Double arcsine transform not appropriate for meta-analysis

TL;DR

This paper critiques the use of the Freeman-Tukey double arcsine transform in meta-analysis, highlighting its mathematical issues that compromise its reliability for combining proportions.

Contribution

The authors demonstrate that the double arcsine transform has fundamental problems with monotonicity and invertibility, making it unsuitable for meta-analytical applications.

Findings

Identifies issues with monotonicity in the transform

Shows problems with invertibility affecting meta-analysis

Recommends against using the transform for meta-analytical purposes

Abstract

The variance-stabilizing Freeman-Tukey double arcsine transform was originally proposed for inference on single proportions. Subsequently, its use has been suggested in the context of meta-analysis of proportions. While some erratic behaviour has been observed previously, here we point out and illustrate general issues of monotonicity and invertibility that make this transform unsuitable for meta-analysis purposes.