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From |
"Newson, Roger B" <r.newson@imperial.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

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 downloaded from SSC using the -ssc- command. 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 1B Manresa Road 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: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/pop 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 Thanks Dr.Newson! I had a couple of follow up questions: 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. Will really appreciate your reply. Thanks VJ ------------------------------------------------------------------------ --------

**References**:**st: RE: RE: ROC curves for ordinal outcomes***From:*vj5@buffalo.edu

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