Nonparametric Methods in Comparing Two Correlated Roc Curves

Receiver Operating Characteristic (ROC) analysis is one of the most widely used methods for summarizing intrinsic properties of a diagnostic system, and is often used in evaluation and comparison of diagnostic technologies, practices or systems. These methods play an important role in public health since they enable researchers to achieve a greater insight into the properties of diagnostic tests and eventually to identify a more appropriate and beneficial procedure for diagnosing or screening for a specific disease or condition. The topic of this dissertation is the nonparametric testing of hypotheses about ROC curves in a paired design setting. Presently only a few nonparametric tests are available for the task of comparing two correlated ROC curves. Thus we focus on this basic problem leaving the extensions to more complex settings for future research. In this work, we study the small-sample properties of the conventional nonparametric method presented by DeLong et al. and develop three novel nonparametric approaches for comparing diagnostic systems using the area under the ROC curve. The permutation approach that we present enables conducting an exact test and allows for an easy-to-use asymptotic approximation. Next, we derive a closed-form bootstrap-variance, construct an asymptotic test, and compare them to the existing competitors. Finally, exploiting the idea of " discordances " we develop a conceptually new conditional approach that offers advantages in certain types of studies.