# [R-meta] Question regarding three-level metaanalysis of proportions

simeo@@zuercher m@iii@g oii upd@u@ibe@ch simeo@@zuercher m@iii@g oii upd@u@ibe@ch
Fri May 28 11:45:28 CEST 2021

```Dear all,
I�m currently working on a three-level meta-analysis of proportions where we look at neurological complications after some infectious diseases. Effect sizes are dependent since several studies report different effect sizes. It�s a large dataset with over 150 effect sizes that are nested within 60 studies. Some prevalence rates are quite extreme with some reaching the limit (e.g. 100% complications). Based on literature I decided to use a double arcsine transformation.

Example Data:
study_id <-  c(1,1,1,1,1,2,2,3,3,3,4)
effect_id <- c(1,2,3,4,5,6,7,8,9,10,11)
xi <- c(2,3,8,10,15,60,80,45,100,100,98)
ni <- rep(100, 11)
mod_age <- c(22.5,22.5,22.5,22.5,22.5, 30.5, 30.5,45,45,45,60)
published <- c(0,0,0,0,0,1,1,1,1,1,0)

code:
ies <- escalc(xi=xi, ni= ni, data = data, measure = "PFT", add = 0)
result <- rma.mv(yi, vi, random = ~ 1 | study_id/effect_id, tdist = TRUE,
data = ies,  method = "REML")
result_pred <- predict(result, transf=transf.ipft.hm, targ=list(ni=data\$ni))
print(result_pred)

While a get plausible results for the pooled effect (which is hopefully correct and quite different from effects by using log or even no transformation), I have some problems with the moderator analysis. After transformation I would like to back-transform to proportions in order to allow a simple interpretation (e.g. percentage point differences between subgroups).

code:
result <- rma.mv(yi,
vi,
random = ~ 1 | study_id/effect_id,
tdist = TRUE,
data = ies,
method = "REML", mods = ~ published)

result_pred <- predict(result, transf=transf.ipft.hm, targ=list(ni=data\$ni))
print(result_pred)

Apparently, back-transformation of the coefficients in moderator analysis is not straight forward and not recommended. I wonder how I can solve this issue. What would be a good way of doing a three-level meta-analysis with proportions (that include extreme values like zero and one)?

I am very grateful for some help with this issue
Many thanks
Simeon

UNIVERSIT�RE PSYCHIATRISCHE DIENSTE BERN (UPD) AG
ZENTRUM PSYCHIATRISCHE REHABILITATION

Simeon Z�rcher, Dr. sc. nat., RN
Wissenschaftlicher Mitarbeiter
Forschung & Entwicklung
Murtenstrasse 46
3008 Bern

Mailto: simeon.zuercher using upd.unibe.ch
Tel. +41 (0)79 889 73 54

www.upd.ch

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