[R-meta] How to compare two independent meta-analyses?

[Viechtbauer, Wolfgang (SP)]

Dear Patrizio,

If there is no overlap of the studies included in the two meta-analyses, then it's quite easy. Say mu-hat = .25 (95% CI: .19 to .31) and mu-hat = .46 (95% CI: .22 to .70) for the two MAs. Then:

yi  <- c(.25, .46)
sei <- c((.31 - .19) / (2*qnorm(.975)), (.70 - .22) / (2*qnorm(.975)))

library(metafor)
rma(yi, sei=sei, mods=c(0,1), method="FE")

which yields:

         estimate      se    zval    pval    ci.lb   ci.ub 
intrcpt    0.2500  0.0306  8.1665  <.0001   0.1900  0.3100  *** 
mods       0.2100  0.1262  1.6638  0.0962  -0.0374  0.4574    .

So 0.21 is the difference between the two estimates, which is not significantly different from zero (p = .096).

See also: https://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates

If there is overlap of the studies, then things get more tricky since the estimates from the two meta-analyses cannot be assumed to be independent then. I vaguely recall reading an article that describes a method that takes this into consideration (without requiring additional information), but can't find it right now.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Patrizio E Tressoldi
>Sent: Tuesday, 22 June, 2021 11:37
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] How to compare two independent meta-analyses?
>
>Hi,
>
>is it possible to compare the results of two m-a having only the effect
>size with their 95% confidence intervals and the number of studies?
>
>If not, which is the recommended procedure?
>
>Thanks
>
>Patrizio
>
>--
>Patrizio E. Tressoldi Ph.D.
>Science of Consciousness Research Group
>Studium Patavinum
>Università di Padova
>Padova - ITALY
>http://www.patriziotressoldi.it
>http://www.socrg.org
>https://orcid.org/0000-0002-6404-0058
>https://opensciences.org/about/manifesto-for-a-post-materialist-science