Koopmeiners Joseph S, Feng Ziding
University of Minnesota.
Ann Stat. 2011;39(6):3234-3261. doi: 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.
受试者工作特征（ROC）曲线、阳性预测值（PPV）曲线和阴性预测值（NPV）曲线是衡量连续诊断生物标志物性能的三种指标。ROC、PPV和NPV曲线通常通过经验估计，以避免对生物标志物的分布形式做出假设。最近，人们一直在推动将序贯方法纳入诊断生物标志物研究的设计中。深入了解序贯经验ROC、PPV和NPV曲线的渐近性质，将为设计序贯诊断生物标志物研究提供更大的灵活性。在本文中，我们使用序贯经验过程理论推导了病例对照抽样下序贯经验ROC、PPV和NPV曲线的渐近理论。我们证明了序贯经验ROC、PPV和NPV曲线收敛于独立 Kiefer 过程的和，并展示了如何利用这些结果推导序贯经验ROC、PPV和NPV曲线汇总的渐近结果。
