Using metafunnel as post estimation command on transformed data

[Tom Yates]

I am undertaking a meta-analysis of prevalence. To avoid studies of similar size getting very different weights, I have used a double arcsine transformation. I then want to use the corrected standard errors to construct a funnel plot. However, I would rather that the effect sizes are presented on the 0-1 scale, which is more intuitive. Is there a neat way to do this, ideally using a post estimation command? I am using an IVhet model.

Here is my current code, and the output, which produces a funnel plot which - I presume - uses transformed proportions.

metan numerator denominator, pr model(ivhet) transform(ftukey, iv) study(study) forestplot(astext(50) textsize(100) boxscale(55) spacing(1.2) leftjustify range(0.0 1.0) dp(2)) extraline(yes) hetinfo(isq h)
metafunnel _ES _LCI _UCI, xtitle(Proportion) ytitle(Standard Error) eform forcenull

Thanks,
Tom

[Tiago Pereira]

Hi, Tom.

The transformation you have used is typically not recommended when there are large differences in sample sizes across studies. If this is your case, you can use the logit transformation or use generalized mixed linear modelling to combine the proportions.

Regarding the funnel plot, the approach you have used is also not recommended. You can check this previous discussion:

https://www.statalist.org/forums/for...alence-studies

[Tom Yates]

Thanks Tiago,

That is very helpful.

Could you flesh out the argument against a double arcsine transformation where there are large differences in sample size? Or point me to a paper making the argument?

With best wishes,
Tom

[Tiago Pereira]

Check these papers:

https://pmc.ncbi.nlm.nih.gov/articles/PMC6767151/
https://onlinelibrary.wiley.com/doi/...1002/jrsm.1591

[Leonardo Guizzetti]

This I came to post the same article as Tiago. There’s no reason to use that particular transformation.

as for the other question about back transformation, this is always appropriate to aid interpretation as long as the transformation is monotonic.