[R-meta] Meta-analysis of prevalence data: back-transformation and polytomous data

Dear Community,

I am trying to do a meta-analysis of prevalence according to the 
recommendations arising from the current literature. I have two problems that 
I cannot handle on my own.

1. I found that there are controversies about a back-transformation method 
for the Freeman-Tukey double arcsine transformation (Schwarzer et al., doi: 
10.1002/jrsm.1348). However, there is a probable resolution that incorporates 
inverse variance instead of harmonic mean (Barendregt-Doi implementation, 
clearly explained in Supplementary Materials in doi: 10.1111/jebm.12445; 
older version introducing it: 10.1136/jech-2013-203104). Unfortunately, I am 
not proficient in programming, so I am not sure how to implement this 
solution on my own. Is there an R implementation of Barendregt-Doi 
back-transformation available or is it possible to add this method to the 
metafor?

2. Are there any available examples of R code to meta-analyze 
ordinal/multinomial prevalence data (e.g., mild, moderate, severe severity)? 
I found one method implemented in MetaXL that used double arcsine 
transformation (mentioned earlier doi: 10.1136/jech-2013-203104), and one 
Bayesian method using the Dirichlet-multinomial model (doi: 
10.1080/03610918.2021.1887229). Unfortunately, the R code is not supplemented 
with the latter article.


Kind regards

Jakub Ruszkowski, M.D.
Department of Physiopathology | Department of Nephrology, Transplantology and 
Internal Medicine
Medical University of Gda?sk