# Re: st: CC exact 95% confidence interval brackets 1 while the P valueis < .05

 From Roger Harbord To statalist@hsphsun2.harvard.edu Subject Re: st: CC exact 95% confidence interval brackets 1 while the P valueis < .05 Date Thu, 28 Sep 2006 09:51:48 +0100

--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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