title: Receiver operating characteristic curve generalization for non-monotone relationships.
abstract: The receiver operating characteristic curve is a popular graphical method frequently used in order to study the diagnostic capacity of continuous markers. It represents in a plot true-positive rates against the false-positive ones. Both the practical and theoretical aspects of the receiver operating characteristic curve have been extensively studied. Conventionally, it is assumed that the considered marker has a monotone relationship with the studied characteristic; i.e., the upper (lower) values of the (bio)marker are associated with a higher probability of a positive result. However, there exist real situations where both the lower and the upper values of the marker are associated with higher probability of a positive result. We propose a receiver operating characteristic curve generalization, [Formula: see text], useful in this context. All pairs of possible cut-off points, one for the lower and another one for the upper marker values, are taken into account and the best of them are selected. The natural empirical estimator for the [Formula: see text] curve is considered and its uniform consistency and asymptotic distribution are derived. Finally, two real-world applications are studied.
authors.affiliation: 1 Oficina de Investigación Biosanitaria de Asturias (OIB-FICYT).|2 Universidad Autonoma de Chile, Chile.
authors.forename: Pablo
authors.initials: P
authors.lastname: Martínez-Camblor
authors.affiliation: 3 Universidad de Oviedo.
authors.forename: Norberto
authors.initials: N
authors.lastname: Corral
authors.affiliation: 3 Universidad de Oviedo.|4 UCI Pediátrica, Departamento de Pediatría, Hospital Universitario Central de Asturias (HUCA).
authors.forename: Corsino
authors.initials: C
authors.lastname: Rey
authors.affiliation: 3 Universidad de Oviedo.|5 Área de Neurociencias, Servicio de Neurología, Hospital Universitario Central de Asturias (HUCA).
authors.forename: Julio
authors.initials: J
authors.lastname: Pascual
authors.affiliation: 3 Universidad de Oviedo.|5 Área de Neurociencias, Servicio de Neurología, Hospital Universitario Central de Asturias (HUCA).
authors.forename: Eva
authors.initials: E
authors.lastname: Cernuda-Morollón
mesh_terms: D019540:Area Under Curve; D015415:Biomarkers; D019274:Botulinum Toxins, Type A / Q000627:therapeutic use; D015740:Calcitonin Gene-Related Peptide / Q000097:blood; D002648:Child; D016638:Critical Illness / Q000401:mortality; D005260:Female; D006801:Humans; D007958:Leukocyte Count; D008881:Migraine Disorders / Q000097:blood / Q000188:drug therapy; D011336:Probability; D012372:ROC Curve; D018805:Sepsis / Q000401:mortality
chemical_list: D015415:Biomarkers; D019274:Botulinum Toxins, Type A; D015740:Calcitonin Gene-Related Peptide
keywords: area under the curve; asymptotic distribution; receiver operating characteristic curve; resampling methods