A Unified Approach to Nonparametric Comparison of Receiver Operating Characteristic Curves for Longitudinal and Clustered Data

Abstract

We present a unified approach to nonparametric comparisons of receiver operating characteristic (ROC) curves for a paired design with clustered data. Treating empirical ROC curves as stochastic processes, their asymptotic joint distribution is derived in the presence of both between-marker and within-subject correlations. A Monte Carlo method is developed to approximate their joint distribution without involving nonparametric density estimation. The developed theory is applied to derive new inferential procedures for comparing weighted areas under the ROC curves, confidence bands for the difference function of ROC curves, confidence intervals for the set of specificities at which one diagnostic test is more sensitive than the other, and multiple comparison procedures for comparing more than two diagnostic markers. Our methods demonstrate satisfactory small-sample performance in simulations. We illustrate our methods using clustered data from a glaucoma study and repeated-measurement data from a startle response study.