RE: st: binominal, excact?

["Nick Cox" <n.j.cox@durham.ac.uk>]

I think the main message here is right, but there is some small
confusion at the end. My understanding is that what is usually cited as
the exact method is that proposed by Clopper and (E.S.) Pearson. The
Agresti-Coull method is a much more recent method which usually comes
close to the Jeffreys and Wilson methods.  

Ronan Conroy

There was a lovely paper years ago in JAMA

Hanley JA, Lippman-Hand A. If nothing goes wrong, is everything all  
right? Interpreting zero numerators. JAMA. 1983 Apr 1;249(13):1743-5.

He points out that if you observe zero occurrences in N trials, then  
the Poisson confidence interval is approximately zero to one events  
per N/3 trials.

In your case

. cii 1000 0, pois

                                                          -- Poisson   
Exact --
     Variable |   Exposure        Mean    Std. Err.       [95% Conf.  
Interval]
------------- 
+---------------------------------------------------------------
              |       1000           0           0                
0    .0036889*

(*) one-sided, 97.5% confidence interval

Close enough; -cii- gives us an upper limit of 3.7 events per thousand.

I wouldn't do a binomial exact confidence interval as the so-called  
'exact' confidence interval isn't exact in the sense that you think  
it is (Stata's options for binomial confidence intervals include two  
methods that come closer to nominal coverage for smaller N and P than  
the Agresti-Coull 'exact' interval - the Wilson and Jeffreys methods.)

But, more important, you are dealing with a rare event (you haven't  
been able to find one yet!) so the name Poisson springs to mind.


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