## The Annals of Applied Statistics

### Functional covariate-adjusted partial area under the specificity-ROC curve with an application to metabolic syndrome diagnosis

#### Abstract

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.

#### Article information

Source
Ann. Appl. Stat., Volume 10, Number 3 (2016), 1472-1495.

Dates
Revised: April 2016
First available in Project Euclid: 28 September 2016

https://projecteuclid.org/euclid.aoas/1475069615

Digital Object Identifier
doi:10.1214/16-AOAS943

Mathematical Reviews number (MathSciNet)
MR3553232

Zentralblatt MATH identifier
06775274

#### Citation

Inácio de Carvalho, Vanda; de Carvalho, Miguel; Alonzo, Todd A.; González-Manteiga, Wenceslao. Functional covariate-adjusted partial area under the specificity-ROC curve with an application to metabolic syndrome diagnosis. Ann. Appl. Stat. 10 (2016), no. 3, 1472--1495. doi:10.1214/16-AOAS943. https://projecteuclid.org/euclid.aoas/1475069615

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#### Supplemental materials

• Supplement to “Functional covariate-adjusted partial area under the specificity-ROC curve with an application to metabolic syndrome diagnosis”. Technical details and supplementary empirical reports. The supplement consists of three parts. The first part provides auxiliary results on the construction of our estimator. The second contains supplemental empirical analysis of the metabolic syndrome data and a comparison with simpler approaches. Finally, the third part contains an additional simulation study and R code to implement our methods.