# [R-meta] robust variance estimator in meta-analyses of rare events (proportions)

Pier-Alexandre Tardif pier-@lex@ndre@t@rdif@1 @ending from ul@v@l@c@
Thu Oct 11 21:34:22 CEST 2018

```Oh, thanks for these precisions, it works well!

I had manage to obtain the same results by internally calling GLMM with metaprop for x event per 1000 observations:

res <- metaprop(cases, total, Study, data=dat, sm ="PLO", method="GLMM", method.ci="CP", method.tau="ML", comb.random=TRUE, backtransf=TRUE, warn=TRUE, pscale=1000)
summary(res)

Cheers,

Pier-Alex

-----Message d'origine-----
De : R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] De la part de Viechtbauer, Wolfgang (SP)
Envoyé : 11 octobre 2018 14:29
À : r-sig-meta-analysis using r-project.org
Objet : Re: [R-meta] robust variance estimator in meta-analyses of rare events (proportions)

As Guido said, just multiply the summary estimates and corresponding CI bounds by whatever factor you want. Using the same example, you would do this in metafor with:

res <- rma(measure="PLO", xi=3:4, ni=c(5678, 1234), method="DL")
res
predict(res, transf=function(x) transf.ilogit(x)*10000, digits=1)

But for rare events, I would go with:

res <- rma(measure="PAS", xi=3:4, ni=c(5678, 1234), method="DL")
res
predict(res, transf=function(x) transf.iarcsin(x)*10000, digits=1)

Using the mixed-effects logistic approach:

res <- rma.glmm(measure="PLO", xi=3:4, ni=c(5678, 1234))
res
predict(res, transf=function(x) transf.ilogit(x)*10000, digits=1)

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Guido Schwarzer
Sent: Thursday, 11 October, 2018 18:20
To: r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] robust variance estimator in meta-analyses of rare events (proportions)

Am 11.10.18 um 16:20 schrieb Pier-Alexandre Tardif:

> Hello again,
>
> Thanks for the follow up. I have compared the two methods (inverse variance with double arcsine vs mixed-effects logistic) and I still have one question.
>
> 1) Summary proportions obtained with either model are really low and relatively similar:
> 1st model (inverse variance, double arcsine): 0.01306 [95% CI: 0.00561-0.02271]
> 2nd model (mixed-effects logistic model): 0.0167 [95% CI: 0.0099-0.0281])
>
> In terms of 'presentation', would it make sense to rescale these proportions and how could we then interpret them?

Yes, you can rescale them. Actually, R function metaprop() from meta has
an argument 'pscale' for this:

library(meta)
print(summary(metaprop(3:4, c(5678, 1234), pscale = 10000)), digits = 1)
Number of studies combined: k = 2

events      95%-CI  z p-value
Fixed effect model     14.9 [7.1; 31.2] --      --
Random effects model   13.4 [2.3; 78.9] --      --

Quantifying heterogeneity:
tau^2 = 1.3581; H = 2.38; I^2 = 82.3% [25.5%; 95.8%]

Test of heterogeneity:
Q d.f. p-value
5.65    1  0.0175

Details on meta-analytical method:
- Inverse variance method
- DerSimonian-Laird estimator for tau^2
- Logit transformation
- Clopper-Pearson confidence interval for individual studies
- Events per 10000 observations

As you can see in the last line, results are expressed as events per
10000 observations (for pscale = 10000).

Best wishes,
Guido
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