I am working on a project where we saw an event occur in 5 of 39 patients. We don't expect this event to occur at all (though we know they occur very rarely, we don't expect to see any in this instance), and my advisor wants me to model to a Poisson distribution (with a p-value) to show that this is more than we would expect by random chance.
He did the math, which I don't have anymore, but I'm not convinced that the values he used were appropriate for Poisson. I didn't think you could do this if you expect 0 events.
I'm hoping someone can explain to me: 1) If possible, how to do this math appropriately 2) If there is another statistical test to show that this event is occurring more than we'd expect by random chance.