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

[Viechtbauer, Wolfgang (SP)]

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