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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 2 Apr 2012 21:44:04 -0400 |

Jessica, To complicate matters further, I must point out that neither of the papers that Cameron cited deals with meta-analysis. In meta-analysis, the arcsine-square-root transformation has the advantage that (to first order) the weights depend only on the sample size(s), which are known. The customary methods for meta-analysis of risk difference, risk ratio, and odds ratio use weights based on estimated variances, but they pretend that those variances are known and, as a result, may have substantial bias. Since you plan to use random effects, you should avoid using the DerSimonian-Laird method for risk difference, risk ratio, or odds ratio. It would be a good idea to examine the heterogeneity in your data carefully, to see whether it involves clusters, outliers, or other interesting structure. For some background on the arcsine-square-root (a.k.a. angular) transformation in meta-analysis, you may want to look at the following paper (and some of its references): Ruecker G, Schwarzer G, Carpenter J, Olkin I. Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta-analysis with zero cells. Statistics in Medicine 2009; 28:721-738. I also suggest the following book: Kulinskaya E, Morgenthaler S, Staudte RG. Meta Analysis: A Guide to Calibrating and Combining Statistical Evidence. Wiley, 2008. The same authors discuss an alternative approach: Kulinskaya E, Morgenthaler S, Staudte RG. Variance stabilizing the difference of two binomial proportions. The American Statistician 2010; 64:350-356. If you do the analysis in the angular scale, you can transform a difference back to the proportion scale by choosing a particular proportion as the "base rate" (a similar consideration applies to the odds ratio and its log). Another possible alternative would take a Bayesian approach, modeling the observed proportions by binomial distributions and expressing the difference between the true proportions on the logit scale. See, for example, Sutton AJ, Abrams KR. Bayesian methods in meta-analysis and evidence synthesis. Statistical Methods in Medical Research 2001; 10:277-303. David Hoaglin * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: using Freeman-Tukey arcsine transformation with metan command***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: st: using Freeman-Tukey arcsine transformation with metan command***From:*Jessica Keithlin <jkeithli@uoguelph.ca>

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