Application of the time-dependent ROC curves for prognostic accuracy with multiple biomarkers

The rapid advancement in molecule technology has led to the discovery of many markers that have potential applications in disease diagnosis and prognosis. In a prospective cohort study, information on a panel of biomarkers as well as the disease status for a patient are routinely collected over time. Such information is useful to predict patients' prognosis and select patients for targeted therapy. In this article, we develop procedures for constructing a composite test with optimal discrimination power when there are multiple markers available to assist in prediction and characterize the accuracy of the resulting test by extending the time-dependent receiver operating characteristic (ROC) curve methodology. We employ a modified logistic regression model to derive optimal linear composite scores such that their corresponding ROC curves are maximized at every false positive rate. We provide theoretical justification for using such a model for prognostic accuracy. The proposed method allows for time-varying marker effects and accommodates censored failure time outcome. When the effects of markers are approximately constant over time, we propose a more efficient estimating procedure under such models. We conduct numerical studies to evaluate the performance of the proposed procedures. Our results indicate the proposed methods are both flexible and efficient. We contrast these methods with an application concerning the prognostic accuracies of expression levels of six genes.