Resilience family of receiver operating characteristic curves

Abstract

A new semiparametric model of the ROC curve based on the resilience family or proportional reversed hazard family is proposed which is an alternative to the existing models. The resulting ROC curve and its summary indices (such as area under the curve (AUC) and Youden index) have simple analytic forms. The partial likelihood method is applied to estimate the ROC curve. Moreover, the estimation methodologies of the resilience family of the ROC curve have been developed based on AUC estimators exploiting Mann-Whitney statistics and the Rojo approach. A simulation study has been carried out to assess the performance of all considered estimators. Real data from the American National Health and Nutrition Examination Survey (NHANES) has been analysed in detail based on the proposed model and the usual binormal model prevalent in the literature. Real data in the context of brain injury-related biomarkers is also analysed in order to compare our model with the Lehmann family of the ROC curves. Finally, we show that the proposed model may be applicable in the misspecification scenario through a Ducheme muscular dystrophy data.

Transformation models for ROC analysis

“…The binormal (Dorfman and Alf Jr 1969) and bilogistic (Ogilvie and Creelman 1968) ROC curves can be obtained by setting F Z to the standard normal distribution function probit −1 = Φ, or the standard logistic distribution function logit −1 (x) = expit(x) = (1 + exp(−x)) −1 , in Equation 3, respectively. Similarly, the proportional hazard (Gönen and Heller 2010) and reverse proportional hazard alternatives (Khan 2022) for the ROC curve also fall within the purview of our transformation model with F Z specified as cloglog −1 (x) = 1 − exp(− exp(x)) (minimum extreme value distribution function) and loglog −1 (x) = exp(− exp(−x)) (maximum extreme value distribution function), respectively.…”