Statistics and Its Interface

Volume 12 (2019)

Number 1

Fine–Gray proportional subdistribution hazards model for competing risks data under length-biased sampling

Pages: 107 – 122

DOI: https://dx.doi.org/10.4310/SII.2019.v12.n1.a10

Authors

Feipeng Zhang (School of Mathematics and Statistics, Hunan Normal University, Changsha, China)

Heng Peng (Department of Mathematics, Hong Kong Baptist University, Hong Kong, China)

Yong Zhou (School of Statistics, East China Normal University, Shanghai, China; and Academy of Mathematics & Systems Science, C.A.S., Beijing, China)

Abstract

In this paper, we study the Fine–Gray proportional subdistribution hazards model for the competing risks data under length-biased sampling. To exploit the special structure of length-biased sampling, we propose an unbiased estimating equation estimator, which can handle both covariate-independent censoring and the covariate-dependent censoring. The large sample properties of the proposed estimator are derived, model-checking techniques for the model adequacy are developed, and the pointwise confidence intervals and the simultaneous confidence bands for the predicted cumulative incidence functions are also constructed. Simulation studies are conducted to assess the finite sample performance of the proposed estimator. An application to the employment data illustrates the method and theory.

Keywords

competing risks data, length-biased sampling, Fine–Gray model, model checking techniques

2010 Mathematics Subject Classification

Primary 62N01, 62N02. Secondary 62P20.

Full Text (PDF format)

The authors are grateful to the editor and two anonymous referees for many helpful comments. Feipeng Zhang’s work is partially supported by the National Natural Science Foundation of China (11771133,11401194). Heng Peng’s research is supported in part by CEGR grant of the Research Grants Council of Hong Kong (No. HKBU 12302615 and HKBU 12303618), FRG grants from Hong Kong Baptist University (FRG2/16-17/042), and the Natural Science Foundation of Hunan Province, China (2017JJ3021). Yong Zhou’s work is partially supported by the State Key Program of National Natural Science Foundation of China (71331006), the State Key Program in the Major Research Plan of National Natural Science Foundation of China (91546202).

Received 19 July 2017

Published 26 October 2018