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

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 at gmail.com]
Sent: Tuesday, 08 March, 2022 2:07
To: r-sig-meta-analysis at 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 at 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 at gmail.com]
Sent: Tuesday, 18 January, 2022 3:53
To: r-sig-meta-analysis at 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 at 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 at gmail.com]
Sent: Monday, 18 October, 2021 19:24
To: r-sig-meta-analysis at 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 at 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 at 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 at r-project.org] On
Behalf Of Arthur Albuquerque
Sent: Monday, 18 October, 2021 18:15
To: r-sig-meta-analysis at 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