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


From   "Roger B. Newson" <r.newson@imperial.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: using Freeman-Tukey arcsine transformation with metan command
Date   Mon, 02 Apr 2012 19:25:40 +0100

PS if Jessica is meta-analysing proportions, instead of differences between proportions, then the obvious alternative might be to use the logit transformation, estimating odds instead of the usual odds ratios. Jessica does not state the Stata version being used. However, in the case of Stata 12, a good source on odds (as distinct from odds ratios) is in the current Stata Journal (Buis, 2012). In previous versions of Stata, the comments on geometric means given in Newson (2003) also apply to odds.

Best wishes

Roger

References

Buis ML. Stata tip 107: The baseline is now reported. The Stata Journal 2012; 12{1}: 165–166. Purchase from
http://www.stata-journal.com/article.html?article=st0251

Newson R. Stata tip 1: The eform() option of regress. The Stata Journal 2003; 3(4): 445. Download from
http://www.stata-journal.com/article.html?article=st0054

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
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

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

On 02/04/2012 18:24, Roger B. Newson wrote:
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

Roger


References

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
http://www.stata-journal.com/article.html?article=snp15_6

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
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/


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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