J Neuropsychiatry Clin Neurosci 1991; 3:436-439
Copyright © 1991 by American Neuropsychiatric Association
ROC curves and the binormal assumption
E Somoza and D Mossman
Psychiatry Service, Department of Veterans Affairs Medical Center, Cincinnati, OH 45220.
Previous articles in this series have described how receiver operating
characteristic (ROC) graphs provide comprehensive graphic representations
of the diagnostic performance of non-binary tests and have explained how
one constructs "trapezoidal" ROC graphs in which discrete cutoff points are
plotted and connected with line segments. In this article, we describe a
set of mathematical assumptions that permit the generation of a continuous,
smooth ROC curve for a given diagnostic test. These assumptions permit us
to characterize a test's performance using a small number of parameters and
also to explore properties of diagnostic tests. In this article, we
describe a set of mathematical assumptions that can be used to link
receiver operating characteristic (ROC) curves to the underlying
distribution of values of the diagnostic variable being measured. We will
illustrate these assumptions using a diagnostic test that distinguishes
alcohol abusers from normal consumers of alcohol and abstainers.
