Transformed Dynamic Quantile Regression on Censored Data

Abstract

We propose a class of power-transformed linear quantile regression models for time-to-event observations subject to censoring. By introducing a process of power transformation with different transformation parameters at individual quantile levels, our framework relaxes the assumption of logarithmic transformation on survival times and provides dynamic estimation of various quantile levels. With such formulation, our proposal no longer requires the potentially restrictive global linearity assumption imposed on a class of existing inference procedures for censored quantile regression. Uniform consistency and weak convergence of the proposed estimator as a process of quantile levels are established via the martingale-based argument. Numerical studies are presented to illustrate the outperformance of the proposed estimator over existing contenders under various settings.

Keywords:

• Censored quantile regression
• Power transformation
• Empirical process
• Survival analysis

Acknowlwedgement

The authors would like to acknowledge the editor, the associate editor and the anonymous referees whose constructive and valuable comments have substantially improved the manuscript. Sit’s work was partially supported by Hong Kong Research Grant Council RGC-14301618 and RGC-14317716. Xu’s work was partially supported by SES-1659328, SES-184674 and DMS-1712717.

Additional information

Notes on contributors

Chi Wing Chu

Chi Wing Chu is PhD student, Department of Statistics, Columbia University, New York, NY 10027 (E-mail: [email protected]).

Tony Sit

Tony Sit is Assistant Professor, Department of Statistics, The Chinese University of Hong Kong, Hong Kong SAR (E-mail: [email protected]).

Gongjun Xu

Gongjun Xu is Assistant Professor, Department of Statistics, University of Michigan, Ann Arbor, MI 48109 (E-mail: [email protected]).