[R-meta] Meta-analysis of intra class correlation coefficients
St Pourcain, Beate
Be@te@StPourc@|n @end|ng |rom mp|@n|
Mon Oct 14 13:49:00 CEST 2024
Dear Wolfgang,
Many thanks, very helpful!
We apply the escalc "COR" option to derive the variance for ICCs, in this case twin correlations, where monozygotic twins (MZ, genetically identical individuals) will always have higher correlations than dizygotic twins (DZ, genetically related like typical siblings).
Following the code from a published study (Austerberry, https://pubmed.ncbi.nlm.nih.gov/35994288/), we report ICCs for MZ and DZ twins and their variance v, derived with escalc "COR", for studies with different N:
e.g. for MZ twins
Study A: ICC=0.96, v= 3.2975E-06, N=1865
Study B: ICC=0.96, v=3.86576E-05, N=160
e.g. for DZ twins
Study A: ICC=0.85, v=4.06365E-05, N=1896
Study C: ICC=0.85, v=0.000496815, N=156
This suggests (to us) that study size is less relevant than ICC magnitude for variance estimations. In other words, irrespective of study size, when meta-analysing MZ and DZ correlations separately, MZ twins will have a smaller SE (higher Z score) than DZ twins. Following the code from (Austerberry), running an Egger regression, we see that (across multiple studies):
egger_seMZ <- regtest(MZdata$yi, MZdata$vi)
egger_seDZ <- regtest(DZdata$yi, DZdata$vi)
rMZ_se_z rDZ_se_z
-22.497 0 -15.359
I also attach the funnel plots, for MZ and DZ twins suggesting the same, with a near linear relationship between
ICC magnitude and variance (code is below). I indicated the sample size of each study through the lightblue pallet ranging between N~70 (lightlblue) to N~1800 (darkblue). I labelled each time the 10 smallest studies indicating that small studies can be found across the entire ICC range of 0-1, whereas the large studies are only found for ICC values of ~ 0.8-1.
It is important for us to understand these variances of the ICC values/ twin correlations, as (twice) the difference of rMZ - rDZ, here based on meta-analysed ICCs, can be used to estimate the heritability of a trait (see also Austerberry).
I am not aware of that variance-stabilizing transformations were applied, but thank you for pointing this out.
Many of the ICC estimates reflect multiple traits from the same studies. Should this be already taken into account during the variance calculation, or is it sufficient to indicate this during the meta-analysis of ICCs values?
Thanks a lot for your guidance,
Beate
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
resMZ <- rma(yi, vi, data=MZdata)
funnel(resMZ,
xlab = "rMZ",
digits = c(2,2),
col = MZdata$n.col,
slab = MZdata$slab,
cex=0.4,
label = 10,
main = "")
resDZ <- rma(yi, vi, data=DZdata)
funnel(resDZ,
xlab = "rDZ",
digits = c(2,2),
col = DZdata$n.col,
slab = DZdata$slab,
cex=0.4,
label = 10,
main = "")
Beate St Pourcain, PhD
Senior Investigator & Group Leader
Room A207
Max Planck Institute for Psycholinguistics | Wundtlaan 1 | 6525 XD Nijmegen | The Netherlands
@bstpourcain
Tel: +31 24 3521964
Fax: +31 24 3521213
ORCID: https://orcid.org/0000-0002-4680-3517
Web: https://www.mpi.nl/departments/language-and-genetics/projects/population-variation-and-human-communication/
Further affiliations with:
MRC Integrative Epidemiology Unit | University of Bristol | UK
Donders Institute for Brain, Cognition and Behaviour | Radboud University | The Netherlands
My working hours may not be your working hours. Please do not feel obligated to reply outside of your normal working schedule.
-----Original Message-----
From: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Sent: Saturday, October 12, 2024 12:40 PM
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: St Pourcain, Beate <Beate.StPourcain using mpi.nl>
Subject: RE: Meta-analysis of intra class correlation coefficients
Dear Beate,
I assume you are talking about ICC(1) values. We did a meta-analysis of ICC(1) values here:
Nicolaï, 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
> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org>
> On Behalf Of St Pourcain, Beate via R-sig-meta-analysis
> Sent: Saturday, October 12, 2024 10:11
> To: r-sig-meta-analysis using r-project.org
> Cc: St Pourcain, Beate <Beate.StPourcain using mpi.nl>
> Subject: [R-meta] Meta-analysis of intra class correlation
> coefficients
>
> Dear R-sig group,
>
> We would like to carry out a meta-analysis of intra class correlation
> (ICC) coefficients (i.e. the correlation between pairs of individuals,
> for the same trait). For this reason, we aim to derive the variance of
> ICCs from published studies, without access to individual data, thus, preventing bootstrapping.
> Could anyone advise us what the options are to derive the variance for
> ICCs using existing R packages?
>
> We were looking into the escalc function from the metafor package, but
> could not find options for ICCs, but options for Pearson
> product-moment correlations ("COR" option).
>
> We have seen research proposing to apply the escalc "COR" option also
> to derive the variance for ICCs. However, we are unsure about this, as
> we may get undesirable properties for the derived variance, given that
> the definition of the correlations is different.
>
> Any advice is welcome!
>
> Best wishes,
> Beate
>
> Beate St Pourcain, PhD
> Senior Investigator & Group Leader
> Room A207
> Max Planck Institute for Psycholinguistics | Wundtlaan 1 | 6525 XD
> Nijmegen | The Netherlands
>
> @bstpourcain
> Tel: +31 24 3521964
> Fax: +31 24 3521213
> ORCID: https://orcid.org/0000-0002-4680-3517
> Web:
> https://www.mpi.nl/departments/language-and-genetics/projects/populati
> on-
> variation-and-human-communication/
> Further affiliations with:
> MRC Integrative Epidemiology Unit | University of Bristol | UK Donders
> Institute for Brain, Cognition and Behaviour | Radboud University |
> The Netherlands
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