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

Tue Mar 8 02:07:07 CET 2022

Hi Wolfgang,

It’s me again about this bivariate model. I am having a hard time trying to figure out if I understood it correctly.

To recap, I wanted to fit a bivariate meta-analysis model (hereafter, mod1) described in Reference [1] below. You replied suggesting it was the "Model 6: the Van Houwelingen bivariate” (mod2) in your article with Jackson et al (Reference [2]).

However, I am now re-reading all these articles and I believe mod1 and mod2 are different. Reference [1] cites Thompson et al. (Reference [3]), and does not cite van Houwelingen. You cited Van Houwelingen et al (Reference [4]). To my knowledge, they seem different models indeed.

In fact, Van Houwelingen in Reference [5] directly cites Thompson suggesting these models are distinct:

"The mix of many 􏱪fixed and a few random e􏱨ffects as proposed by Thompson et al. … are more in the spirit of the functional approach. These methods are meant to impose no conditions on the distribution of the true baseline risks… In a letter to the editor by Van Houwelingen and Senn following the article of Thompson et al. , Van Houwelingen and Senn argue that putting Bayesian priors on all nuisance parameters, as done by Thompson et al., does not help solving the inconsistency problem."

Are they indeed different model?

Please ignore this email if this question is out of the scope of your mailing list. Sorry in advance.

Kind regards,

Arthur M. Albuquerque

Medical student
Universidade Federal do Rio de Janeiro, Brazil

References:

[1] Xiao, Mengli, Yong Chen, Stephen R Cole, Richard F MacLehose, David B Richardson, and Haitao Chu. ‘Controversy and Debate: Questionable Utility of the Relative Risk in Clinical Research: Paper 2: Is the Odds Ratio “Portable” in Meta-Analysis? Time to Consider Bivariate Generalized Linear Mixed Model’. Journal of Clinical Epidemiology 142 (February 2022): 280–87. https://doi.org/10.1016/j.jclinepi.2021.08.004

[2] Jackson, Dan, Martin Law, Theo Stijnen, Wolfgang Viechtbauer, and Ian R. White. ‘A Comparison of Seven Random-Effects Models for Meta-Analyses That Estimate the Summary Odds Ratio’. Statistics in Medicine 37, no. 7 (30 March 2018): 1059–85. https://doi.org/10.1002/sim.7588

[3] Thompson, Simon G., Teresa C. Smith, and Stephen J. Sharp. ‘Investigating Underlying Risk as a Source of Heterogeneity in Meta-Analysis’. Statistics in Medicine 16, no. 23 (15 December 1997): 2741–58. https://doi.org/10.1002/(SICI)1097-0258(19971215)16:23<2741::AID-SIM703>3.0.CO;2-0

[4] Van Houwelingen, Hans C., Koos H. Zwinderman, and Theo Stijnen. ‘A Bivariate Approach to Meta-Analysis’. Statistics in Medicine 12, no. 24 (30 December 1993): 2273–84. https://doi.org/10.1002/sim.4780122405

[5] Houwelingen, Hans C. van, Lidia R. Arends, and Theo Stijnen. ‘Advanced Methods in Meta-Analysis: Multivariate Approach and Meta-Regression’. Statistics in Medicine 21, no. 4 (28 February 2002): 589–624. https://doi.org/10.1002/sim.1040
On Jan 27, 2022, 4:04 PM -0300, Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
> Dear Arthur,
>
> I can't dig through these details as I need to limit my computer usage to a minimum at this time due to a broken arm/wrist.
>
> But I recently have added additional functionality to rma.glmm() that allows one to fit all models described in that article:
>
> https://wviechtb.github.io/metafor/reference/rma.glmm.html
>
> See arguments 'coding' and 'cor'.
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: Arthur Albuquerque [mailto:arthurcsirio using gmail.com]
> > Sent: Tuesday, 18 January, 2022 3:53
> > To: r-sig-meta-analysis using r-project.org; Michael Dewey; Viechtbauer, Wolfgang (SP)
> > Subject: RE: [R-meta] Bivariate generalized linear mixed model with {metafor}
> >
> > 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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