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

[Garry Anderson <g.anderson@unimelb.edu.au>]

Hi,

Thank you Roger for your suggestion of using -exactcci-
However, this does not calculate a risk difference and the 95% CI.

I suppose I am suggesting to the folks at Stata that a revised formula be 
used in -csi- to calculate the 95% CI of the risk difference when there is 
a small number of observations, and one or both have a 100% risk. Currently 
it is possible for the upper bound to go beyond the theoretical maximum of 
100% difference.

I would appreciate opinions on this by others on the list.

Newcombe RG (1998) Interval estimation for the difference between 
independent proportions: comparison of eleven methods. Statistics in 
Medicine 17: 873-890

Kind regards, Garry


At 05:17 PM 18/03/2004 +0000, you wrote:

> 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
> 42 Weston Street
> London SE1 3QD
> United Kingdom
>
> Tel: 020 7848 6648 International +44 20 7848 6648
> Fax: 020 7848 6620 International +44 20 7848 6620
>   or 020 7848 6605 International +44 20 7848 6605
> 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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