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

Wed Mar 9 20:36:48 CET 2022

Dear Wolfgang,

Thank you in advance. I contacted Reference [1] authors, and they sent me this data:

structure(list(study.name = c("Cutler1995", "Dahlof1991", "Dowson2002", "Ensink1991", "Geraud2000", "Goadsby1991", "Goadsby2000", "Havanka2000", "Kaniecki2006", "Mathew2003", "Myllyla1998", "Nappi1994", "Patten1991", "Pfaffenrath1998", "Sandrini2002", "Sargent1995", "Sheftell2005", "Tfelt-Hansen1995", "Tfelt-Hansen1998", "Visser1996"), n1 = c(66L, 275L, 194L, 131L, 504L, 89L, 129L, 98L, 131L, 831L, 42L, 142L, 142L, 277L, 170L, 46L, 902L, 122L, 388L, 72L), n2 = c(65L, 182L, 99L, 78L, 56L, 93L, 142L, 91L, 127L, 419L, 41L, 81L, 101L, 91L, 84L, 47L, 892L, 126L, 160L, 85L), r1 = c(37L, 180L, 123L, 60L, 304L, 45L, 63L, 59L, 64L, 471L, 33L, 73L, 95L, 175L, 85L, 26L, 649L, 63L, 239L, 33L), r2 = c(17L, 48L, 42L, 14L, 24L, 9L, 30L, 28L, 47L, 105L, 12L, 25L, 22L, 27L, 25L, 8L, 375L, 30L, 64L, 15L)), row.names = c(NA, 20L), class = "data.frame")

Best,

Arthur M. Albuquerque

Medical student
Universidade Federal do Rio de Janeiro, Brazil

On Mar 8, 2022, 7:07 PM -0300, Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
> Hi Arthur,
>
> I don't want to start re-reading all those articles right now, but who cites who isn't the best indication of whether people are talking about the same model or not.
>
> In [1], the authors use data from a Cochrane review to illustrate the model. If you provide these data here using dput(), so that I can immediately reproduce the exact dataset, then I could see whether I can reproduce their results. It's time-consuming extracting data manually from pdfs, so I'll leave this up to you whether you want to do this.
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: Arthur Albuquerque [mailto:arthurcsirio using gmail.com]
> > Sent: Tuesday, 08 March, 2022 2:07
> > To: r-sig-meta-analysis using r-project.org; Viechtbauer, Wolfgang (SP)
> > Subject: RE: [R-meta] Bivariate generalized linear mixed model with {metafor}
> >
> > 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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