I am conducting a meta analysis that is comparing dichotomous outcomes for two groups. So for each study, I have the proportion of the outcome for both groups and the sample size of each group, and I am using Comprehensive Meta Analysis software to get the odds ratio for each.
One study that I would like to include if possible only provided the proportions (42% in group A and 51% in group B) and the p-value (p=.03). I believe he p-value only depends on the proportion and sample size (which is all you need to construct a 2x2 contingency table), so I would assume one could reverse engineer the sample size from the p-value. However, I have not found a formula to do so, and it is not an option in my software to enter this data (though it includes many other options like "chi-square and sample size" or "sample size and p-value"). I'm not sure if perhaps you'd need to know the test they used as well, like Z-test for proportions or fisher's exact test.
Does anyone know how to reverse-compute the sample size given this data? I know that a study that didn't even report the overall sample size is not a great paper (non-peer reviewed journal), but we want our meta-analysis to be comprehensive and include everything out there, included unpublished (and thus also not peer-reviewed) studies.