Non-parametric quantile estimate for length-biased and right-censored data with competing risks

ABSTRACT

In this article, we propose a non-parametric quantile inference procedure for cause-specific failure probabilities to estimate the lifetime distribution of length-biased and right-censored data with competing risks. We also derive the asymptotic properties of the proposed estimators of the quantile function. Furthermore, the results are used to construct confidence intervals and bands for the quantile function. Simulation studies are conducted to illustrate the method and theory, and an application to an unemployment data is presented.

KEYWORDS:

• Competing risks
• Cumulative incidence function
• Length-biased and right-censored data
• Quantile.

MATHEMATICS SUBJECT CLSSIFICATION:

• 62N01, 62N02

Acknowledgments

The authors are grateful to the editor, an associate editor, and a anonymous reviewer for their insightful comments and constructive suggestions that lead to a significant improvement in the revised manuscript. We thank Professor Jacobo de Ua-lvarez for sharing the Galician unemployment data and providing helpful suggestions.

Additional information

Funding

Zhang’s work is partially supported by National Natural Science Foundation of China (NSFC) (11401194, 11771133), Fund for the Growth Plan of Young Teachers in Hunan University (531107050739). Zhou’s work was supported by National Natural Science Foundation of China (NSFC) (71271128), the State Key Program of National Natural Science Foundation of China (71331006 and 91546202), NCMIS, Key Laboratory of RCSDS, AMSS, CAS(2008DP173182) and Shanghai First-class Discipline A, Program for Changjiang Scholars (PCSIRT) and Innovative Research Team in SUFEIRT13077).