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

• Published in: Journal of the American Statistical Association Vol. 103; no. 482; pp. 705 - 713
• Main Authors: Li, Gang, Zhou, Kefei
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2008; American Statistical Association; Taylor & Francis Ltd
• Subjects: Algorithms; Applications; Approximation; Area under the receiver operating characteristic curve; Asymptotic methods; Bootstrap resampling; Cluster analysis; Clustered data; Combinatorics; Combinatorics. Ordered structures; Comparative analysis; Confidence band; Confidence interval; Confidence intervals; Correlations; Density; Density estimation; Designs and configurations; Diagnostic systems; Diagnostic tests; Distribution; Estimation methods; Exact sciences and technology; Experimental design; Eyes; General topics; Glaucoma; Intersection-union tests; Longitudinal data; Longitudinal studies; Markers; Mathematics; Measurement; Medical diagnostic tests; Monte Carlo simulation; Multiple comparison; Nonparametric statistics; Paired design; Partial area under the receiver operating characteristic curve; Probability and statistics; Quantile process; Regression analysis; Repeated measurement; Sciences and techniques of general use; Significance level; Startle response; Statistical methods; Statistics; Stochastic models; Stochastic processes; Theory and Methods; Visual fields; United States > US; Density estimation; Correlation; Empirical process; Paired comparison; Statistical distribution; Cluster analysis (statistics); Non parametric estimation; Clustered data; Longitudinal data; Multivariate analysis; Stochastic method; Stochastic process; Paired design; Partial area under the receiver operating characteristic curve; Quantile process; Confidence set; Diagnostic test; Intersection-union tests; Confidence band; Distribution function; Repeated measurement; Approximation theory; Monte Carlo method; Approximate method; Roc curve; Statistical association; Statistical estimation; Multiple comparison; Joint distribution; Confidence interval; Statistical method; Statistical regression; Area under the receiver operating characteristic curve; Numerical analysis; Simulation; Correlation analysis; Experimental design; Receiver operating characteristic curves; Small sample; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214508000000364

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.