[R-meta] Questions metafor random slope

[Mathias Weis Damkjær]

Dear Wolfgang,

Thanks again for the reply. It is indeed combining the results from multiple meta-analyses, although I acknowledge not all may find this
Evidence on the influence of study characteristics have, however, been provided this way.  In frequentist statistics see Siersma (multilevel models) https://doi.org/10.1002/sim.2752 and by Sterne et al. (two-step) models https://doi.org/10.1002/sim.1184.

Final question, I was wondering if somehow it was possible to get rid - in a meaningful way of course - the "extra" random-intercept at the meta-analysis-level?

In STATA it seems to be possible to get the desired structure: (source: https://www.stata.com/manuals/metametameregress.pdf)

  *
Perform a three-level meta-analysis of effect-size y with random intercepts by region and by trial nested within region
     *
meta meregress y || region: || trial:, essevariable(se)
  *
As above, but perform a three-level meta-regression on moderator x, add a random slope on x at the region level:
     *
meta meregress y x || region: x || trial:, essevariable(se)

I.e., the study characteristic is allowed to vary across meta-analyses, and it accounts for the "cluster-effect" of trials nested within meta-analysis by having random-intercepts at these levels, and estimate the between-trial and between-meta-analysis variation.

I am not sure what the equivalent model specification in the metafor-package is. The above STATA model only have one random-intercept at the meta-analysis level.


Mathias

________________________________
Fra: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Sendt: 20. november 2024 16:59
Til: Mathias Weis Damkj�r <mwdamkjaer using health.sdu.dk>; R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Emne: RE: Questions metafor random slope

I think that your interpretations are correct. I am just a bit confused by you speaking of a 'meta-analysis level' as this sounds as if you are combining the results from multiple meta-analyses in your analysis, but I guess this is what you are doing.

Best,
Wolfgang

> -----Original Message-----
> From: Mathias Weis Damkj�r <mwdamkjaer using health.sdu.dk>
> Sent: Monday, November 11, 2024 21:19
> To: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>; R
> Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
> Subject: Re: Questions metafor random slope
>
> Thank you so much for replying, Wolfgang.
>
> So, just to make sure I get it right (and other readers as well :)):
>
> ma_id = meta-analyses level
> trial_id = study level,
>
> res <- rma.mv(yi, vi, mods = ~ moderator, random = list(~ moderator | ma_id, ~ 1
> | ma_id / trial_id), struct="GEN", data=d)
>
> This would give the following:
> 1. A nested structure with random-intercepts for trial_id (studies) nested
> within (meta-analyses), and this will estimate the nested variation / cluster-
> effect.
> 2. And a random slope for moderator at ma_id (meta-analysis) level and random-
> intercept for meta-analysis. This will allow moderator's effect to vary across
> meta-analyses, and will estimate variation of factor at the ma_id (meta-
> analysis) level.
> 'id' in the previous reply would be meta-analysis level, yes, but that would
> give me answer pct. two, right, i.e., variation of the moderator at the ma_id
> (meta-analysis) level?
>
> Of course this would be a complex model, so it requires a big dataset
>
> Thank you once again!
>
> Mathias
>
> PhD-student
> ________________________________________
> From: Viechtbauer, Wolfgang (NP)
> <mailto:wolfgang.viechtbauer using maastrichtuniversity.nl>
> Sent: Monday, November 11, 2024 4:20:46 PM
> To: R Special Interest Group for Meta-Analysis <mailto:r-sig-meta-analysis using r-
> project.org>
> Cc: Mathias Weis Damkj�r <mailto:mwdamkjaer using health.sdu.dk>
> Subject: RE: Questions metafor random slope
>
> Dear Mathias,
>
> See below for my responses.
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: R-sig-meta-analysis <mailto:r-sig-meta-analysis-bounces using r-project.org>
> On Behalf
> > Of Mathias Weis Damkj�r via R-sig-meta-analysis
> > Sent: Friday, November 8, 2024 15:50
> > To: mailto:r-sig-meta-analysis using r-project.org
> > Cc: Mathias Weis Damkj�r <mailto:mwdamkjaer using health.sdu.dk>
> > Subject: [R-meta] Questions metafor random slope
> >
> > Hello everyone,
> >
> > I have a few questions about a more complicated model specification in
> metafor.
> > I have also created a stackoverflow thread with no replies yet here:
> > https://stackoverflow.com/questions/79165730/random-slopes-and-intercepts-in-<https://stackoverflow.com/questions/79165730/random-slopes-and-intercepts-in->
> > the-metafor-package-model-specification-and-out
> >
> > I have read the e-mail correspondence: https://stat.ethz.ch/pipermail/r-sig-<https://stat.ethz.ch/pipermail/r-sig->
> > meta-analysis/2019-August/001650.html with interest.
> >
> > However, I do have some questions.
> >
> >   1.  Question 1:
> >
> > The model specification:
> >
> >   *   res <- rma.mv(logOR, logOR.var, mods = ~ CF1_Women..IMP, random = list(~
> > CF1_Women..IMP | id, ~ 1 | row), struct="GEN", data=d)
> >
> > Adds a multilevel structure AND random slopes for the covariate within meta-
> > analyses.
> >
> > I was wondering why one should not specify the model with: ~ 1 | id/row as the
> > last element in the list of random-effects? That is the notation for instance
> in
> > the lme4 package.
>
> This would add a random intercept at the level of 'id' twice, once via '~
> CF1_Women..IMP | id' and once via '~ 1 | id/row'. Note that the latter is a
> shortcut for '~ 1 | id' and '~ 1 | row %in% id' just like in lme4. So I suspect
> that this model would be overparameterized. But you can always try it out with
> your data and profile the variance components with profile() to see if they are
> identifiable.
>
> >   1.  Question 2:
> >
> > The tau2 estimates (variance components) from this model:
> >
> > Variance Components:
> >
> >             estim    sqrt  nlvls  fixed    factor
> >
> > sigma^2    X  X    X     no  trial_id
> >
> > outer factor: id       (nlvls = X)
> > inner term:   ~factor (nlvls = X)
> >
> >               estim    sqrt  fixed  rho:  intr    c_SP
> > intrcpt        X      X                 no           -  X
> > factor     X        X no          no       -
> >
> > Sigma2 is for trial_level.
> >
> > Is it correct that intrcpt is for the meta-analyses level?
>
> I can't answer that question, since I don't know what you mean by 'meta-analyses
> level'. The variance corresponding to 'intrcpt' is the estimated variance of the
> intercepts at the 'id' level. Maybe that helps?
>
> > Thanks in advance!
> >
> > Best,
> > Mathias, Phd. Student

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