I have a systematic review to compare incidence of an illness (Y) with or without an intervention (so groups A and B). These groups are relatively homogeneous, so aside from unmeasured confounders I think it is a reasonable (enough) assumption to compare groups A and B to each other. In a meta-analysis, I would do a random effects model based on trials of A vs B on outcome Y to pool the individual RR with appropriate weights.
The issue is that the intervention I'm interested in does not have RCTs or direct comparison studies; I have a bunch of studies with incidence of Y for group A, and a bunch of studies with incidence of Y for group B.
Is it reasonable to report a relative risk for A vs B by doing a simple pooling of the data? E.g. (sum(events in A)/sum(patients in A)) / (sum(events in B)/sum(patients in B)) with the appropriate confidence intervals? (i.e. "there were 200 events (2%) in group A, compared to 50 events (1%) in group B, RR 2.0 95% CI aa-bb).
Or am I limited to presenting an independent pooled estimate for each group individually? (i.e. "there were 200 events (2%) in group A, compared to 50 events (1%) in group B)."