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Peer-reviewedCC BY 4.0Axioms

A Cox-Based Framework for Quantile Estimation

  • Rocío Fernández-Iglesias1,2,3
  • Sonia Pérez-Fernández4
  • Miguel García-Villarino1,2,5
  • Pablo Martínez-Camblor6
6 affiliations
  1. 1Department of Medicine, University of Oviedo, 33006 Oviedo, Spain
  2. 2Instituto Universitario de Oncología del Principado de Asturias, 33006 Oviedo, Spain
  3. 3CIBER of Epidemiology and Public Health, Instituto de Salud Carlos III (ISCIII), 28029 Madrid, Spain
  4. 4Department of Statistics and Operations Research and Mathematics Didactics, University of Oviedo, 33007 Oviedo, Spain
  5. 5Instituto de Investigación Sanitaria del Principado de Asturias (ISPA), 33011 Oviedo, Spain
  6. 6Department of Anesthesiology, Geisel School of Medicine at Dartmouth, 7 Lebanon Street, Suite 309, Hinman Box 7261, Lebanon, NH 03751, USA
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Abstract

Quantile regression (QR) provides a flexible framework for characterizing conditional distributions and can offer useful insights for quantile estimation. In this paper, we provide intuition for the interpretation of QR by highlighting the approach that it is a reparameterization of more popular conditional cumulative distribution function regression. From this approach, we naturally explore the use of the proportional hazards Cox regression model in the QR context. Therefore, we propose a framework based on the Cox regression model for estimating conditional quantiles, obtained through a reparameterization of the conditional cumulative distribution function under a proportional hazards structure. We establish the large-sample properties of the resulting estimator and investigate its behavior in finite samples through a Monte Carlo simulation study. An empirical application illustrates its practical implementation in a real-world context. Furthermore, we introduce the average quantile effect, a summary measure for quantifying the effects of covariates across conditional quantiles. The proposed estimator behaves adequately under the required assumptions, although inferences on the associated parameters strongly depend on these premises.

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Cite

BibTeXRIS
BibTeX
@article{fernandeziglesias2026coxbased,
  title = {{A Cox-Based Framework for Quantile Estimation}},
  author = {Rocío Fernández-Iglesias and Sonia Pérez-Fernández and Miguel García-Villarino and Pablo Martínez-Camblor},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100768},
  url = {https://www.mdpi.com/2075-1680/15/10/768},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Cox-Based Framework for Quantile Estimation
AU  - Rocío Fernández-Iglesias
AU  - Sonia Pérez-Fernández
AU  - Miguel García-Villarino
AU  - Pablo Martínez-Camblor
PY  - 2026
DA  - 2026/10/14
JO  - Axioms
DO  - 10.3390/axioms15100768
UR  - https://www.mdpi.com/2075-1680/15/10/768
AB  - Quantile regression (QR) provides a flexible framework for characterizing conditional distributions and can offer useful insights for quantile estimation. In this paper, we provide intuition for the interpretation of QR by highlighting the approach that it is a reparameterization of more popular conditional cumulative distribution function regression. From this approach, we naturally explore the use of the proportional hazards Cox regression model in the QR context. Therefore, we propose a framework based on the Cox regression model for estimating conditional quantiles, obtained through a reparameterization of the conditional cumulative distribution function under a proportional hazards structure. We establish the large-sample properties of the resulting estimator and investigate its behavior in finite samples through a Monte Carlo simulation study. An empirical application illustrates its practical implementation in a real-world context. Furthermore, we introduce the average quantile effect, a summary measure for quantifying the effects of covariates across conditional quantiles. The proposed estimator behaves adequately under the required assumptions, although inferences on the associated parameters strongly depend on these premises.
SN  - 2075-1680
ER  -