¹Oficina de Investigación Biosanitaria, CAIBER, Oviedo, Spain. Universidad de Oviedo, Departamento de Estadística e I.O. y D.M., Oviedo, Spain. Biostatistics and Associate professor. Email: pablomc@ficyt.es

The study of diagnostic tests is a hot topic which has direct applications in biomedical sciences. Despite of the relevance, in a diagnostic process, of the threshold (or cutoff point) employed on the decision taken by the physician, the study and comparison of the accuracy among different diagnostic criterions has been the main field of study. In this paper, the authors are interested in the study of the involved cutoff point estimation in diagnostic tests with weighted errors. With this goal, a nonparametric smoothed utility function estimator is considered. The bootstrap and the asymptotic distributions for the related M-estimator are derived. Finally, the obtained results are applied to study the Procalcitonin level which determines whether a child within the Pediatric Intensive Care Unit (UCIP) has a virical sepsis.

Key words: Kernel density estimator, Sensitivity, Specificity, Threshold, Utility function.

El estudio de tests diagnósticos es un tema candente con aplicaciones directas en las ciencias biomédicas. Aunque en la práctica, a la hora de tomar una decisión, los clínicos deben fijar un valor umbral (o punto de corte) a pesar de la relevancia que este valor tiene, el estudio y la comparación de la calidad entre diferentes criterios diagnósticos ha sido el principal campo de estudio. En este trabajo, los autores están interesados en el estudio de la estimación del punto de corte involucrado en un test diagnóstico con errores ponderados. Con este objetivo, se considera un estimador suavizado para una función de utilidad. Se estudian las distribuciones bootstrap y asintóticas del M-estimador resultante. Finalmente, los resultados obtenidos son aplicados al estudio de los niveles de Procalcitonina que determinan si un niño ingresado en la Unidad de Cuidados Intensivos Pediátricos (UCIP) tiene infección vírica.

Palabras clave: especificadas, estimador núcleo para la densidad, función de utilidad, sensibilidad, umbral.

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