Re: st: Meta analysis of diagnostic test?

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

At 13:32 30/11/02 +0100, Jannik Helweg-Larsen wrote:
> I'm trying to get some sort of conclusion from more than 15 very
> heterogenous PCR diagnostic studies.
>
> Considered to do some sort of meta analysis- but I've been unable (by
> findit) to locate any specific Stata programs for such analysis.
>
> Any suggestions or references?. Would summary ROC be useful and has anybody
> written ado for these?
Typing -findit meta- reveals a large number of Stata programs for 
meta-analysis in general, including Jonathan Sterne's -metacum- for 
cumulative meta-analysis, which takes, as input, variables containing the 
estimates and standard errors of the parameter of interest for each study, 
and does a meta-analysis. The parameter of interest might be a log odds 
ratio, but might equally well be a ROC area, or even a difference between 2 
ROC areas. Jannik's problem therefore seems to me to be how to calculate 
the ROC areas (or differences) and their standard errors for input to 
-metacum- or another meta-analysis program. (Correct me if I'm wrong.)

The official Stata commands -roctab-, -rocfit-, -rocplot-, -roccomp- and 
-rocgold-  carry out ROC analyses, computing estimates and their standard 
errors, which are output to the log and to the returned results -r(area)- 
and -r(se)-. These commands are documented in -[R] roc-. An alternative way 
of calculating ROC areas and their standard errors is my package -somersd-, 
downloadable from SSC (type -ssc desc somersd- to find out about the latest 
version). If X is a quantitative test result and Y is a binary variable 
indicating a disease (1 for diseased, 0 for non-diseased), then Somers' D 
is related to the ROC area by the formula

D(X|Y) = 2*A(X,Y) - 1

and therefore

A(X,Y)= (D(X|Y)+1)/2
SE(A(X,Y)) = SE(D(X|Y))/2

where D(X|Y) is the Somers' D of X with respect to Y, A(X,Y) is the ROC 
area for X as a predictor of Y, and SE(.) denotes standard error. A 
possible advantage of using -somersd- rather than the official Stata -roc- 
programs is that -somersd- can be used with -lincom- to calculate standard 
errors and 95% CIs for differences between Somers' D values and therefore 
for differences between ROC areas, whereas -roccomp- only calculates a 
chi-squared statistic for the hypothesis that that difference is zero. For 
instance, if W and X are 2 quantitative tests for the disease indicated by 
Y, we might type

somersd Y W X
lincom (W-X)/2

and calculate CIs for the 2 Somers' D parameters and for the difference 
between the 2 ROC areas.

The relationship between Somers' D and the ROC area is discussed in a paper 
of mine which appeared in The Stata Journal earlier this year (Newson, 
2002), and demonstrates the calculation of CIs for Somers' D and for the 
difference between 2 ROC curves..

I hope this helps

Roger

References

Newson R. 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
Fax: 020 7848 6620 International +44 20 7848 6620
  or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk

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

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