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Re: st: using Freeman-Tukey arcsine transformation with metan command

From   "Roger B. Newson" <>
Subject   Re: st: using Freeman-Tukey arcsine transformation with metan command
Date   Mon, 02 Apr 2012 18:24:16 +0100

I don't know whether Jessica is really meta-analyzing proportions, or differences between proportions (which would seem a more appropriate parameter for which to use the arcsine transformation, at least to me). However, the arcsine was proposed tentatively by Daniels and Kendall (1947) as a possible Normalizing and variance-stabilizing transformation for Kendall's tau. The -somersd- package (Newson, 2006) is downloadable from SSC, and estimates Somers' D and Kendall's tau-a, offering the arcsine transformation, and the alternative hyperbolic arctangent or Fisher's z transformation, for the purposes of defining confidence intervals for both of these parameters. And, of course, a difference between proportions is a special case of Somers' D. It should be entirely possible to use either of these transformations to meta-analyze differences between proportions, using the SSC packages -metan- and/or -parmhet- and/or -regpar- and or -parmest- (which has a -metaparm- module to do meta-analyses).

I hope this helps. Let me know if you have any further queries.

Best wishes



Daniels, H. E., and M. G. Kendall. 1947. The significance of rank correlation where parental correlation exists. Biometrika 34: 197–208.

Newson R. Confidence intervals for rank statistics: Somers' D and extensions. The Stata Journal 2006; 6(3): 309-334. Download from

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Web page:
Departmental Web page:

Opinions expressed are those of the author, not of the institution.

On 02/04/2012 17:38, Jessica Keithlin wrote:
Hello Stata Community,

This is my first post on Statalist so I hope it turns out OK =)

I was wondering if anyone has any experience using the Freeman-Tukey arcsine transformation/back-transformation for a meta-analysis? I will be performing a meta-analysis on proportions (as opposed to the typical OR/RR etc) and much of the literature recommends this transformation as a way of dealing with the weighting/variance issue. After the transformation I plan on running a random effects analysis using the metan command (a lot of heterogeneity between my studies). Has anyone used this approach before? Does anyone have recommendations for the coding of the back transformation after the analysis is performed? Any cautions or thoughts on the transformation or alternative approaches I might not have heard of?

Any input would be greatly appreciated.

Thank you!

Jessica Keithlin
Centre for Public Health and Zoonoses
University of Guelph

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