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

Mon, Feb 28, 2022 9:18 AM

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

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On
Behalf Of CHAPPELL Francesca
Sent: Thursday, 24 February, 2022 12:37
To: R?ver, Christian; 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 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-----
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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

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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:

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

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

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