Skip to content

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

4 messages · Jakub Ruszkowski, Röver, Christian, CHAPPELL Francesca +1 more

Jakub Ruszkowski
# 
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
Röver, Christian
# 
Dear Jakub,

I think Schwarzer et al. (2019; https://doi.org/10.1002/jrsm.1348) have
a valid point, and that the double arcsine transform is not really
suitable for meta-analysis purposes. The approach by Barendregt et al.
(2013; https://doi.org/10.1136/jech-2013-203104) seems to me more like
a kind of workaround, and I am not sure whether it will actually work
generally, or would only "fix" the issue (or at least won't fail
immediately) in some cases.

I guess a quick and simple solution might be to go for the ("simple")
arcsine transformation instead, or otherwise check out one of the more
appropriate alternative approaches that were pointed out by Schwarzer
et al. (2019).

Cheers,

Christian
On Wed, 2022-02-23 at 12:06 +0100, Jakub Ruszkowski wrote:
CHAPPELL Francesca
# 
This paper argues for modelling the within-study variance directly as binomial (https://pubmed.ncbi.nlm.nih.gov/18083461/)  and provides a SAS program to do so. I think R can do it too with glmer, though I don't have a handy program. But see https://journals.lww.com/epidem/Fulltext/2020/09000/Meta_analysis_of_Proportions_Using_Generalized.16.aspx , specifically the appendices for R code. I haven't come across a multinomial version that doesn't use WinBUGS.

Francesca

-----Original Message-----
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> On Behalf Of R?ver, Christian
Sent: 24 February 2022 08:43
To: jakub.ruszkowski at gumed.edu.pl; r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Meta-analysis of prevalence data: back-transformation and polytomous data

This email was sent to you by someone outside the University.
You should only click on links or attachments if you are certain that the email is genuine and the content is safe.

Dear Jakub,

I think Schwarzer et al. (2019; https://doi.org/10.1002/jrsm.1348) have a valid point, and that the double arcsine transform is not really suitable for meta-analysis purposes. The approach by Barendregt et al.
(2013; https://doi.org/10.1136/jech-2013-203104) seems to me more like a kind of workaround, and I am not sure whether it will actually work generally, or would only "fix" the issue (or at least won't fail
immediately) in some cases.

I guess a quick and simple solution might be to go for the ("simple") arcsine transformation instead, or otherwise check out one of the more appropriate alternative approaches that were pointed out by Schwarzer et al. (2019).

Cheers,

Christian
On Wed, 2022-02-23 at 12:06 +0100, Jakub Ruszkowski wrote:
_______________________________________________
R-sig-meta-analysis mailing list
R-sig-meta-analysis at r-project.org
https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th? ann an Oilthigh Dh?n ?ideann, cl?raichte an Alba, ?ireamh cl?raidh SC005336.
4 days later
Wolfgang Viechtbauer
# 
Definitely would avoid the double arcsine transformation. It's just fraught with problems in this context. The regular arcsine transformation comes close anyway and doesn't have the same issues.

As for multinomial data:

You could go with a multilevel multinominal model. See this post on SO for some relevant packages: https://stackoverflow.com/questions/21082396/multinomial-logistic-multilevel-models-in-r

If the various events are not all rare, an alternative approach would be to use a 'normal' multivariate model with (logit-transformed) proportions corresponding to the various events. Say a study reports the number of cases for 3 different events. Let p1, p2, and p3 be the proportions for the three events and n the total number of cases. Under multinomial sampling, the (estimated) var-cov matrix of the proportions is then:

      [p1*(1-p1)                    ]
1/n * [-p1*p2    p2*(1-p2)          ]
      [-p1*p3    -p2*p3    p3*(1-p3)]

So this is the 3x3 part of the V matrix for this study. Actually, I would suggest to logit-transform the proportions, in which case the var-cov matrix is:

      [1/(p1*(1-p1))                                      ]
1/n * [-1/((1-p1)*(1-p2)) 1/(p2*(1-p2))                   ]
      [-1/((1-p1)*(1-p3)) -1/((1-p2)*(1-p3)) 1/(p3*(1-p3))]

Same for other studies. Let y be the vector with all the logit-transformed proportions and V the block-diagonal V matrix with all the var-cov matrices. Then we are back to rma.mv(y, V, ...), adding whatever moderators and random effects deemed necessary.

Best,
Wolfgang