The generalized Lehmann ROC curves: Lehmann family of ROC surfaces

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.