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

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.