Comparing correlated ROC curves for continuous diagnostic tests under density ratio models

A family of nonparametric statistics to comparing ROC curves for continuous diagnostic tests was proposed by Wieand et al. [Wieand, S., Gail, M.H., James, B.R., James, K.L., 1989. A family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data. Biometrika 76, 585–592]. In this paper, we study the semiparametric counterpart. We propose a two-sample semiparametric bivariate density ratio model, under which new ROC curve estimators are constructed and a family of semiparametric statistics for comparing ROC curves are proposed. We derive the asymptotic results on the newly proposed ROC curve estimators and show that they are more efficient than the nonparametric counterparts. We also show the proposed method for comparing ROC curves is more efficient than the nonparametric counterpart. A simulation study and the analysis of two real examples are also presented.