Robust estimation of conditional ROC curves

BIANCO, ANA; BOENTE, GRACIELA

Toulouse

Conferencia; International Conference on Robust Statistics (ICORS 2023); 2023

Toulouse School of Economics - TSE

Diagnostic tests based on a continuous marker are a key tool in medical decisions.For that reason, it is of extreme importance to evaluate the ability of the test todistinguish between different states, such as healthy individuals from diseased ones.Receiver Operating Characteristic (ROC) curves are a very helpful instrument toassess the performance of a test based on a continuous marker.Several factors, such as gender or blood pressure, may improve the discriminatoryability of the marker. In this cases, conditional ROC curves are useful to includecovariate effects in the ROC analysis and to avoid oversimplification. The indirectmethod provides a way of adjusting ROC curves to covariates by means ofregression models. When an infinite-dimensional covariate is measured, the indirectmethodology is still suitable, but it would involve a functional covariate.Aware of the impact that outliers may have on the diagnostic test accuracy, wefocus on the robust aspects of the estimation procedures of the conditional ROCcurve. In fact, since regression models are involved in the indirect approach, atypicaldata among the marker or the covariates may severely affect the estimationmethods. With this motivation, we generalize the proposal given in Bianco et al.(2022) to a very general scenario in which the markers are modelled in terms of afunctional partially linear model. The considered situations include the functionallinear regression model and also the nonparametric or additive regression ones withreal valued covariates.The given approach enables us to cover a wide range of cases using a robust perspective.We obtain consistency results under standard regularity conditions. Througha Monte Carlo study, we compare the performance of the proposed estimators withthat of the classical ones in clean and different scenarios of contamination.