Diagnostic accuracy analysis for ordinal competing risk outcomes using ROC surface

Many medical conditions are marked by a sequence of events or statuses that are associated with continuous changes in some biomarkers. However, few works have evaluated the overall accuracy of a biomarker in separating various competing events. Existing methods usually focus on a single cause and compare it with the event-free controls at each time. In our study, we extend the concept of ROC surface and the associated volume under the ROC surface (VUS) from multi-category outcomes to ordinal competing risks outcomes. We propose two methods to estimate the VUS. One views VUS as a numerical metric of correct classification probabilities representing the distributions of the diagnostic marker given the subjects who have experienced different cause-specific events. The other measures the concordance between the marker and the sequential competing outcomes. Since data are often subject to lost of follow up, inverse probability of censoring weight is introduced to handle the missing disease status due to independent censoring. Asymptotic results are derived using counting process techniques and U-statistics theory. Practical performances of the proposed estimators in finite samples are evaluated through simulation studies and the procedure of the methods are illustrated in two real data examples. Public Health Significance: ROC curve has long been treated as a gold standard in evaluating the accuracy of continuous predictors in separating binary outcomes in various fields including biomedical, financial, and geographical areas. Our proposed methods extend its utilization in multi-category events outcomes to competing risks censoring. Our methods aim to assess a global accuracy of a biomarker’s predictive power to each simultaneously, especially, to which stages of disease progression that patients would land by a specific time in followup. Our work provides much-needed global assessment for the predictive power of a biomarker for disease progression