[R-meta] Question regarding three-level metaanalysis of proportions

[Michael Dewey]

Dear Simeon

In your example you have 100 for ni for all studies. Does that mean the 
xi are in fact percentages or is it just a toy example? If the former 
then I think that is not correct.

For your substantive problem you could always model the raw proportions 
adding 1/2 or some other constant to the zeroes. This would give you 
directly interpretable moderator coefficients at the cost of possibly 
being a less defensible model.

Michael

On 28/05/2021 10:45, simeon.zuercher using upd.unibe.ch wrote:
> Dear all,
> I�m currently working on a three-level meta-analysis of proportions where we look at neurological complications after some infectious diseases. Effect sizes are dependent since several studies report different effect sizes. It�s a large dataset with over 150 effect sizes that are nested within 60 studies. Some prevalence rates are quite extreme with some reaching the limit (e.g. 100% complications). Based on literature I decided to use a double arcsine transformation.
> 
> Example Data:
> study_id <-  c(1,1,1,1,1,2,2,3,3,3,4)
> effect_id <- c(1,2,3,4,5,6,7,8,9,10,11)
> xi <- c(2,3,8,10,15,60,80,45,100,100,98)
> ni <- rep(100, 11)
> mod_age <- c(22.5,22.5,22.5,22.5,22.5, 30.5, 30.5,45,45,45,60)
> published <- c(0,0,0,0,0,1,1,1,1,1,0)
> 
> code:
> ies <- escalc(xi=xi, ni= ni, data = data, measure = "PFT", add = 0)
> result <- rma.mv(yi, vi, random = ~ 1 | study_id/effect_id, tdist = TRUE,
>                     data = ies,  method = "REML")
> result_pred <- predict(result, transf=transf.ipft.hm, targ=list(ni=data$ni))
> print(result_pred)
> 
> While a get plausible results for the pooled effect (which is hopefully correct and quite different from effects by using log or even no transformation), I have some problems with the moderator analysis. After transformation I would like to back-transform to proportions in order to allow a simple interpretation (e.g. percentage point differences between subgroups).
> 
> code:
> result <- rma.mv(yi,
>                   vi,
>                   random = ~ 1 | study_id/effect_id,
>                   tdist = TRUE,
>                   data = ies,
>                   method = "REML", mods = ~ published)
> 
> result_pred <- predict(result, transf=transf.ipft.hm, targ=list(ni=data$ni))
> print(result_pred)
> 
> Apparently, back-transformation of the coefficients in moderator analysis is not straight forward and not recommended. I wonder how I can solve this issue. What would be a good way of doing a three-level meta-analysis with proportions (that include extreme values like zero and one)?
> 
> I am very grateful for some help with this issue
> Many thanks
> Simeon
> 
> 
> 
> 
> 
> 
> 
> 
> UNIVERSIT�RE PSYCHIATRISCHE DIENSTE BERN (UPD) AG
> ZENTRUM PSYCHIATRISCHE REHABILITATION
> 
> 
> Simeon Z�rcher, Dr. sc. nat., RN
> Wissenschaftlicher Mitarbeiter
> Forschung & Entwicklung
> Murtenstrasse 46
> 3008 Bern
> 
> Mailto: simeon.zuercher using upd.unibe.ch
> Tel. +41 (0)79 889 73 54
> 
> www.upd.ch
> 
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-- 
Michael
http://www.dewey.myzen.co.uk/home.html