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

Fri, Dec 6, 2024 3:15 AM #

For some reason, some of my posts do not seem to get through. Not sure if they are getting caught in some spam filter. I am going to try sending this again. Apologies for the noise in case the message below (which was sent almost 2 hours ago) does finally show up on the list.

Best,
Wolfgang

-----Original Message-----
From: Viechtbauer, Wolfgang (NP)
Sent: Friday, December 6, 2024 10:28
To: St Pourcain, Beate <Beate.StPourcain at mpi.nl>; R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Subject: RE: R-sig-meta-analysis Digest, Vol 89, Issue 13

I assume you are referring to model 'model0r.mlcon' below and coef(model0r.mlcon)[1] is the DZ coefficient (i.e., the estimated average r-to-z transformed ICC) and coef(model0r.mlcon)[2] the MZ coefficient and vcov(model0r.mlcon) gives the corresponding var-cov matrix. Then

res <- deltamethod(model0r.mlcon, fun=function(z1,z2) c(tanh(z1), tanh(z2)))
res

will give you the back-transformed estimates (i.e., estimated ICCs) with corresponding SEs and CIs and

res$vcov

is the full var-cov matrix of these back-transformed estimates. And

deltamethod(model0r.mlcon, fun=function(z1,z2) 2*(tanh(z2)-tanh(z1)))

will give you the estimated H^2 based on Falconer's formula with corresponding SE/CI.

Best,
Wolfgang

-----Original Message-----
From: St Pourcain, Beate <Beate.StPourcain at mpi.nl>
Sent: Tuesday, December 3, 2024 19:47
To: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>; R
Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Subject: RE: R-sig-meta-analysis Digest, Vol 89, Issue 13

Dear Wolfgang,

Many thanks for your advice and sorry about the delay.
I added my answers below! Most things are sorted and clear! However, I did not
follow your reply about the back-transformation of the directly estimated
co/variance for fixed effects, i.e. from the rZ to the r the level, using the
deltamethod. I can see how you derive the SE for the fixed effects at the back-
transformed level with deltamethod, but not the variance and covariance. Could
you please help here?

Many thanks,
Beate

-----Original Message-----
From: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Sent: Monday, November 11, 2024 4:13 PM
To: St Pourcain, Beate <Beate.StPourcain at mpi.nl>; R Special Interest Group for
Meta-Analysis <r-sig-meta-analysis at r-project.org>
Subject: RE: R-sig-meta-analysis Digest, Vol 89, Issue 13

Dear Beate,

Some brief comments from my side to your questions below.

Best,
Wolfgang

-----Original Message-----
From: St Pourcain, Beate <Beate.StPourcain at mpi.nl>
Sent: Tuesday, November 5, 2024 19:16
To: Viechtbauer, Wolfgang (NP)
<wolfgang.viechtbauer at maastrichtuniversity.nl>; R Special Interest
Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Subject: RE: R-sig-meta-analysis Digest, Vol 89, Issue 13

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?

Unless your sample sizes are small, the difference between ML and REML should be
negligible. For model selection including fixed effects, ML is the sensible
choice.

R: Perfect. Thank you!

2)    What would be the best way to estimate I2 for each MZ and DZ group using

and the raw correlations? (We have an idea how to do this with nested
models but not for bivariate models).

Maybe this is useful:

https://www.metafor-
project.org/doku.php/tips:i2_multilevel_multivariate#multivariate_models

R: Very helpful, thank you!

Also does it make sense to estimate heterogeneity in rZ 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

I can't answer that because you would first have to define what you mean by
'residual heterogeneity'.

R: We aimed to estimate the heterogeneity in rZ-scores, analogous to the
bivariate example approach (but now with two random effects)
https://www.metafor-project.org/doku.php/analyses:vanhouwelingen2002

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.

The deltamethod() function from metafor can give you the full back-transformed
var-cov matrix.

R: Sorry for being slow here, I do not know how to proceed. The variance
covariance matrix is directly estimated and there is not transformation
involved.  Could you please advise

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))

I don't understand the question. What do you mean by 'more elegant'?
R: No worries, we will sort this out. I just meant a "shorter" way, but this is
not a problem.

Many thanks again for all your help,
Beate