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Fitting Roc Curves Using Non-linear Binomial Regression

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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.
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Keywords: meta-analysis; non-linear regression; over-dispersion; receiver operating characteristic; vigilance data.

Document Type: Research Article

Affiliations: Australian Graduate School of Management, University of New South Wales, Sydney, NSW 2052, Australia

Publication date: June 1, 2000

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