# Meta Analysis for one proportion

I have data summarizing proportion of events from 5 different papers. The proportions are in %'s. For example, in paper number 1, there was a report of 2000 people and a proportion of 10%. I want a general proportion and CI's. I tried using a generalized linear mixed model with PROC GLIMMIX in SAS, but for some reason, the probability estimate I got was equal to the average of all proportions, and not the weighted average as I would expect. I used a binomial link function, and declared: model proportion/n = / solution cl; and random intercept / subject=paper; I took the model's estimate, and calculated the probability using (1)/(1+e^-estimate). As I mentioned, I got the exact mean of the percentages, and not the weighted mean like my logic say I should have got. I can easily calculate the weighted mean by hand, but I need a CI. Can you help me do it, preferably with SAS, if not, then with R ?

• You must look for some indication of spread in each of your papers, be it Confidence Intervals, Standard Deviations or Mean Square Errors. What do you find? – Dirk Horsten Aug 2 '15 at 21:43
• I do not have this information, all I have is the proportion of each paper. I used an older method of Tukey and Freeman (arcsin transformation), which gave two results: fixed effect and random effect. The fixed effect was equal to the weighted mean while the random effect was not. I don't understand why. – user3275222 Aug 3 '15 at 9:48