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

simeo@@zuercher m@iii@g oii upd@u@ibe@ch simeo@@zuercher m@iii@g oii upd@u@ibe@ch
Wed Jun 23 12:51:30 CEST 2021

```Dear Wolfgang,

Tank you very much for the fast answer.

I have a studyID which is the same Doi for a single study and unique numbers for effectIDs. The data is structured as follows (example data):

StudyID             EffectID

DoiNR_study1    1

DoiNR_study1    2

DoiNR_study3    3

DoiNR_study4    4

DoiNR_study4    5

DoiNR_study4    6

Estimating the proportions for each timepoint using the arcsine transformation (instead double arcsine) yields the same results. Time 1 = 0.22, Time 2 =  0.17, Time 3 =0.19

I used now used the arcsine transformation to calculate the model

ies <- escalc(xi=postitive_cases, ni= sample_size, data = ies, measure = "PAS")

estimates <- rma.mv(yi, vi, mods = ~ timepoint, random = list(~ 1 | effect_id, ~ 1 |doi), tdist = TRUE,

data = ies, method = "REML")

Output:

Multivariate Meta-Analysis Model (k = 99; method: REML)

Variance Components:

estim    sqrt  nlvls  fixed     factor

sigma^2.1  0.0069  0.0833     99     no  effect_id

sigma^2.2  0.0216  0.1469     47     no        doi

Test for Residual Heterogeneity:

QE(df = 96) = 1310.2448, p-val < .0001

Test of Moderators (coefficients 2:3):

F(df1 = 2, df2 = 96) = 3.8752, p-val = 0.0241

Model Results:

estimate      se     tval    pval    ci.lb    ci.ub

intrcpt(timepoint 1)                          0.5027  0.0272  18.4506  <.0001   0.4486   0.5568  ***

timepoint 2                                      -0.0443  0.0459  -0.9632  0.3379  -0.1355   0.0469

timepoint 3)                                     -0.1458  0.0538  -2.7092  0.0080  -0.2526  -0.0390   **

backtransformation of estimates yield

sin(0.5027)^2 = 0.23,

sin(-0.0443)^2 = 0.0020,

sin(-0.1458)^2 = 0.021

I think this is much more plausible. F.i. the difference between timepoint 1 and 3 is now  -0.02 (or two percentage points).

What do you think. Does it look plausible to you?

again, many thanks,

Simeon

________________________________
Von: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Gesendet: Mittwoch, 23. Juni 2021 10:57:48
An: Z�rcher, Simeon (UPD); r-sig-meta-analysis using r-project.org
Betreff: RE: [R-meta] Question regarding three-level metaanalysis of proportions

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.

Best,
Wolfgang

>-----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 =
>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

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