[R-meta] Classic fail-safe N

Hi all,
I was conducting a meta-analysis of single proportions(i.e. without a
control group) using the metafor package. When I performed a classic
fail-safe N, I noticed that the result (the number of missing studies that
would bring p-value to the alpha, to be exact)was different than that I got
in Comprehensive Meta-Analysis Version 2.0. I wonder why R and CMA got
different results.

*Below is the R code:*
dat=read.table("Your working directory\\Example.csv",header=T,sep=",")
transf.ies=escalc(xi=cases,ni=total,measure="PLO",data=dat) #I transform
the data using the logit transformation first. In CMA, it also uses the
logit transformation.
transf.pes=rma(yi,vi,data=transf.ies,method="DL",weighted=TRUE) #Pooling
individual effect sizes in the logit scale.
ranktest(transf.pes) #Performing the fail-safe N.

*Below are the results from R:*
Fail-safe N Calculation Using the Rosenthal Approach
Observed Significance Level: <.0001
Target Significance Level:   0.05
Fail-safe N: 8446

*Below are the Classic fail-safe N results from CMA:*
Z-value for observed studies 19.91594
P-value for observed studies 0.00000
Alpha 0.05000
Tails 2.00000
Z for alpha 1.95996
Number of observed studies 58.00000
Number of missing studies that would bring p-value to > alpha 5931.00000

Notice that I got 8446 in R and 5931 in CMA.

Can anyone shed some light on this discrepancy? Thank you!

You can find my data set here: https://drive.google.com/open?id=
0B41wTxciaMqtTEJWZE9sX20wOXM

Best,
Naike

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