Dear Garance,
Please see my responses below.
Best,
Wolfgang
-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On
Behalf Of Garance Delagneau
Sent: Friday, 18 June, 2021 2:53
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] (no subject)
Hi everyone,
I'm a bit stuck and would really appreciate any help on my issue.
I'm doing a meta analysis (using R). There are several instances where authors
reported multiple effect sizes (e.g., reported effect sizes for different
timepoints) that I need to combine. I've tried to aggregate my multiple effect
sizes using both the?metafor package and the formula in Borenstein's manual
(chapter 24 - using the mean effect size weighted according to the sample size and
the formula attached to this email to calculate the variance).
The equation you showed assumes that an *unweighted* average is taken of the two effect sizes. So if you computed a weighted mean, then this equation is not correct.
While variances
using these two techniques are quite similar, the computed effect sizes are very
different.
My questions are:
? Why/how does yi (combined effect size) change?quite a lot based on the value of
rho when using the?metafor package?
I assume you are talking about the aggregate() function and you are using something like:
aggregate(dat, cluster=dat$study, struct="CS", rho=<>)
The function by default computes weighted averages of the effects within studies (based on the variance-covariance matrix of the effects, which is constructed based on the sampling variances and the assumed value of rho). When rho changes, the var-cov matrix changes and hence the weighted averages change. You can also use weighted=FALSE in which case unweighted averages are computed and then rho does not affect these averages (although it still affects the variances of the computed averages).
? Are?the yi's that we get when using the metafor package correct?
? The combined effect sizes using these methods are quite different from using the
mean effect size. Is it correct to use the Metafor package?
This is the example I've been working on
Authors??????? N?? Time? corr
Polanska? 2017 337 2???? -0.09
Polanska? 2017 219 1???? -0.02
Using R's?metafor package, I obtained a combined effect size of??-0.0718. Using
Borenstein's method, I obtain an effect size of -0.06255.
Please provide a fully reproducible example. I had to guess what exactly you did with metafor, but it might have been this:
library(metafor)
dat <- data.frame(study=1, ni=c(337,219), ri=c(-.09,-.02))
dat <- escalc(measure="COR", ri=ri, ni=ni, data=dat)
aggregate(dat, cluster=dat$study, struct="CS", rho=0.555)
At least this yields yi=-0.0718.
aggregate(dat, cluster=dat$study, struct="CS", rho=0.555, weighted=FALSE)
gives an unweighted average of -0.0550 (following Borenstein). Not sure what you did but
weighted.mean(dat$ri, dat$ni)
gives -0.06242806 which is close to -0.06255 but not identical (and again this is not what Borenstein suggests).
Note. I often have fewer than 10 articles to combine in my meta-analyses (it
varies between 3 and 10). I expect heterogeneity to be moderate to high in most of
my analyses.
Thank you very much,
--
GARANCE DELAGNEAU
PhD Student (Clinical Neuropsychology)
M: 0452 323 762
E:?garance.delagneau at monash.edu