--On 27 September 2006 13:15 -0700 Bill Warburton <bill.warburton@ubc.ca>
wrote:
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
The 95% CI includes 1 because the 1-sided P-value is greater than 0.025. The
second tail is empty so the 1-sided and 2-sided Fisher exact P-values that
Stata reports are the same. The second tail is empty because there is no 2x2
table with the same marginal totals but a greater proportion of controls than
cases exposed that has probability the same or less than the observed table
under the null hypothesis. Some authors (sorry i can't remember who offhand)
prefer to report twice the 1-sided P-value from exact tests rather the
2-sided exact P as given by Stata. Personally i have a lot of sympathy with
this approach, and it would resolve your apparent inconsistency here as 2P =
0.0542.
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.
Sorry i can't follow this last bit of your message.
Hope that's some help,
Roger.
--
Roger Harbord roger.harbord@bristol.ac.uk
MRC Health Services Research Collaboration & Dept. of Social Medicine
University of Bristol http://www.epi.bris.ac.uk/staff/rharbord.htm
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