# Meta-analysis of proportions

I am conducting a meta-analysis on 20 studies. The outcome of interest in each study is represented by a proportion/percentage. The sample size n is known and is different for each study. I have three aims:

• To realize a pooled analysis in order to calculate a summary effect (a weighted proportion)
• To calculate heterogeneity across the studies
• To explore this heterogeneity by considering potential effect modifiers in a meta-regression analysis

Can someone help me in identifying the more correct method to realize all this in STATA or R? Thank you!

Yes it is perfectly possible to do this either in Stata or in R. Since I use R I offer a few hints to get you going.

A list of software for meta-analysis in R is available in the CRAN Task View (Disclaimer, I maintain it). There are several packages there which will do what you are proposing. I personally use metafor but there are other options.

You will almost certainly need to choose a transformation for your proportions before doing the meta-analysis and then back-transforming for interpretation. This is so your estimates are more approximately normally distributed. I would suggest the logit is worth considering. If you have any zeroes you will need to deal with them by adding a constant.

Adding moderator variables presents no new problems but with 20 primary studies you cannot add too many at once.

After fitting there is a range of graphical techniques you can use to display your model. Forest plots are commonly used for this but there are others available.

And finally it is worth, if you do use metafor to check the author's web-site which has many examples and hints. Particularly relevant may be these two here and here

This is a meta-analysis of proportions. Just as you mentioned, the m-a of proportions is a little different than other types of meta-analysis- it includes studies that do not use controls. You can use R to do a meta-analysis of proportions. I recently made a tutorial on that on YouTube and shared my code on Github. This hands-on tutorial provides a step-by-step guide showing you how to conduct a full meta-analysis of proportions, including all the goals you mentioned in your post. My code allows you to conduct your analysis with either the logit transformation or double-arcsine transformation. You can also do it without transformation using my code. The R script shown in the video is readily adaptable for you to use for your own analyses.

Check out the tutorial here: https://youtu.be/2wbXTFvaRnM.