Time‐dependent classification accuracy curve under marker‐dependent sampling

Abstract

Evaluating the classification accuracy of a candidate biomarker signaling the onset of disease or disease status is essential for medical decision making. A good biomarker would accurately identify the patients who are likely to progress or die at a particular time in the future or who are in urgent need for active treatments. To assess the performance of a candidate biomarker, the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are commonly used. In many cases, the standard simple random sampling (SRS) design used for biomarker validation studies is costly and inefficient. In order to improve the efficiency and reduce the cost of biomarker validation, marker-dependent sampling (MDS) may be used. In a MDS design, the selection of patients to assess true survival time is dependent on the result of a biomarker assay. In this article, we introduce a nonparametric estimator for time-dependent AUC under a MDS design. The consistency and the asymptotic normality of the proposed estimator is established. Simulation shows the unbiasedness of the proposed estimator and a significant efficiency gain of the MDS design over the SRS design.

Auxiliary variable–enriched biomarker‐stratified design

“…They should be distinguished from the common, but misleading, use of the term “enrichment design” to refer simply to a biomarker-positive targeted design. Similar designs and sampling strategies have been proposed and successfully used in observational studies to test association between disease and risk factors 31,32,33,34 and to estimate the accuracy of biomarkers in predicting disease condition 35,36,37 . These papers demonstrate that biased sampling with enrichment of relevant patient subgroups, those that contain more information on estimands, leads to more efficient studies that requires significantly fewer patients and lower study cost.…”