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# Re: st: binominal, excact?

 From Ronan Conroy To statalist@hsphsun2.harvard.edu Subject Re: st: binominal, excact? Date Tue, 19 Feb 2008 14:10:39 +0000

On 19 Feb 2008, at 11:19, Maren Weischer wrote:

When a study has tested 500 cases and 500 controls, and has not found
any carrier of a mutation.
How do I based on these numbers calculated a maximum frequency of the
mutation in the population studied? With 95% Confidence interval? Is it
possible in STATA?
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.

P Before printing, think about the environment
=================================
Ronan Conroy
rconroy@rcsi.ie
Royal College of Surgeons in Ireland
Epidemiology Department,
120 St Stephen's Green, Dublin 2, Ireland
+353 (0)1 402 2431
+353 (0)87 799 97 95
http://www.flickr.com/photos/ronanconroy/sets/72157601895416740/

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