The Annals of Statistics

Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling

Joseph S. Koopmeiners and Ziding Feng

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 39, Number 6 (2011), 3234-3261.

Dates
First available in Project Euclid: 5 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1330958678

Digital Object Identifier
doi:10.1214/11-AOS937

Mathematical Reviews number (MathSciNet)
MR3012407

Zentralblatt MATH identifier
1246.62145

Subjects
Primary: 62L12: Sequential estimation
Secondary: 62G05: Estimation

Keywords
Group sequential methods empirical process theory diagnostic testing

Citation

Koopmeiners, Joseph S.; Feng, Ziding. Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling. Ann. Statist. 39 (2011), no. 6, 3234--3261. doi:10.1214/11-AOS937. https://projecteuclid.org/euclid.aos/1330958678


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