As clarified already by @mdewey, it is inappropriate to talk about odds ratios when you have only one group. In such instance, you can instead focus on proportions (the ratio of patients with events/all patients) or odds (the ratio of patients with events/patients without events). Another possibility is to focus on rates (the ratio of patients with events/all patients over a given period of time).
As reported elsewhere, you can compute the standard error of the proportion as square root of the product of P * (1 - P) / N, where P is the ratio of patients with events/all patients, and N is the sample size (ie all patients). I am not aware of any formula to compute the standard error of an odds, but it is reasonable you could find one.
Once you have for each study the point estimate and the standard error, it is easy to combine them with a statistical package (eg metan in Stata, meta or metafor in R). Note indeed that the R meta package offers the metaprop command which will directly suit you, as clarified by this illustrative code:
studyid <- c(1:10)
events <- sample(5:20, 10, replace = T) # randomly generated event counts
patients <- sample (50:200, 10, replace = T) # randomly generated sample sizes
mydata <- data.frame(cbind(studyid, events, patients))
metaprop1 <- metaprop(mydata$events, mydata$patients)
# various graphs
trimfill1 <- trimfill(metaprop1)