st: re: CI Question

[Roger Newson <roger.newson@kcl.ac.uk>]

At 10:16 25/07/03 -0400, Laura Novelli wrote:
> Is there a way to calculate an upper 95% CI bound if the relative risk
> (from a 2x2 table) is equal to zero?
Not for the relative risk, but you can for the odds ratio. Unfortunately, 
you don't seem to be able to do that in Stata's -cci- command, either. If 
you type

. cci 0 1 1 0,exact

then the results look as follows:

                                                        Proportion
                 |   Exposed   Unexposed  |     Total     Exposed
-----------------+------------------------+----------------------
           Cases |         0           1  |         1      0.0000
        Controls |         1           0  |         1      1.0000
-----------------+------------------------+----------------------
           Total |         1           1  |         2      0.5000
                 |                        |
                 |      Point estimate    |  [95% Conf. Interval]
                 |------------------------+----------------------
      Odds ratio |                0       |         0           .  (Cornfield)
 Prev. frac. ex. |                1       |         .           1  (Cornfield)
 Prev. frac. pop |                .       |
                 +-----------------------------------------------
                                1-sided Fisher's exact P = 0.5000
                                2-sided Fisher's exact P = 1.0000

 Note: exact confidence levels not possible with zero count cells

The unofficial Stata command -exactcci- produces similarly disappointing 
results. So it seems that Stata can't do this. (Somebody correct me if I'm 
wrong.)

This is a great pity, if it is the case. However,  I know for a fact that 
you can get CIs around a zero odds ratio using EpiInfo. If you type into 
EpiInfo the table I typed into -cci-, you get an odds ratio of 0.00, with 
the so-called "exact" confidence limits 0.00 to 39.00. (These confidence 
limits are not really exact, but they are guaranteed to be, if anything 
conservative. The reference for the formula is Mehta et al., 1985.) So it 
looks as if the way to go is to use EpiInfo for the time being, and hope, 
in the long run, that Stata will catch up with EpiInfo. EpiInfo can be 
downloaded for free from
http://www.cdc.gov/epiinfo/Epi6/ei6.htm
For what it's worth, EpiInfo can handle zero odds ratios, but not infinite 
odds ratios. I once wrote a SAS macro which handles both zero and infinite 
odds ratios, and I should be able to dig it out of my floppy disk archives 
if anybody wants a copy. However, if anybody at StataCorp is listening, 
then it looks as if CIs for zero and infinite odds ratios should be on a 
wish list, and possibly should be programmed at the C executable level 
rather than at the ado-file level, and certainly could be a good use for 
Stata 8's multiple missing values.

I hope this helps.

Best wishes

Roger

References

Mehta CR, Patel NR, Gray R. Computing an exact confidence interval for the 
common odds ratio in several 2x2 contingency tables. Journal of the 
American Statistical Association 1985; 80:: 969-973.



--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
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United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
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Email: roger.newson@kcl.ac.uk
Website: http://www.kcl-phs.org.uk/rogernewson

Opinions expressed are those of the author, not the institution.

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