[R-meta] I2 in fixed-effect or equal-effects meta-analysis

[Mathias Weis Damkjær]

Dear Yefeng Yang,

"Fixed effects" and "equal effects" meta-analyses have different assumptions. Although the analysis and model output is identical, the interpretation or "estimand" is different, i.e., the target of inference.

Wolfgang has written a post on the difference here:
https://wviechtb.github.io/metafor/reference/misc-models.html

I found this paper helpful aswell:
https://research-information.bris.ac.uk/ws/portalfiles/portal/146974606/FixedEffectsPaperRev3.pdf

However, there as several papers on this, and you might find one that you like more.

Kind regards,
Mathias




Mathias Weis Damkj�r

MD, PhD-student

Cochrane Denmark &

Centre for Evidence-Based Medicine Odense (CEBMO)

University of Southern Denmark

T +45 21274558
E mwdamkjaer using health.sdu.dk<mailto:dlaursen using health.sdu.dk>

W http://www.cebmo.dk/<http://www.cebmo.dk/>; http://www.cochrane.dk/<http://www.cochrane.dk/>

[cid:8187f40c-b01f-4dca-bfb7-59cabd5b85d9]


________________________________
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> on behalf of Yefeng Yang via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org>
Sent: Thursday, May 22, 2025 5:57:00 AM
To: r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>
Cc: Yefeng Yang <yefeng.yang1 using unsw.edu.au>
Subject: [R-meta] I2 in fixed-effect or equal-effects meta-analysis

Dear community,

Recently, I played with the fixed-effect or equal-effects meta-analysis implemented in `metafor` package and surprinsly found that the model output provides I^2 value. To me this is a bit confusing, because the fixed-effect or equal-effects meta-analysis assumes that there is no heterogeneity (no tau^2 and so no I2). All observed differences in effect sizes are assumed to be due to sampling variance of the effect size estimates. Although one can computationally get I2 value from  fixed-effect or equal-effects meta-analysis via 100% * (Q-(k-1))/Q, but what does I2 exactly mean here?

Interestingly, the I2 provided by equal-effects meta-analysis is exactly the same as random-effects meta-analysis. The so-called fixed-effects meta-analysis (the true effect sizes are fixed across k studies rather than randomly drawn from a population) also gives I2.

The reproducible example:
library(metafor)
dat <- dat.bangertdrowns2004
# fixed-effect
res <- rma(yi, vi, data=dat, method="EE"), with the output:
Equal-Effects Model (k = 48)

I^2 (total heterogeneity / total variability):   56.12%
H^2 (total variability / sampling variability):  2.28

# random-effects
res2 <- rma(yi, vi, data=dat)

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