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

TL;DR

This paper develops the asymptotic theory for sequential empirical ROC, PPV, and NPV curves in case-control sampling, aiding the design of group sequential diagnostic studies.

Contribution

It derives the asymptotic properties of these curves using sequential empirical process theory, providing a theoretical foundation for sequential biomarker study design.

Findings

Sequential empirical ROC, PPV, NPV converge to sum of independent Kiefer processes.

Results enable asymptotic analysis of summaries of these curves.

Theoretical framework supports flexible design of diagnostic studies.

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.