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

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Wed Jun 23 10:57:48 CEST 2021

Dear Simeon,

I generally would avoid meta-analyzing proportions directly. Instead of the double arcsine transformation (which indeed leads to issues with the back-transformation), you could use the logit transformation or the arcsine square root transformation, both of which are easy to back-transform.

This aside, for a more direct comparison of the two modeling approaches, I would suggest to use the same transformation. Also, can you show how 'effect_id' is coded? In other words, is it a unique value for every row of the dataset? It might also help if you would post the actual output from the model.


>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of simeon.zuercher using upd.unibe.ch
>Sent: Wednesday, 23 June, 2021 10:32
>To: lists using dewey.myzen.co.uk; r-sig-meta-analysis using r-project.org
>Subject: Re: [R-meta] Question regarding three-level metaanalysis of proportions
>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 =
>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,

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