Using the meta-prop function of R, I estimated two meta-analyzed proportions (A and B). Each of these proportions comes with an estimate and 95% confidence interval.
I would like to test whether these proportions are equal (CHI-square), however this method requires that I specify the number of events and total number. If I would use the estimate and total number for both groups I could come up with these arguments; however the detail of the confidence interval etc. is lost. What can I do?
There are two ways of doing this using standard meta-analysis software.
Take the estimates from each original meta-analysis with their standard errors and then do a meta-regression on just those two with a moderator variable having two levels to distinguish the studies. It seems a bit strange to do a meta-analysis on two studies but this works.
If you have all the primary studies at hand you can just do a meta-analysis combining them all with a moderator variable to distinguish between the two sources from which the primary studies came.
These are not identical since the first one (assuming you used random effects) allows for heterogeneity to be different in the two subsets whereas the second fixes it to be the same. You can allow for different hetrogeneity using the second method and see http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates for a worked example using the metafor package in R.
Typically, you would not use a standard chi-squared test when running a meta-analysis. Depending on your field, the more generally-accepted procedure would be a Cochran's Q test or a z test (assuming the samples that contributed to the proportions are independent)
