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

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Thu Oct 11 20:29:09 CEST 2018

```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
```