95% CI for binary, single arm analysis

What is actually the math behind the 95% CIs for a proportion when entering binary outcome of single arm studies.
E.g. 3 events of 5 treated yields 0.2 to 0.9. Already these "round" numbers make me suspicous. Furthermore comparing these values with a couple of 95%CI for proportions (Wald, Wald with correction modified Wald, Wilson, Wilson w/ correction, Clopper Pearson, Blaker) none come even close to the values calculated by MetaAnalyst for small N. For large N the values approximate the Wilson method.

I would be happy for any insight.

Hi Beutner; thanks again for the feedback. Here's a reply from one of our many resident statistical geniuses:

Quote :

The meta-analysis of proportions necessitates transformation of the proportions using a function that stabilizes their variance. Here we used the logit transformation. An alternative (not implemented yet is the angular transformation of Tuckey - 2* arcsin(sqrt(p)) -- it is in the TO DO list)

Therefore the CI's per study are only approximate. If you want to report study-level CI's in a table, you are better off using an exact method. (if I am not mistaken all the above use the central limit theorem for asymptotic normality).

Alternatively, the Bayesian version that uses the exact binomial likelihood for a proportion (does not use normality assumptions) will give more accurate results, based on simulations, and are OK even for small sample sizes.

Hope this helps. You can always consult our methods doc: https://research.tufts-nemc.org/metaanalyst/metaanalyst_methods.html to find out what algorithm(s) we're using.