# st: RE: RE: RE: ROC curves for ordinal outcomes

 From "Newson, Roger B" To Subject st: RE: RE: RE: ROC curves for ordinal outcomes Date Fri, 13 Feb 2009 11:19:51 -0000

```The somersd command calculates Harrell's c index (which is equal to the
ROC area in binary outcomes) for non-binary outcomes, but does not draw
ROC curves for non-binary outcomes. The ROC curve is a plot of true
positive rate against false positive rate, and these concepts both
assume a binary outcome.

To extend ROC curves to non-binary outcomes, you would have to plot
multiple ROC curves. This could presumably be done in one of 2 ways:

1. We might draw a separate ROC curve for each pair of possible values
of the non-binary outcome, measuring the ability of the test to
discriminate between those 2 values of the non-binary outcome. In that
case, the Harrell c index of the test, with respect to the non-binary
outcome, would be a linear combination of the ROC areas for each pair of
values for the non-binary outcome, weighted by the products of the
probabilities of the paired values for the non-binary outcome. This
would imply k*(k-1)/2 ROC curves, where k is the number of distinct
values for the non-binary outcome.

2. We might want to draw a separate ROC curve for all values of the
binary outcome except for the highest, measuring, for each outcome
value, the ability of the test to discriminate between outcomes above
that value and outcomes at or below that value. In that case, the Harell
c index would be a different linear combination of the ROC areas, with
different weightings from the first case.

Either of these could, in principle, be done in Stata, using multiple
graphs generated by the -by()- option. A useful tool for calculating the
individual ROC curves would be the -senspec- package, which calculates
sensitivities and specificities from the original data, and which can be

I hope this helps.

Best wishes

Roger

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
genetics/reph/

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

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
vj5@buffalo.edu
Sent: 12 February 2009 23:38
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: RE: ROC curves for ordinal outcomes

1) -somersd- command doesnot have an option for graphing the ROC curve.
Is there one that I'm missing?
2) -roccomp- command would not let me use an outcome variable which is
not coded 0 & 1. Is there a way to plot
for multiple outcome categories?

Sorry if this is a dumb question. I have not tried this before.