The generalized Lehmann ROC curves: Lehmann family of ROC surfaces

Abstract

Receiver operating characteristic (ROC) research has been limited to binary choice. Recently, the method was generalized based on the Lehmann assumption also known as the proportional hazards specification. This model accommodates a variety of research questions such as covariate adjustments. By applying this method to three-class ROC analysis, simple analytical forms of ROC surface and volume under the surface were derived without and with covariates. Furthermore, the model parameters and the corresponding asymptotic variances were evaluated. Simulation studies were performed to assess the validity of our proposed method in finite samples and extension work for dimension higher than three-class is considered.

Configuration of intrusion prevention systems based on a legal user: the case for using intrusion prevention systems instead of intrusion detection systems

“…The ROC (receiver operating characteristic) curve for a security technology can be derived analytically or experimentally [18,19]. In the following paragraph, we illustrate the analytical derivation of the ROC curve for an IPS.…”

Estimating diagnostic accuracy for clustered ordinal diagnostic groups in the three-class case—Application to the early diagnosis of Alzheimer disease

“…whereF À is the estimated distribution function of U À ,Ĝ þ is the estimated complementary cumulative distribution function of W þ , andf 0 is the estimated density function of V 0 . With the three subjects all drawn from the same cluster, the second equality of equation (5) indicates that sss is equivalent to estimating VUS for independent subjects when restricted to the subjects in the same cluster only. The third equality of equation (5) is proved in Xiong et al 4 In the general linear mixed effect model that assumes the normal random cluster effect and normal error distributions, let ' and È be the density and distribution function of the standard normal distribution, respectively.…”

“…1,2 The diagnostic accuracy of a diagnostic marker when the gold standard diagnosis is an ordinal rating scale of more than two options is summarized by a receiver operating characteristic (ROC) surface or manifold from which a summary index of diagnostic accuracy, such as the volume under the surface (VUS) or the partial volume under the surface, can be derived. 3–7…”

“…1,2 The diagnostic accuracy of a diagnostic marker when the gold standard diagnosis is an ordinal rating scale of more than two options is summarized by a receiver operating characteristic (ROC) surface or manifold from which a summary index of diagnostic accuracy, such as the volume under the surface (VUS) or the partial volume under the surface, can be derived. [3][4][5][6][7] Most of the research in diagnostic accuracy of diagnostic markers when there are more than two ordinal diagnostic groups has focused on the data types in which subjects from multiple diagnostic groups are statistically independent. In many biomedical studies, however, subjects are enrolled in clusters, resulting in potential correlations on the diagnostic markers from the same members of the clusters.…”