Figure 3
Influence of sample size on results of hepatitis C virus (HCV) meta‐analysis using inverse of Freeman‐Tukey double arcsine transformation according to Miller11
Figure 4
Figure 4
Forest plot of hepatitis C virus (HCV) meta‐analysis using classic method and logit transformation. Confidence intervals for individual studies are based on normal approximation for logit transformed proportions
Figure 5
Figure 5
Forest plot of hepatitis C virus (HCV) meta‐analysis using generalized linear mixed model. Confidence intervals for individual studies are based on Clopper‐Pearson method(14, 15)
See this image and copyright information in PMC

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