The area under the receiver operating characteristic (ROC) curve, AUC, is commonly used to assess the ability of a diagnostic test to correctly classify individuals into diseased and nondiseased populations. When there are two diagnostic tests available, it is of interest to evaluate and compare their performances. Based on the difference of two placement values, we propose a two-sample empirical likelihood method for comparing AUCs of two ROC curves. The proposed empirical likelihood ratio statistic converges in distribution to a scaled chi-squared random variable. Simulation results show that the proposed empirical likelihood method has a better finite-sample performance than other competitors.
Receiver operating characteristic curve Area under curve Empirical likelihood Placement value Sensitivity Specificity
AMS Subject Classification
62G05 62G20 62G86
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Bamber, D. 1975. The area above the ordinal dominance graph and the area below the receiver operating characteristic curve graph. J. Math. Psychol., 12, 387–415.MathSciNetCrossRefGoogle Scholar
Campbell, G. 1994. Advances in statistical methodology for the evaluation of diagnostic and laboratory tests. Stat. Med., 13, 499–508.CrossRefGoogle Scholar
Delong, E., D. Delong, and D. Clarke-Pearson. 1988. Comparing the areas under two or more correlated receiver operating characteristic curves: A nonparametric approach. Biometrics, 44, 837–845.CrossRefGoogle Scholar
Greenhouse, S., and N. Mantel. 1950. The evaluation of diagnostic tests. Biometrics, 6, 399–412.CrossRefGoogle Scholar
Hall P., and B. La Scala. 1990. Methodology and algorithm of empirical likelihood. Int. Stat. Rev., 58, 109–127.CrossRefGoogle Scholar
Hanley, J., and B. McNeil. 1983. A method of comparing the area under receiver operating characteristic curves derived from the same cases. Radiology, 148, 839–843.CrossRefGoogle Scholar
Van Der Vaart, A. 1998. Asymptotic statistics. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Venkatraman, E., and C. Begg. 1996. A distribution free procedure for comparing receiver operating characteristic curves from a paired experiment. Biometrika, 83, 835–848.MathSciNetCrossRefGoogle Scholar
Wieand, S., M. Gail, B. James, and K. James. 1989. A family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data. Biometrika, 76, 585–592.MathSciNetCrossRefGoogle Scholar
Zou, K. 2001. Comparison of correlated receiver operating characteristic curves derived from repeated diagnostic test data. Acad. Radiol., 8, 225–233.CrossRefGoogle Scholar