Meta-analysis on proportions

[linda_ec]

Dear all,

I have a question regarding meta-analysis on pooled proportions (e.g. proportion persistent with a certain drug after 12 months), which I would be really grateful if you can help me with. I have been recearching the available literature for some time now and I am still unsure if I am doing this correctly or not.

I have pooled the proportions and their standarerrors (sometimes calculated based on n and p) from several articles.

In stata
I first transform my proportions in stata using the Freeman-Tukey arcsin transform to stabilize variances
gen p12transf = asin(sqrt(n12/(n+1))) + asin(sqrt((n12+1)/(n+1)))
gen se12transf = sqrt(1/(n+1))

I thereafter conduct a meta-analysis using inverse variance weighting in a random effect model (lots of heterogeniety was seen in the results) by:
metan p12transf se12transf, randomi

Finally I transform the received estimates back to proportions by:
gen p12all = ((sin(1.6/ 2))^2)*100
gen p12low= ((sin(1.4 / 2))^2)*100
gen p12high= ((sin(1.7 / 2))^2)*100

Would you say this is the correct way to conduct a meta-analysis of proportions using a random effect model or is there a better way?

Thank you so much for your help and happy easter!

Kind regards,

Linda

[Timothy Mak]

This seems reasonable, especially if you have a reference you can refer to. However, perhaps a more straightforward and intuitive approach is to apply a random-effects logistic regression using -xtglm-.

[Joe Canner]

Meta analysis of single proportions is a thorny subject apparently. Here are some previous Statalist discussions that cover both of the the previously mentioned methods, and more:

1. arcsin transformation: http://www.stata.com/statalist/archi.../msg00368.html
2. xtlogit: http://www.stata.com/statalist/archi.../msg00408.html
3. metan with vwls: http://www.stata.com/statalist/archi.../msg00240.html

Also see the documentation for metandi (from SSC) which does something similar with sensitivity and specificity.

One of the big things to be aware of, whatever method is used, is how proportions near 0 and 1 are handled. Some methods require transformation, others add a constant to the numerator and denominator, others don't have a problem with this. In any case, if you have such proportions in your data you should know how the method you choose is dealing with them.