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Theory & Methods: Fitting Roc Curves Using Non‐linear Binomial Regression
Author(s) -
Lloyd Chris J.
Publication year - 2000
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00118
Subject(s) - mathematics , receiver operating characteristic , statistics , linear regression , curve fitting
The performance of a diagnostic test is summarized by its receiver operating characteristic (ROC) curve. Empirical data on a test's performance often come in the form of observed true positive and false positive relative frequencies, under varying conditions. This paper describes a family of models for analysing such data. The underlying ROC curves are specified by a shift parameter, a shape parameter and a link function. Both the position along the ROC curve and the shift parameter are modelled linearly. The shape parameter enters the model non‐linearly but in a very simple manner. One simple application is to the meta‐analysis of independent studies of the same diagnostic test, illustrated on some data of Moses, Shapiro & Littenberg (1993). A second application to so‐called vigilance data is given, where ROC curves differ across subjects, and modelling of the position along the ROC curve is of primary interest.