[R-meta] Rare dependent variable with correlation among effect sizes

[Viechtbauer, Wolfgang (NP)]

When using a logistic model for the analysis, the data structure is changed into a long / arm-based format. One then adds fixed (or random) effects for studies, a fixed effect for group, and a random effect for group (to account for heterogeneity in the treatment effects). This circumvents the issue of a shared control group. This is in essence the same as what happens in a network meta-analysis using an arm-based instead of a contrast-based model (in the latter case, we need to deal with the dependency in three- or more-arm studies, but not in the arm-based model).

>-----Original Message-----
>From: Arthur Albuquerque [mailto:arthurcsirio using gmail.com]
>Sent: Monday, 06 March, 2023 22:22
>To: R Special Interest Group for Meta-Analysis; Viechtbauer, Wolfgang (NP)
>Subject: RE: [R-meta] Rare dependent variable with correlation among effect sizes
>
>My effect size of interest is the odds ratio.
>
>A random effect logistic regression with random intercept by study won’t account
>for the shared control group within each study.
>
>What other alternative do I have over the sandwich estimator?
>
>On Mar 6, 2023, 6:19 PM -0300, Viechtbauer, Wolfgang (NP)
><wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
>
>I don't see the need to use a sandwich estimator, and with 4 studies, this is
>unlikely to be all that useful.
>
>-----Original Message-----
>From: Arthur Albuquerque [mailto:arthurcsirio using gmail.com]
>Sent: Monday, 06 March, 2023 22:01
>To: R Special Interest Group for Meta-Analysis; Viechtbauer, Wolfgang (NP)
>Subject: RE: [R-meta] Rare dependent variable with correlation among effect sizes
>
>Hi Wolfang, thanks for the quick reply.
>
>About 2), would you fit the model in lme4 then use a sandwich estimator? As you
>said, a regular random-effect model in lme4 would be analog to rma.glmm().
>
>On Mar 6, 2023, 5:45 PM -0300, Viechtbauer, Wolfgang (NP)
><wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
>
>Hi Arthur,
>
>Just a small correction: vcov() should be vcalc().
>
>But to your actual question: rma.glmm() doesn't handle that. Some options:
>
>1) use rma.mv() with a measure like "AS" and use vcalc() to construct the V
>matrix.
>
>2) go straight to lme4::glmer(). Except for the non-central hypergeometric model,
>rma.glmm() is in essence just a wrapper for lme4::glmer() (or GLMMadaptive /
>glmmTMB as alternatives).
>
>Best,
>Wolfgang
>
>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Arthur Albuquerque via R-sig-meta-analysis
>Sent: Monday, 06 March, 2023 21:17
>To: R meta
>Cc: Arthur Albuquerque
>Subject: [R-meta] Rare dependent variable with correlation among effect sizes
>
>Hi all,
>
>Tl;dr: I want to meta-analyze studies with a rare dependent variable with
>correlation among effect sizes.
>
>I have four randomized controlled trials. Within each RCT, there is one “control”
>group and multiple (>3) “experimental” groups. Thus, there is a shared control
>group which induces correlation among the effect sizes within each RCT.
>
>I am aware that constructing a variance-covariance matrix with vcov() then
>fitting the model with rma.mv() is an appropriate solution (per topic 5 in
>“Details” in ?vcov). Such approach requires one to first estimate effect sizes
>with escalc().
>
>However, I am dealing with RCTs with a rare dependent variable. In these cases,
>using an exact likelihood (in this case, Binomial) is preferable. I believe
>rma.mv() does not support such likelihood.
>
>How can I fit such model with rma.glmm() considering correlation among effect
>sizes? Ideally, I’d like to fit a random effect model.
>
>Best,
>
>Arthur

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