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Re: st: meta-analysis for diagnostic test

From   Roger Newson <>
Subject   Re: st: meta-analysis for diagnostic test
Date   Thu, 12 Jun 2003 20:01:34 +0100

At 14:10 12/06/03 -0400, wrote:
How can I perform a meta-analysis for a diagnostic test? I'd like to calculate
the summary ROC.
I would use the -somersd- package, downloadable from SSC. If X is the disease indicator and Y is the quantitative diagnostic test variable, then Somers' D of Y with respect to X (D(Y|X)) is related to the ROC area A by the formula


The -somersd- package saves the estimates and covariance matrices of Somers' D as estimation results. Therefore, you could calculate a Somers' D and its variance for each of the individual studies, extract the estimates vextor and variance matrix for each Somers' D, concatenate the estimates vectors for the individual studies to form a vector of Somers' D estimates, create a diagonal matrix of the variances of the individual studies, use -estimates store- to store these as the current estimation results, and then use -lincom- to get a confidence interval for whatever weighted mean of the individual study Somers' D values you wanted, and convert that confidence interval to a confidence interval for the weighted mean ROC area.

A reference on Somers' D and ROC areas is my Stata Journal article on the subject (Newson, 2002). A pre-publication draft of this can be downloaded from my website at

which also contains manuals for the -somersd- package. It can be accessed either using a browser or using the -net- command in Stata.

I hope this helps.

Best wishes



Newson R. Parameters behind "nonparametric" statistics: Kendall's tau, Somers' D and median differences. The Stata Journal 2002; 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
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605

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

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