Improving Classification Accuracy by Combining Longitudinal Biomarker Measurements Subject to Detection Limits

ABSTRACT: Diagnostic or prognostic performance of a biomarker is commonly assessed by the area under the receiver operating characteristic (ROC) curve. Longitudinal information of a biomarker may lead to better performance than a single time point measurement. However, incorporating repeated measurements in the ROC analysis is not straightforward, and the evaluation may be even complicated by the limitation of technical accuracy that causes biomarker measurements being left or right censored at detection limits. Ignorance of correlated nature of longitudinal data and censoring issue may yield spurious estimation of the area under the ROC curve (AUC), and could rule out potentially informative biomarkers from further investigation. In this article, we introduce a linear combination of longitudinal measurements under the goal of optimizing AUC, while accounting for censored observations. Investigators are able to not only evaluate the potential classification power of a marker, but also determine relative importance of each time point in the clinical decision-making process. Our method is assessed in the simulation study and illustrated using a real dataset collected from hospitalized patients with community acquired pneumonia.