Power-transformed linear regression on quantile residual life for censored competing risks data

ABSTRACT

This paper proposes a power-transformed linear quantile regression model for the residual lifetime of competing risks data. The proposed model can describe the association between any quantile of a time-to-event distribution among survivors beyond a specific time point and the covariates. Under covariate-dependent censoring, we develop an estimation procedure with two steps, including an unbiased monotone estimating equation for regression parameters and cumulative sum processes for the Box–Cox transformation parameter. The asymptotic properties of the estimators are also derived. We employ an efficient bootstrap method for the estimation of the variance–covariance matrix. The finite-sample performance of the proposed approaches are evaluated through simulation studies and a real example.

Keywords:

• Box–Cox transformation
• Competing risks
• Empirical process
• Quantile residual life.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N01, 62N02

Acknowledgment

Thanks for the Editor, Associate Editor and referees for their useful comments.

Fan's work is partially supported by Graduate Creation Funds of Shanghai University of Finance and Economics (CXJJ-2013-449), Shanghai Young Teacher Training Scheme of Universities in 2016 (ZZSWM15019), Shanghai Summit and Plateau Discipline and Scientific and Technological projects of Shenyang (F14-231-1-39). Zhang's work is partially supported by National Natural Science Foundation of China (NSFC) (11401194) and the Fundamental Research Funds for the Central Universities (531107050739). Zhou's work is partially supported by National Natural Science Foundation of China (NSFC) (71271128), the State Key Program of National Natural Science Foundation of China (71331006 and 91546202), National Center for Mathematics and Interdisciplinary Sciences (NCMIS), Key Laboratory of RCSDS, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS) (2008DP173182) and Shanghai First-class Discipline A, Program for Changjiang Scholars (PCSIRT) and Innovative Research Team in Shanghai University of Finance and Economics (SUFE) (IRT13077).