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

Wed Jun 23 10:32:14 CEST 2021

Dear all,

Only recently, I had a question regarding three-level meta-analysis of proportions where we look at neurological complications after some infectious diseases which was kindly answered (Thank you again). We effect sizes are dependent since some studies report several effect sizes. It’s a large dataset with over 150 effect sizes (effect_id) that are nested within 60 studies (doi).

Based on the advice we did not transform proportions with double arcsine for the meta-regression since a back-transformation after model estimation is not straight forward. However, we have now the following issue: I have performed a meta-regression on timepoint as moderator (timepoint = factor variable including three timepoints 1,2 and 3).

The meta-analysis (with double arcsine transformation) gave the following proportion for each timepoint separately: Time 1 = 0.22, Time 2 =  0.17, Time 3 =  0.19

However, if I run a meta-regression on proportions to see whether the timepoints differ I get very strange results.

result_0 <- rma.mv(yi, vi, random = list(~ 1 | effect_id, ~ 1 | doi),

                  mods = ~ timepoint, tdist = TRUE, data = data, method = "REML")

Intercept (timepoint 1): 0.24 (seems plausible)

Time 2: -0.032 (seems also plausible),

Time 3: -0.15 (is not plausible)

The estimate for Time 3 vs. Time 1 is very strange. Even if I remove the outliers, I got such an extreme result. Is there something wrong in this code? Maybe the definition of the random effects?

Many thanks for your further help!

Kind regars,

Simeon

________________________________
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> im Auftrag von simeon.zuercher using upd.unibe.ch <simeon.zuercher using upd.unibe.ch>
Gesendet: Freitag, 28. Mai 2021 19:21:58
An: lists using dewey.myzen.co.uk; r-sig-meta-analysis using r-project.org
Betreff: Re: [R-meta] Question regarding three-level metaanalysis of proportions

Dear Michael,

thank you very much for the quick reply and help. In this case I will apply this approach.

To answer your question: this was just toy data.

Kind regards

Simeon

________________________________
Von: Michael Dewey <lists using dewey.myzen.co.uk>
Gesendet: Freitag, 28. Mai 2021 14:28
An: Zürcher, Simeon (UPD); r-sig-meta-analysis using r-project.org
Betreff: Re: [R-meta] Question regarding three-level metaanalysis of proportions

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
>
>
>        [[alternative HTML version deleted]]
>
>
>
>
> _______________________________________________
> R-sig-meta-analysis mailing list
> R-sig-meta-analysis using r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>

--
Michael
http://www.dewey.myzen.co.uk/home.html

        [[alternative HTML version deleted]]

_______________________________________________
R-sig-meta-analysis mailing list
R-sig-meta-analysis using r-project.org
https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis

	[[alternative HTML version deleted]]