On the time-varying predictive performance of longitudinal biomarkers: Measure and estimation

In many biomedical studies, participants are monitored at periodic visits until the occurrence of the failure event. Biomarkers are often measured repeatedly during these visits, and such measurements can facilitate updated disease prediction. In this work, we propose a two-dimensional incident dynamic area under curve (AUC), to capture the variability due to both the biomarker assessment time and the prediction time to comprehensively quantify the predictive performance of a longitudinal biomarker. We propose a pseudo partial-likelihood to achieve consistent estimation of the AUC under two realistic scenarios of visit schedules. Variance estimation methods are designed to facilitate inferential procedures. We examine the finite-sample performance of our method through extensive simulations. The methods are applied to a study of chronic myeloid leukemia to evaluate the predictive performance of longitudinally collected gene expression levels.