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

Guido Schwarzer, Hiam Chemaitelly, Laith J. Abu-Raddad, Gerta Rücker

Research output: Contribution to journalArticle

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)476-483
Number of pages8
JournalResearch Synthesis Methods
Issue number3
Publication statusPublished - 1 Sep 2019



  • back-transformation
  • generalized linear mixed model
  • harmonic mean
  • random intercept logistic regression
  • variance stabilization

ASJC Scopus subject areas

  • Education

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