Our 2016 (Shuster and Walker) paper proposes an ideal solution to this problem. It uses relative risk, widely preferred by epidemiologists to odds ratios.
Our solution has random effects (logistic regression requires common odds ratios ours works in a distribution-free manner). It accommodates zero and low event arms very easily, and requires no more than proc corr, Probt, and tinv in SAS (or equivalents in other software).
Here is the reference:
Shuster J. J., and Walker M. A., (2016) Low-event-rate Meta-Analyses of clinical trials: implementing good practices,. Stat Med, 35,2467-78.
Simple and easy to explain, minimizes distributional assumptions. The only assumption is that is asymptotic in the number of studies, but for fewer studies (5-20) this is the most vetted meta-analysis method (100,000 replications of each of nearly 40,000 scenarios). See Shuster et. al (2012) referenced below for details.
Shuster J. J,, Guo J. D., and Skyler J. S., (2012) Meta-Analysis of safety for low event-rate binomial trials, Res Synth Methods, 3, 30-50.
Best wishes to all. Sorry for the slow response.
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Jon Shuster
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