How to calculate a (possible) chance from a zero-incidence sample? This is probably a very simple problem, but I want to make sure I have a correct understanding. I have a sample of $500$ events, in which a complication $C$ didn't occur. How do I calculate a reasonably correct chance for $C$?
Would that be just $<1/500$? My intuition is that it would be a bit higher, as there is a sampling effect.
Obviously, it is impossible to calculate the chance exactly, but does something like some kind of confidence interval exist for these types of observations?
Much obliged,
Joris
 A: Here's a possible answer.  I'm no statistician, but I remember this from many years ago when I worked for a large public accounting firm.  When doing an audit, they might want to be say $95\%$ confident that a particular procedure was followed at least $95\%$ at the time.  They would pick a certain number $n$ of transactions to sample so that if the procedure was followed exactly $95\%$ of the time, then then probability of finding no exceptions would be less than $5\%$.  That is, determine $n$ so that $.95^n<.05$
Your situation seems a bit different, as you seem to have already made $500$ experiments, but following the logic above would give that we can be $99.07\%$ confident that there is no complication at least $99.07\%$ of the time, since $$.9907^{500}\approx.009355$$ That is, with about $99\%$ confidence, the chance of $C$ is less than $.0093,$ which is considerably higher than $1/500=.002$
As I say, I'm no statistician, but I would be more comfortable with this if the number of trials, and the interpretation in the event of no complication were determined in advance.           
