A direct method to evaluate the time-dependent predictive accuracy for biomarkers

Abstract

Time-dependent receiver operating characteristic (ROC) curves and their area under the curve (AUC) are important measures to evaluate the prediction accuracy of biomarkers for time-to-event endpoints (e.g., time to disease progression or death). In this article, we propose a direct method to estimate AUC(t) as a function of time t using a flexible fractional polynomials model, without the middle step of modeling the time-dependent ROC. We develop a pseudo partial-likelihood procedure for parameter estimation and provide a test procedure to compare the predictive performance between biomarkers. We establish the asymptotic properties of the proposed estimator and test statistics. A major advantage of the proposed method is its ease to make inference and to compare the prediction accuracy across biomarkers, rendering our method particularly appealing for studies that require comparing and screening a large number of candidate biomarkers. We evaluate the finite-sample performance of the proposed method through simulation studies and illustrate our method in an application to AIDS Clinical Trials Group 175 data.