ROC curve analysis for functional markers

TL;DR

This paper develops ROC curve analysis methods for functional data in medical diagnosis, introducing linear and quadratic discrimination rules with proven consistency, and demonstrates their effectiveness through simulations and real data applications.

Contribution

It introduces a new index for ROC analysis of functional data, compares linear and quadratic discrimination rules, and provides consistency results for these methods.

Findings

Quadratic discrimination rule performs better with different covariance operators.

Consistency of linear and quadratic indexes is theoretically established.

Numerical experiments show advantages of the quadratic rule.

Abstract

Functional markers become a more frequent tool in medical diagnosis. In this paper, we aim to define an index allowing to discriminate between populations when the observations are functional data belonging to a Hilbert space. We discuss some of the problems arising when estimating optimal directions defined to maximize the area under the curve of a projection index and we construct the corresponding ROC curve. We also go one step forward and consider the case of possibly different covariance operators, for which we recommend a quadratic discrimination rule. Consistency results are derived for both linear and quadratic indexes, under mild conditions. The results of our numerical experiments allow to see the advantages of the quadratic rule when the populations have different covariance operators. We also illustrate the considered methods on a real data set.