Dynamic Thresholds and a Summary ROC Curve: Assessing the Prognostic Accuracy of Longitudinal Markers

Abstract: 

Cancer patients, chronic kidney disease (CDK) patients, and subjects infected with HIV are commonly monitored over time using biomarkers that represent key health status indicators. Furthermore, biomarkers are frequently used to guide initiation of new treatments or to inform changes in intervention strategies. Since key medical decisions can be made on the basis of a longitudinal biomarker it is important to evaluate the potential accuracy associated with longitudinal monitoring. We introduce a summary receiver operating characteristic (ROC) curve that displays the overall sensitivity associated with a time-dependent threshold that controls specificity. The proposed statistical methods are similar to concepts considered in disease screening, yet our methods are novel in choosing a potentially time-dependent threshold to dene a positive test, and our methods allow time-specific control of the false-positive rate. Finally, the proposed summary ROC curve is a natural averaging of time-dependent incident/dynamic ROC curves proposed by Heagerty and Zheng (2005) and therefore provides a single summary of net error rates that can be achieved in the longitudinal setting.