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

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

At 16:37 18/03/04 +1100, Garry Anderson wrote:
> 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.
One possibility is to use the -somersd- package, downloadable (complete 
with a .pdf manual) from SSC, using its -transform()- option. The 
difference between 2 proportions is a special case of Somers' D, and the 
-somersd- package offers a choice of transformations appropriate for 
Somers' D, notably the hyperbolic arctangent (or z) transformation or the 
arcsine transformation. If -diseased- and -exposed- are 2 binary (0,1) 
variables indicating disease and exposure, respectively, then Garry might type

somersd exposed diseased, tr(z)

or, alternatively,

somersd exposed diseased, tr(asin)

and get a confidence interval for the difference between the proportion of 
exposed individuals with the disease and the proportion of unexposed 
individuals with the disease, using a normalizing and variance-stabilizing 
transformation.

However, it should be stressed that, with Garry's example, there is a zero 
cell (for exposed noncases), so one of the proportions is either zero or 
one, so a normalizing or variance-stabilizing transformation might be 
inappropriate because the sample size is so low. In such circumstances, it 
might be better to use the -exactcci- package to define a conservative 
confidence interval for the odds ratio, which may have an infinite upper 
limit or a zero lower limit. If Garry uses -findit- to find and install the 
-exactcci- fackage and types

exactcci 5 1 0 4, exact

then the so-called "exact" confidence interval is generated. (Note, 
however, that this confidence interval is conservative, not exact. It is 
called "exact" because it uses the exact hypergeometric distribution to 
calculate conservative confidence limits.)

I hope this helps.

Roger


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