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

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

2012-03-14

arxiv.org/abs/1203.3014v1

Annals of Statistics 2011, Vol. 39, No. 6, 3234-3261

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS937 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS937

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.

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