ASYMPTOTIC PROPERTIES OF THE SEQUENTIAL EMPIRICAL ROC, PPV AND NPV CURVES UNDER CASE-CONTROL SAMPLING

• 成果类型: Article
• 署名作者: Koopmeiners, Joseph S.; Feng, Ziding
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Fred Hutchinson Cancer Center
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS937
• 发表日期: 2011
• 页码: 3234-3261
• 关键词: ACCURACY

摘要

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.