[R-meta] R-sig-meta-analysis Digest, Vol 89, Issue 13

St Pourcain, Beate Be@te@StPourc@|n @end|ng |rom mp|@n|
Tue Nov 5 19:16:06 CET 2024 

Dear Wolfgang,
We have taken the project a few steps further now following vanhouwelingen2002. Thanks for all your advice! However, bivariate models have of course a slightly different structure compared to nested models that we usually use and we have transformations and multiple random effects. Thus, we had a few questions.  We have a model like this:

Study_ID: Unique ID for each independent cohort
ESID_code: Unique ID for study-specific assessment coded as nested within each study (following Austerberry) 
MZDZ: MZ coded 1, DZ coded 0
zi and vzi: Z transformed correlations and their variance

model0r.mlcon <- rma.mv(
  zi,
  vzi,
  random = list(~ MZDZ_factor | Study_ID, ~ MZDZ_factor | ESID_code), struct="UN",
  data = data,
  mods = ~ 0 + MZDZ_factor,
  method = "ML",
  tdist = TRUE,
  cvvc="varcov",
  control=list(nearpd=TRUE))

1)	We changed now from REML to ML to allow for model building with fixed effects. Is there any major drawback?
2)	What would be the best way to estimate I2 for each MZ and DZ group using Z and the raw correlations? (We have an idea how to do this with nested models but not for bivariate models). Also does it make sense to estimate residual heterogeneity as:

tau_het<-round(model0r.mlcon$tau2[1] + model0r.mlcon$tau2[2] - 2*model0r.mlcon$rho*sqrt(model0r.mlcon$tau2[1]*model0r.mlcon$tau2[2]), 3)

gamma_het<-round(model0r.mlcon$gamma2[1] + model0r.mlcon$gamma2[2] - 2*model0r.mlcon$phi*sqrt(model0r.mlcon$gamma2[1]*model0r.ml$gamma2[2]), 3)

res_het<-tau_study + gamma_type

3)	We can estimate the SE for the raw scores
rDZse<- deltamethod(~ (exp(2*x1) - 1) / (exp(2*x1) + 1), coef(model0r.mlcon), vcov(model0r.mlcon))
rMZse<- deltamethod(~ (exp(2*x2) - 1) / (exp(2*x2) + 1), coef(model0r.mlcon), vcov(model0r.mlcon))
Is there an option to backtransform vcov(model0r.mlcon) from the modelled rZ to raw r scores? Especially we are interested in the covariance for raw r to derive a correlation between raw rMZ and rDZ, including SE.

4)	For adding further covariates as fixed effects, we were wondering how to best predict manually rMZ and rDZ for different levels of the covariate e.g. age

model.age.r.mlcon <- rma.mv(
  zi,
  vzi,
  random = list(~ MZDZ_factor | Study_ID, ~ MZDZ_factor | ESID_code), struct="UN",
  data = data,
  mods = ~ 0 + MZDZ_factor + MZDZ_factor:I(Age -24), #age centered at 24 years
  method = "ML",
  tdist = TRUE)
model.age.r.mlcon snippet

                            estimate      se    tval  df    pval   
MZDZ_factor0                0.7264  0.1201  7.7141  78  <.0001  
MZDZ_factor1                1.3193  0.2464  6.1661  78  <.0001  
MZDZ_factor0:I(Age - 24)    0.0160  0.0040  4.0432  78  0.0001  
MZDZ_factor1:I(Age - 24)    0.0276  0.0038  7.2905  78  <.0001  

We could now predict the twin correlations at different ages using the predict function (and did this). However, this does not help with the deltamethod. Is there a more elegant way to estimate the SE?
e.g.
age.20 <- -4
rDZ_20 <-(exp(2*(model.age.r.mlcon$b[1] + model.age.r.mlcon$b[3]*age.20)) - 1) / (exp(2*(model.age.r.mlcon$b[1] + model.age.r.mlcon$b[3]*age.20)) + 1)

rMZ_20 <-(exp(2*(model.age.r.mlcon$b[2] + model.age.r.mlcon$b[4]*age.20)) - 1) / (exp(2*(model.age.r.mlcon$b[2] + model.age.r.mlcon$b[4]*age.20)) + 1)
 
rDZ_20.se <-deltamethod(~(exp(2*(x1 + x3*age.20)) - 1) / (exp(2*(x1 + x3*age.20)) + 1), coef(model.age.r.mlcon), vcov(model.age.r.mlcon))

rMZ_20.se <-deltamethod(~(exp(2*(x2 + x4*age.20)) - 1) / (exp(2*(x2 + x4*age.20)) + 1), coef(model.age.r.mlcon), vcov(model.age.r.mlcon))

Many thanks again for all your help,
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/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: Thursday, October 31, 2024 1:22 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: R-sig-meta-analysis Digest, Vol 89, Issue 13

Hi Beate,

The simulations I mentioned are not published, but Fisher (1925) directly states this as well, so you can stick to that reference.

By the way, I just added a deltamethod() function to the development version of the metafor package. So, coming back to this model:

model <- rma.mv(
   zi,
   vzi,
   random = list(~ MZDZ_factor | Study_ID, ~ MZDZ_factor | ESID), struct="UN",
   data = data,
   mods = ~ 0 + MZDZ_factor,
   method = "REML",
   tdist = TRUE)

you can now just do:

deltamethod(model, fun=function(b1,b2) 2*(transf.ztor(b2) - transf.ztor(b1)))

and you will directly get the estimate of h^2 and the corresponding SE and CI.

Best,
Wolfgang

> -----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: Sunday, October 20, 2024 21:25
> To: r-sig-meta-analysis using r-project.org
> Cc: St Pourcain, Beate <Beate.StPourcain using mpi.nl>
> Subject: Re: [R-meta] R-sig-meta-analysis Digest, Vol 89, Issue 13
>
> Hi Michael,
>
> Thanks for pointing this out! The Fisher reference will certainly do. 
> I had hoped to get the reference for "simulation studies I have done 
> confirm this", but that's an added bonus.
>
> Have a nice evening,
> Beate
>
> Date: Sat, 19 Oct 2024 15:16:22 +0100
> From: Michael Dewey <lists using dewey.myzen.co.uk>
> To: R Special Interest Group for Meta-Analysis
>         <r-sig-meta-analysis using r-project.org>, "Viechtbauer, Wolfgang (NP)"
>         <wolfgang.viechtbauer using maastrichtuniversity.nl>
> Cc: "St Pourcain, Beate" <Beate.StPourcain using mpi.nl>
> Subject: Re: [R-meta] Meta-analysis of intra class correlation
>         coefficients
>
> Dear Beate
>
> Somewhere buried in this thread Wolfgang said
>
> ==========================
> 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.
> ======================
>
> Michael
>
> On 18/10/2024 19:43, St Pourcain, Beate via R-sig-meta-analysis wrote:
> > Dear Wolfgang,
> > No worries, I am aware of the difference and fully agree with your 
> > comments. I
> was just surprised by the similarity in estimates and had hoped for an 
> approximation that  might provide a quick workaround in the current situation.
> Thanks again for all your help, we will take it from here.
> >
> > In case you would have (at some point) a reference for the variance 
> > of Z
> scores for ICCs as
> >
> > 1/( n-3/2)
> >
> > that would be great, no rush!
> >
> > Enjoy your weekend,
> > Beate

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