[R-meta] Separate tau for each subgroup in mixed-effect models

[Arthur Albuquerque]

Wolfgang,

I now realized this discussion is related to the discussion presented in this book: https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/subgroup.html

To my understanding, they argue - while citing Borenstein & Higgins 2013 - that the models you discussed treat subgroups as “fixed-effects”, but also assume studies within subgroups follow the random-effects model (see their Figure 7.1).

Thus, I conclude these model impose a conditional inference to the subgroups analyzed.

What do you think?

Best,

Arthur M. Albuquerque

Borenstein, Michael, and Julian P. T. Higgins. ‘Meta-Analysis and Subgroups’. Prevention Science 14, no. 2 (April 2013): 134–43. https://doi.org/10.1007/s11121-013-0377-7



On Sep 1, 2022, 5:18 AM -0300, Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
> This has also been possible with the rma.mv() function:
>
> https://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates#meta-regression_with_all_studies_but_different_amounts_of_residual_heterogeneity
>
> So, actually, there are three different ways one can do this:
>
> 1) Fit separate RE models within subgroups.
>
> dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
>
> res1 <- list(rma(yi, vi, data=dat, subset=alloc=="alternate"),
> rma(yi, vi, data=dat, subset=alloc=="random"),
> rma(yi, vi, data=dat, subset=alloc=="systematic"))
>
> dat.comp <- data.frame(meta = c("alternate","random","systematic"),
> estimate = sapply(res1, coef),
> stderror = sqrt(sapply(res1, vcov)),
> tau2 = sapply(res1, \(x) x$tau2))
> dat.comp <- dfround(dat.comp, 4)
> dat.comp
>
> 2) Fit an rma.mv() model with a random effects structure that allows tau^2 to differ across groups.
>
> res2 <- rma.mv(yi, vi, mods = ~ 0 + alloc, random = ~ alloc | trial, struct="DIAG", data=dat)
> res2
>
> 3) Use a location-scale model with a categorical scale variable.
>
> res3 <- rma(yi, vi, mods = ~ 0 + alloc, scale = ~ 0 + alloc, data=dat)
> res3
> predict(res3, newscale=diag(3), transf=exp)
>
> Instead of using the (default) log link, we can also use an identity link to fit this model:
>
> res4 <- rma(yi, vi, mods = ~ 0 + alloc, scale = ~ 0 + alloc, data=dat, link="identity")
> res4
>
> Compare the log likelihoods:
>
> sum(sapply(res1, logLik)) # add up the three log likelihoods
> logLik(res2)
> logLik(res3)
> logLik(res4)
>
> The results match up nicely, as they should.[1] This is in fact a nice confirmation that the underlying code - which is rather different for these different approaches - works as intended.
>
> [1] You might actually see minor discrepancies here and there. They can arise due to differences in how these models are fitted and the optimization routines used.
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
> > Behalf Of James Pustejovsky
> > Sent: Thursday, 01 September, 2022 2:06
> > To: Arthur Albuquerque
> > Cc: R meta
> > Subject: Re: [R-meta] Separate tau for each subgroup in mixed-effect models
> >
> > Hi Arthur,
> >
> > Yes, these sorts of models are now supported in metafor::rma.uni(). For
> > details, see
> > https://wviechtb.github.io/metafor/reference/rma.uni.html#location-scale-models
> > For a sub-group analysis with a categorical moderator called `mod`, the
> > syntax would look something like
> > rma.uni(yi = yi, sei = sei, mods = ~ mod, scale = ~ mod, data = dat, method
> > = "REML")
> >
> > Best,
> > James
> >
> > On Wed, Aug 31, 2022 at 6:43 PM Arthur Albuquerque <arthurcsirio using gmail.com>
> > wrote:
> >
> > > Hi all,
> > >
> > > I plan to fit a mixed-effects meta-regression model with metafor::rma().
> > > The moderator would be categorical (3 subgroups). If I’m not mistaken,
> > > rma() estimates a common tau^2 across subgroups.
> > >
> > > Is it possible to estimate a separate tau for each subgroup?
> > >
> > > I believe it is possible in the {meta} package through the tau.common
> > > argument (https://cran.r-project.org/web/packages/meta/meta.pdf).
> > >
> > > Thanks,
> > >
> > > Arthur M. Albuquerque
> > >
> > > Medical student
> > > Universidade Federal do Rio de Janeiro, Brazil

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