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Biometrika 2003 90(3):585-596; doi:10.1093/biomet/90.3.585
© 2003 by Biometrika Trust
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Using logistic regression procedures for estimating receiver operating characteristic curves

Jing Qin1 and Biao Zhang2

1 Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, 1275 York Avenue, New York, New York 10021, U.S.Aqinj{at}biosta.mskcc.org 2 Department of Mathematics, University of Toledo, Toledo, Ohio 43606, U.S.A.bzhang{at}math.utoledo.edu

Estimation of a receiver operating characteristic, ROC, curve is usually based either on a fully parametric model such as a normal model or on a fully nonparametric model.In this paper, we explore a semiparametric approach by assuming a density ratio model for disease and disease-free densities. This model has a natural connection with the logistic regression model. The proposed semiparametric approach is more robust than a fully parametric approach and is more efficient than a fully nonparametric approach. Two real examples demonstrate that the ROC curve estimated by our semiparametric method is much smoother than that estimated by the nonparametric method.

Key Words: Bootstrap; Density ratio model; Diagnostic test; Gaussian process; Logistic regression model; ROC curve; Semiparametric likelihood; Sensitivity; Specificity

Received October 2001. Revised February 2003


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