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December 2011 Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling
Joseph S. Koopmeiners, Ziding Feng
Ann. Statist. 39(6): 3234-3261 (December 2011). DOI: 10.1214/11-AOS937

Abstract

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper, we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries of the sequential empirical ROC, PPV and NPV curves.

Citation

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Joseph S. Koopmeiners. Ziding Feng. "Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling." Ann. Statist. 39 (6) 3234 - 3261, December 2011. https://doi.org/10.1214/11-AOS937

Information

Published: December 2011
First available in Project Euclid: 5 March 2012

zbMATH: 1246.62145
MathSciNet: MR3012407
Digital Object Identifier: 10.1214/11-AOS937

Subjects:
Primary: 62L12
Secondary: 62G05

Keywords: diagnostic testing , Empirical process theory , Group sequential methods

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 6 • December 2011
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