Re: st: confidence intervals for differences between medians

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

At 16:11 02/07/03 +0200, Gerben ter Riet wrote:
> Dear All,
> Someone advised me the approach by Gardner and Altman to calculate 95%
> CIs for differences between medians. I'd prefer to use Stat's qreg
> command. Is this allowed? How do the results from qreg compare to the
> results from the Gardner/Altman approach?
The Gardner-Altman approach is implemented in Duolao Wang's -npshift- 
command, and also in Patrick Royston's -cid- command.. (Type -findit 
npshift- or -findit cid- to find out more, including how to download them.)

A limitation of this method is that it assumes that the 2 population 
distributions differ only in location, which implies (among other things) 
equal variances. This assumption does not always hold. A way around this 
limitation is to use the -cendif- program in the -somersd- package, 
downloadable from SSC. (Type -ssc desc somersd- tofind out more about 
-somersd-.) -cendif- calculates confidence intervals for the median 
difference between values sampled from two groups. The median difference is 
not always equal to the difference between medians, but is equal to the 
difference between medians if the 2 population distributions are different 
only in location. The -cendif- program therefore is an unequal-variance 
version of -cid- or -npshift-. The methods of -cendif- and -somersd- are 
given in the manuals to the -somersd- package, and discussed in a Stata 
Juornal article (Newson, 2002). A pre-publication draft of this article can 
be downloaded by typing

net from  http://www.kcl-phs.org.uk/rogernewson/papers

and following the instructions.

The Stata -qreg- package uses a slightly different method, which is based 
on M-estimation, and estimates beta-values which minimize a weighted sum of 
magnitudes of residuals. The beta-coefficients will not always be either 
median differences or differences between medians, but will be related to 
percentiles of residuals. I haven't compared -qreg- to -cendif-, -npshift- 
and -cid- on the same data, but the 3 methods measure slightly different 
parameters, and comparing them will therefore compare different questions, 
rather than different answers to the same question. (I would expect the 3 
methods to give similar answers in the equal-variance case.)

I hope this helps.

Roger

References

Newson R. 2002. Parameters behind "nonparametric" statistics: Kendall's 
tau, Somers' D and median differences. The Stata Journal 2(1): 45-64.


--
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
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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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