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SV: st: binominal, excact?


From   "Maren Weischer" <MARWEI01@heh.regionh.dk>
To   <statalist@hsphsun2.harvard.edu>
Subject   SV: st: binominal, excact?
Date   Tue, 19 Feb 2008 15:14:46 +0100

Thank you very much for your time. 
Fantastic. 
Regards
Maren Weischer

-----Oprindelig meddelelse-----
Fra: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] På vegne af Ronan Conroy
Sendt: 19. februar 2008 15:11
Til: statalist@hsphsun2.harvard.edu
Emne: Re: st: binominal, excact?

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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