Desktop Survival Guide
by Graham Williams

ROC Curves

"Discrimination refers to the ability to distinguish high risk subjects from low risk subjects, and is commonly quantified by a measure of concordance, the c statistic. For binary outcomes, c is identical to the area under the receiver operating characteristic (ROC) curve (Hanley and McNeil, 1982). C varies between 0.5 and 1.0 for sensible models; the higher the better. The c statistic is calculated as the fraction of patients with the outcome among pairs of patients where one has the outcome and one not, the patient with the highest prediction being classified as the one with the outcome. Hence, when a model provides no information, c=0.5. The c statistic has been generalized for survival analysis. "

(from http://symptomresearch.nih.gov/chapter_8/sec7/cess7pg11.htm)

Also see http://www.ncbi.nlm.nih.gov/pubmed/7063747?dopt=Abstract

The c statistic is equivalent to the AUC for logistic regression. However, it extends to multinomial also, which AUC does not.


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