Functional Censored Quantile Regression

Abstract

We propose a functional censored quantile regression model to describe the time-varying relationship between time-to-event outcomes and corresponding functional covariates. The time-varying effect is modeled as an unspecified function that is approximated via B-splines. A generalized approximate cross-validation method is developed to select the number of knots by minimizing the expected loss. We establish asymptotic properties of the method and the knot selection procedure. Furthermore, we conduct extensive simulation studies to evaluate the finite sample performance of our method. Finally, we analyze the functional relationship between ambulatory blood pressure trajectories and clinical outcome in stroke patients. The results reinforce the importance of the morning blood pressure surge phenomenon, whose effect has caught attention but remains controversial in the medical literature. Supplementary materials for this article are available online.

Keywords:

• B-spline
• Censored quantile regression
• Functional regression
• Generalized approximate cross-validation
• Time-varying effect

Supplementary Materials

The supplementary material contains the proofs of the theoretical results and additional numerical results.

Acknowledgments

The authors would like to thank the editor, associate editor, and the referees for their constructive comments.

Additional information

Funding

This research is partially supported by GRF 17326316 for Prof. Yin and ECS 27304117 and GRF 17307218 for Dr. Jiang from the Research Grants Council of Hong Kong. The authors Dr. Jiang and Haipeng Shen are supported by grant 2017YFC1310903 from the Ministry of Science and Technology Major Project of China.