The "exact" confidence limits are not really exact confidence limits for
the odds ratio, but conservative confidence limits for the odds ratio,
derived using the exact hypergeometric distribution of the top left cell
of your table, assuming the marginal totals. As they are conservative,
you expect them sometimes to bracket 1 when the Fisher exact P-value is
slightly greater than 0.05.
The so-called "exact" confidence limits for the binomial proportion and
the Poisson mean, given by -cii-, are also conservative in a similar
way.
I hope this helps.
Roger
Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Bill
Warburton
Sent: 27 September 2006 21:15
To: statalist@hsphsun2.harvard.edu
Subject: st: CC exact 95% confidence interval brackets 1 while the P
value is < .05
Can you tell me why the exact 95% confidence interval brackets 1 while
the P
value is < .05?
In a logistic regression I was suspicious of the rather narrow
confidence
intervals in the analysis of a relatively rare event so I checked using
a
2x2 table with an exact test (results below) and the exact confidence
interval does indeed bracket 1, but the p-value given is less than
.05(?).
Can you tell me how to interpret/report this?
. cc xp1 disease ,e;
Proportion
| Exposed Unexposed | Total Exposed
-----------------+------------------------+------------------------
Cases | 2 99 | 101 0.0198
Controls | 7 3315 | 3322 0.0021
-----------------+------------------------+------------------------
Total | 9 3414 | 3423 0.0026
| |
| Point estimate | [95% Conf. Interval]
|------------------------+------------------------
Odds ratio | 9.5671 | .9562236 50.98143
(exact)
Attr. frac. ex. | .8954751 | -.0457805 .980385
(exact)
Attr. frac. pop | .0177322 |
+-------------------------------------------------
1-sided Fisher's exact P = 0.0271
2-sided Fisher's exact P = 0.0271
Other information: Bitest assuming that the true proportion is .0021
gives P
= 0.019410 which is very close to the probability of observing 2 or more
cases out of 101 exposed in a Poisson distribution with mean .0021.
Bill
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