A diagnostic test has two purposes: (1) to provide reliable information about the patient's condition and (2) to influence the physician's plan for managing the patient. A test can serve these purposes only if the physicians know how to interpret it. This information is required through an assessment of the test's diagnostic accuracy, which is the ability of a test to discriminate between the presence or absence of the disease. When the response of a diagnostic test is continuous, its diagnostic accuracy is best represented by the receiver operating characteristic (ROC) curve. Currently most widely used methods for estimating ROC curves with covariates are parametric or semi-parametric. However, estimated ROC curves can be very sensitive to the parametric assumption on the link function. Finally, most current ROC studies employ fixed sample designs, which are not efficient. Although there are many good reasons for the use of group sequential designs in ROC studies, the group sequential design has not been used widely in ROC studies because of the lack of available methodology for conducting the GSD in ROC studies. In this proposal we will develop non-parametric regression models for ROC curves with covariates and estimation methods that are invariant under the monotone transformation of data. We will also develop nonparametric regression models for partial or full regions of ROC curves with covariates and estimation methods. Finally, we will develop general group sequential designs for comparative ROC studies using nonparametrically estimated ROC curves. [unreadable] [unreadable]