[R-meta] Metafor: meta regression using rma function for proportion with categorical and continuous variable using PFT transformation

Dear Daidai,

Using the FT transformation for a meta-analysis is actually quite
problematic:

Schwarzer, G., Chemaitelly, H., Abu-Raddad, L. J., & R?cker, G. (2019).
Seriously misleading results using inverse of Freeman-Tukey double arcsine
transformation in meta-analysis of single proportions. Research Synthesis
Methods, 10(3), 476?483. https://doi.org/10.1002/jrsm.1348

R?ver, C., & Friede, T. (2022). Double arcsine transform not appropriate
for meta?analysis. Research Synthesis Methods, 13(5), 645?648.
https://doi.org/10.1002/jrsm.1591

So I would generally advise against its use. Good alternatives are the
standard arcsine or logit transformations.

The appropriate back-transformations are transf.iarcsin() and
transf.ilogit() (the latter is really just plogis()). But you cannot
back-transform the coefficients with these transformations, since these are
non-linear transformations (so the influence of one moderator depends on
the values of the other moderators). You can however back-transform
predicted values based on the model. Consider this example:

library(metafor)

dat <- dat.debruin2009
dat <- escalc(measure="PLO", xi=xi, ni=ni, data=dat)

res <- rma(yi, vi, mods = ~ scq + ethnicity, data=dat)
res

# compute predicted values for scq=11 and scq=12 for ethnicity=caucasian
out <- predict(res, newmods=cbind(c(11,12),0), transf=transf.ilogit)
out
out$pred[2] - out$pred[1]

# compute predicted values for scq=11 and scq=12 for ethnicity=other
out <- predict(res, newmods=cbind(c(11,12),1), transf=transf.ilogit)
out
out$pred[2] - out$pred[1]

Notice that the difference between predicted values that differ by one
unit on scq depends on ethnicity.

For logit-transformed proportions, you can however exponentiate the
coefficients, which then correspond to odds ratios:

round(exp(coef(summary(res)))[c(1,5,6)], digits=2)

So, a one-unit increase in scq corresponds to a 1.05 times increase in the
odds (or the odds are 5% higher when scq is one unit higher) and this holds
true whether ethnicity=caucasian or ethnicity=other.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org>

On Behalf

Of Danyang Dai via R-sig-meta-analysis
Sent: Sunday, September 29, 2024 14:14
To: Michael Dewey <lists at dewey.myzen.co.uk>
Cc: Danyang Dai <danyan.dai01 at gmail.com>; R Special Interest Group for

Meta-

Analysis <r-sig-meta-analysis at r-project.org>
Subject: Re: [R-meta] Metafor: meta regression using rma function for

proportion

with categorical and continuous variable using PFT transformation

Hi Michael and the community

Thanks for your suggestion. I tried log transformation and I could go

with

log transformation as well. I chose Freeman-Tukey transformation as the
prevalences we have ranged from 2% up to 80%. If I were to use log
transformation, how should I backgransform the coefficients for
interpretation? Thank you for your help!

Kind regards
Daidai

On Sun, Sep 29, 2024 at 9:10?PM Michael Dewey <lists at dewey.myzen.co.uk>
wrote:

Dear Daidai

Are you committed to using the Freeman-Tukey transformation? It is
easier to back-transform using log or log-odds.

Michael

On 29/09/2024 05:05, Danyang Dai via R-sig-meta-analysis wrote:

Dear community members

I am preparing meta regression using escalc and rma function from the
Metafor package. I would like to control for study mean age

(continuous

variable), percentage of CKD patients (continuous variable between 0

and

1) and the region where the study was conducted (categorical

variable).

The effect size is a proportion (xi/ni). For the first step, I used

the

PFT to transform the data using: icu_ies <- escalc(data =
data_icu_meta_join_2, xi = events, ni = icu_all, measure = "PFT").

To conduct the meta regression, I then run: icu_region_ckd_age <-

rma(yi

= yi, vi = vi, data = icu_ies, mods = ~region

+ckd_pre+age_all_mean_1 ).

See the output:
Screenshot 2024-09-29 at 13.49.30.png
I am having trouble*interpreting the estimated coeffections* from the
output above. I could tell that the omnibus test suggests that we

cannot

reject the null hypothesis which indicates that the joint parameters
were not significant. If we ignore the significance of the

parameters,

how should we interpret the estimates? For example, if we take

region =

North America, controlling for the CKD percentage and mean age of the
study population, North America has shown a higher prevalence

(0.2135)

compared to the baseline region. As we have done the PFT

transformation

upfront, I am not sure if that is the correct interpretation. I tried
use prediction function to calculate the backtranformed values:
predict(icu_region_ckd_age, transf=,
targs=list(ni=icu_ies$icu_all),transf=transf.pft), but this would

return

the individual backtranformed value for each study. I would like to
calculate the backtranformed coeffections for the purpose of
interpretation. Thank you all for your suggestions and help!

Kind regards
Daidai
Github: https://github.com/DanyangDai <https://github.com/DanyangDai

University email: danyang.dai at uq.edu.au <mailto:

danyang.dai at uq.edu.au>