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[R-meta] Meta-analysis of intra class correlation coefficients

Wolfgang Viechtbauer 
Dear Beate,

I assume you are talking about ICC(1) values. We did a meta-analysis of ICC(1) values here:

Nicola?, S. P. A., Viechtbauer, W., Kruidenier, L. M., Candel, M. J. J. M., Prins, M. H., & Teijink, J. A. W. (2009). Reliability of treadmill testing in peripheral arterial disease: A meta-regression analysis. Journal of Vascular Surgery, 50(2), 322-329. https://doi.org/10.1016/j.jvs.2009.01.042

For ICC(1) values, one can apply a variance-stabilizing transformation with:

y = 1/2 * log((1 + (m-1)*icc) / (1 - icc))

where 'm' is the number of measurement occasions and 'n' is the number of participants. The large-sample variance is then:

Var[y] = m / (2*(m-1)*(n-2)).

This goes back to Fisher (1925; Statistical methods for research workers).

In your application (where you dealing with pairs), n is the number of pairs and m is 2. In that case, you can treat ICC(1) values like regular correlations. However, if you do apply the r-to-z transformation, then Fisher suggests to use 1/(n-3/2) as the variance (instead of 1/(n-3) as we typically use for r-to-z transformed Pearson product-moment correlation coefficients) and simulation studies I have done confirm this.

Best,
Wolfgang

--
Wolfgang Viechtbauer, PhD, Statistician | Department of Psychiatry and
Neuropsychology | Maastricht University | PO Box 616 (VIJV1) | 6200 MD
Maastricht, The Netherlands | +31(43)3884170 | https://www.wvbauer.com

Thread (10 messages)

St Pourcain, Beate Meta-analysis of intra class correlation coefficients Oct 12 Wolfgang Viechtbauer Meta-analysis of intra class correlation coefficients Oct 12 St Pourcain, Beate Meta-analysis of intra class correlation coefficients Oct 14 Wolfgang Viechtbauer Meta-analysis of intra class correlation coefficients Oct 14 St Pourcain, Beate Meta-analysis of intra class correlation coefficients Oct 16 Wolfgang Viechtbauer Meta-analysis of intra class correlation coefficients Oct 16 St Pourcain, Beate Meta-analysis of intra class correlation coefficients Oct 18 Wolfgang Viechtbauer Meta-analysis of intra class correlation coefficients Oct 18 St Pourcain, Beate Meta-analysis of intra class correlation coefficients Oct 18 Michael Dewey Meta-analysis of intra class correlation coefficients Oct 19