Open Access
September 2016 Functional covariate-adjusted partial area under the specificity-ROC curve with an application to metabolic syndrome diagnosis
Vanda Inácio de Carvalho, Miguel de Carvalho, Todd A. Alonzo, Wenceslao González-Manteiga
Ann. Appl. Stat. 10(3): 1472-1495 (September 2016). DOI: 10.1214/16-AOAS943


Due to recent advances in technology, medical diagnosis data are becoming increasingly complex and, nowadays, applications where measurements are curves or images are ubiquitous. Motivated by the need of modeling a functional covariate on a metabolic syndrome case study, we develop a nonparametric functional regression model for the area under the specificity receiver operating characteristic curve. This partial area is a meaningful summary measure of diagnostic accuracy for cases in which misdiagnosis of diseased subjects may lead to serious clinical consequences, and hence it is critical to maintain a high sensitivity. Its normalized value can be interpreted as the average specificity over the interval of sensitivities considered, thus summarizing the trade-off between sensitivity and specificity. Our methods are motivated by, and applied to, a metabolic syndrome study that investigates how restricting the sensitivity of the gamma-glutamyl-transferase, a metabolic syndrome marker, to certain clinical meaningful values, affects its corresponding specificity and how it might change for different curves of arterial oxygen saturation. Application of our methods suggests that oxygen saturation is key to gamma-glutamyl transferase’s performance and that some of the different intervals of sensitivities considered offer a good trade-off between sensitivity and specificity. The simulation study shows that the estimator associated with our model is able to recover successfully the true overall shape of the functional covariate-adjusted partial area under the curve in different complex scenarios.


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Vanda Inácio de Carvalho. Miguel de Carvalho. Todd A. Alonzo. Wenceslao González-Manteiga. "Functional covariate-adjusted partial area under the specificity-ROC curve with an application to metabolic syndrome diagnosis." Ann. Appl. Stat. 10 (3) 1472 - 1495, September 2016.


Received: 1 November 2014; Revised: 1 April 2016; Published: September 2016
First available in Project Euclid: 28 September 2016

zbMATH: 06775274
MathSciNet: MR3553232
Digital Object Identifier: 10.1214/16-AOAS943

Keywords: Arterial oxygen saturation , average specificity , biomarker , functional covariate-adjustment , gamma-glutamyl transferase , kernel regression , metabolic syndrome , partial area under the curve , Sensitivity , specificity-receiver operating characteristic curve

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 3 • September 2016
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