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# st: Confidence interval of difference between two proportions and -csi-

 From Garry Anderson To statalist@hsphsun2.harvard.edu Subject st: Confidence interval of difference between two proportions and -csi- Date Thu, 18 Mar 2004 16:37:54 +1100

Hi,

I am enquiring if a more appropriate method could be used please to calculate the 95% CI of the difference between two proportions in the -csi- command?

At the moment it is possible for the upper bound of the confidence interval of the difference between two proportions to be greater than 1.0. I realize that the approximation that is used is not appropriate for small sample sizes, however I think that reporting of results that are impossible should be avoided.

For example
-csi 5 1 0 4,e-

|   Exposed   Unexposed  |     Total
-----------------+------------------------+----------
Cases |         5           1  |         6
Noncases |         0           4  |         4
-----------------+------------------------+----------
Total |         5           5  |        10
|                        |
Risk |         1          .2  |        .6
|                        |
|      Point estimate    |  [95% Conf. Interval]
|------------------------+----------------------
Risk difference |               .8       |   .449391    1.150609
Risk ratio |                5       |   .866228    28.86076
Attr. frac. ex. |               .8       | -.1544305    .9653509
Attr. frac. pop |         .6666667       |
+-----------------------------------------------
1-sided Fisher's exact P = 0.0238
2-sided Fisher's exact P = 0.0476

The value of 1.15 is not desirable.

One potential solution to this is to use a method that is described in
Newcombe RG (1998) Interval estimation for the difference between independent proportions: comparison of eleven methods. Statistics in Medicine 17: 873-890

The -ci- command gives an exact 95% CI for a proportion, therefore I think that it is desirable that the difference between two proportions have sensible 95% confidence intervals.

Kind regards, Garry

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