[R-meta] Freeman-Tukey double arcsine transformation and harmonic mean

Fri, Jul 7, 2017 4:18 PM

Thank you for your answer, Dr. Viechtbauer.
I think you were right. MetaXL seems to apply the inverse transformation of
the arcsine transformation to double arcsine transformed proportions in
order to pool an average proportion. I tested this assumption with
the example dataset "SchizophreniaPrev" built in MetaXL and yielded very
similar results.
Here's my code:

dat=read.csv("your working directory\\schizophreniaprev.c
sv",header=T,sep=",")
transf.ies=escalc(measure="PFT",xi=cases,ni=total,data=dat, add=0) #computing
individual transformed proportions using the double arcsine transformation
transf.pes=rma(yi,vi,data=transf.ies,method="DL",weighted=TRUE) #pooling
transformed proportions under the random effect size model
pes=predict(transf.pes,transf=transf.iarcsin) #back-transforming
with inverse of the arcsine transformation
print(pes,digits=4)

pred         ci.lb       ci.ub
0.5856    0.5089   0.6603

pred         ci.lb       ci.ub
0.5875 0.5098   0.6632

Thank you again for your time.

Cheers,
Naike

2017-07-07 9:41 GMT-04:00 Viechtbauer Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl>:

Hi Naike,

The first linked got mangled up. It is: http://www.metafor-project.
org/doku.php/analyses:miller1978

The exact back/inverse transformation of the Freeman-Tukey (double
arcsine) transformation requires that we specify the sample size for the
transformed value. So:

library(metafor)
dat <- escalc(measure="PFT", xi=4, ni=10)

dat

      yi     vi
1 0.6936 0.0238

transf.ipft(dat$yi, ni=10)

yields a proportion of 0.4 as expected.

Now if you synthesize a whole bunch of transformed values and you want to
back-transform that value to a proportion, you still need to specify some
value for the sample size if you want to use the exact back-transformation.
Miller (1978), who derived the back-transformation, suggested to use the
harmonic mean of the sample sizes. That is what transf.ipft.hm() does.
Using the harmonic mean of the sample sizes is a rather heuristic method
that may or may not work so well. I would be interested in any published
papers that show this to be a problem.

I don't know what MetaXL does for the back-transformation, but maybe it
just pretends that the values are arcsine-square-root transformed
proportions and then uses the back-transformation for that -- which does
not require one to specify the sample size. The difference is typically
negligible:

transf.iarcsin(dat$yi)

yields 0.4086998. But then, one might as well just do the meta-analysis
directly with the AS transformed proportions:

dat <- escalc(measure="PAS", xi=4, ni=10)
dat

dat

      yi     vi
1 0.6847 0.0250

transf.iarcsin(dat$yi)

gives back 0.4 exactly.

Or one could go directly to a logistic mixed-effects model for the
analysis. You can do that with rma.glmm().

Best,
Wolfgang

--
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-
project.org] On Behalf Of Naike Wang
Sent: Friday, July 07, 2017 15:25
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] Freeman-Tukey double arcsine transformation and harmonic
mean

Hi all,
I have two questions.
1) In this article
<https://mail.jjay.cuny.edu/owa/redir.aspx?C=

jnnID1xyBS33HM9BECtjC_Z23ilF5

4mDEf0zdCS88qMPhZkvMsXUCA..&URL=http%3a%2f%2fwww.metafor-
project.org%2fdoku.php%2fanalyses%3amiller1978>,
Dr. Wolfgang Viechtbauer used the harmonic mean of the sample sizes to
back-transform the estimated average transformed proportion (the pooled
proportion). If I don't want to use the harmonic mean,  is it possible to
use the *transf.ipft*, instead of the *transf**=**transf.ipft.hm
<http://transf.ipft.hm>*, to get the pooled proportion? If so, how do I

do

that?

2) One of the reasons I asked the question is due to this article:
Meta-analysis
of prevalence
<https://drive.google.com/open?id=0B41wTxciaMqtNXVSNEFGazdPWFU>. The
authors of this article developed an Exel-based meta-analysis add-in
(MetaXL). MetaXL uses a different method to perform the double arcsine
transformation. The differences are two-fold.
First, MetaXL uses a different definition of  the Freeman-Tukey
transformation. The PFT values (yi) are twice as large as the values
computed by metafor and the variances (vi) are four times as large. The
different definitions are also explained here
<http://www.metafor-project.org/doku.php/faq#how_is_the_freeman-
tukey_trans>
.
Second, it does not use the harmonic mean to perform the
back-transformation. According to the authors, it is better not to use the
harmonic mean because their simulation studies suggest that the harmonic
mean is not stable.
Basically, I'm asking how to get metafor to get the same results as
obtained in MetaXL? Do you agree with the MetaXL authors that it is better
not to use the harmonic mean?

I hope my questions make sense. Feel free to ask me anything if you don't
understand.

P.S. Dowload MetaXL here: http://www.epigear.com/index_files/metaxl.html
P.S.S. After you install MetaXL, open example "SchizophreniaPrev" to get a
sense of how it performs meta-analysis of proportions.

Cheers,
Naike

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[R-meta] Freeman-Tukey double arcsine transformation and harmonic mean

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