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

Tue Mar 8 23:07:15 CET 2022

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