A test for comparing conditional ROC curves with multidimensional covariates

Abstract

The comparison of Receiver Operating Characteristic (ROC) curves is frequently used in the literature to compare the discriminatory capability of different classification procedures based on diagnostic variables. The performance of these variables can be sometimes influenced by the presence of other covariates, and thus they should be taken into account when making the comparison. A new non-parametric test is proposed here for testing the equality of two or more dependent ROC curves conditioned to the value of a multidimensional covariate. Projections are used for transforming the problem into a one-dimensional approach easier to handle. Simulations are carried out to study the practical performance of the new methodology. The procedure is then used to analyse a real data set of patients with Pleural Effusion to compare the diagnostic capability of different markers.

KEYWORDS:

• Bootstrap
• covariates
• hypothesis testing
• projections
• ROC curves

Acknowledgements

The authors would like to thank the Associate Editor and the anonymous reviewers for their constructive comments and suggestions on an earlier version of this manuscript. The Supercom puting Center of Galicia (CESGA) is acknowledged for providing the computational resources that allowed to run most of the simulations. Dr. F. Gude (Unidade de Epidemioloxía Clínica, Hospital Clínico Universitario de Santiago) is thanked for providing the data set analysed in this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of A. Fanjul-Hevia is supported by the Ministerio de Educación, Cultura y Deporte (fellowship FPU14/05316), as well as by the Spanish Ministerio de Educación y Formación Profesional (Mobility Grant EST18/00673). A. Fanjul-Hevia, W. González-Manteiga and I. Van Keilegom acknowledge the support by the Grant PID2020-116587GB-I00 from Spanish Ministerio de Ciencia e Innovación (MCIN/AEI/ 10.13039/501100011033). J.C. Pardo-Fernández acknowledges financial support by the Grant PID2020-118101GB-I00 from Spanish Ministerio de Ciencia e Innovación (MCIN/AEI/10.13039/501100011033). I. Van Keilegom is financially supported by the European Research Council (2016-2021, Horizon 2020 / ERC grant agreement No. 694409).