[R-meta] Bivariate generalized linear mixed model with {metafor}

[Arthur Albuquerque]

Dear Wolfgang,

We had this discussion back in October, so you might not remember. In brief, I wanted to fit a Bivariate model and you pointed towards the Model 6 in your excellent article:

Jackson, D., Law, M., Stijnen, T., Viechtbauer, W., & White, I. R. (2018). A comparison of seven random-effects models for meta-analyses that estimate the summary odds ratio. Statistics in Medicine, 37(7), 1059-1085. https://doi.org/10.1002/sim.7588

In this article, you fitted the model using the command:

lme4::glmer(cbind(event,n-event)~factor(treat)+(control+treat-1|study), data=thedata1, family=binomial(link="logit"))

Today, I found a page in your metafor webpage (http://www.metafor-project.org/doku.php/analyses:vanhouwelingen2002), fitting the same Model 6 mentioned above. However, you used metafor, not lme4 (of course), and the random effect structure seems a little bit different:

res <- rma.mv(yi, vi, mods = ~ group - 1, random = ~ group | trial, struct="UN", data=dat.long, method="ML")

Thus, I would like to first confirm if they are indeed the same model. If not, what are their differences and what would be major implications?

Thank you very much,

Arthur M. Albuquerque

Medical student
Universidade Federal do Rio de Janeiro, Brazil

On Oct 18, 2021, 2:53 PM -0300, Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
> As far as I can tell, that seems to be Model 6: the "Van Houwelingen bivariate" model as discussed in our paper.
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: Arthur Albuquerque [mailto:arthurcsirio using gmail.com]
> > Sent: Monday, 18 October, 2021 19:24
> > To: r-sig-meta-analysis using r-project.org; Viechtbauer, Wolfgang (SP); Michael Dewey
> > Subject: Re: [R-meta] Bivariate generalized linear mixed model with {metafor}
> >
> > Dear Michael,
> >
> > I’m sorry, my bad.
> >
> > It’s a binomial model with the logit link, in which the average baseline and
> > treatment risks are treated as fixed effects. Moreover, there are two study-
> > specific parameters (random-effects), and these are assumed to follow a bivariate
> > normal distribution with covariance matrix “E”. This matrix includes the between-
> > study variances for the baseline and treatment odds +  the correlation between
> > the baseline and treatment risks in the logit scale.
> >
> > The authors then explain how to estimate marginal and conditional effects from
> > this model using formulas. I am also not sure how to estimate these using
> > metafor.
> >
> > They suggest using this model “to include the baseline risk and report the
> > variation in the effect measure with baseline risks in addition to the marginal
> > effect, regardless of the measure of choice”.
> >
> > Sorry for the confusion, it’s my first time asking here and it is a quite
> > complicated topic (at least for me).
> >
> > Best,
> >
> > Arthur M. Albuquerque
> >
> > Medical student
> > Universidade Federal do Rio de Janeiro, Brazil
> >
> > On Oct 18, 2021, 2:10 PM -0300, Michael Dewey <lists using dewey.myzen.co.uk>, wrote:
> >
> > Dear Arthur
> >
> > You might get more helpful replies if you summarise the model for us
> > rather than relying on someone here to do that for you.
> >
> > Michael
> >
> > On 18/10/2021 17:51, Arthur Albuquerque wrote:
> >
> > Dear Wolfgang,
> >
> > Thank you for the super quick reply! I wasn’t aware of that article, yet I
> > believe it does not include the model I mentioned.
> >
> > The model is thoroughly described at the end of this article, section "Appendix
> > B. The bivariate generalized linear mixed model
> > (BGLMM)”: https://doi.org/10.1016/j.jclinepi.2021.08.004
> >
> > Best,
> >
> > Arthur M. Albuquerque
> >
> > Medical student
> > Universidade Federal do Rio de Janeiro, Brazil
> >
> > On Oct 18, 2021, 1:31 PM -0300, Viechtbauer, Wolfgang (SP)
> > <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
> >
> > Dear Arthur,
> >
> > rma() does not fit generalized linear mixed models -- rma.glmm() does. I don't
> > have the time right now to dig into those papers to figure out what specific
> > model they are suggesting. In this context, many different models have been
> > suggested; see, for example:
> >
> > Jackson, D., Law, M., Stijnen, T., Viechtbauer, W., & White, I. R. (2018). A
> > comparison of seven random-effects models for meta-analyses that estimate the
> > summary odds ratio. Statistics in Medicine, 37(7), 1059-1085.
> > https://doi.org/10.1002/sim.7588
> >
> > (and this is not even an exhaustive list). The paper also indicates how these
> > models can be fitted, either with metafor::rma.glmm() or one can do this directly
> > with lme4""glmer().
> >
> > Best,
> > Wolfgang
> >
> > -----Original Message-----
> > From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
> > Behalf Of Arthur Albuquerque
> > Sent: Monday, 18 October, 2021 18:15
> > To: r-sig-meta-analysis using r-project.org
> > Subject: [R-meta] Bivariate generalized linear mixed model with {metafor}
> >
> > Hi all,
> >
> > I need some help to figure out how to fit a bivariate generalized linear mixed
> > model using metafor.
> >
> > In the past year, the Journal of Clinical Epidemiology has posted several
> > articles on a controversy between using risk ratio or odds ratio in meta-
> > analyses. Summary of the controversy here:
> >
> > George A. Wells , Commentary on Controversy and Debate 4 paper series:
> > Questionable utility of the relative risk in clinical research, Journal of
> > Clinical Epidemiology (2021), doi: https://doi.org/10.1016/j.jclinepi.2021.09.016
> >
> > One of the articles (https://doi.org/10.1016/j.jclinepi.2021.08.004) suggested
> > fitting a bivariate generalized linear mixed model (BGLMM),  which "obtains
> > effect estimates conditioning on baseline risks with the estimated model
> > parameters, including the correlation parameter.”
> >
> > They fitted this model using the PROC NLMIXED command in SAS. I would like to fit
> > this model using metafor, could anyone help me by sending the appropriate code of
> > this model with metafor::rma()?
> >
> > Kind regards,
> >
> > Arthur M. Albuquerque
> >
> > Medical student
> > Universidade Federal do Rio de Janeiro, Brazil

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