Lifetime Data Analysis

, Volume 25, Issue 1, pp 79–96 | Cite as

Model diagnostics for the proportional hazards model with length-biased data

  • Chi Hyun LeeEmail author
  • Jing Ning
  • Yu Shen


Length-biased data are frequently encountered in prevalent cohort studies. Many statistical methods have been developed to estimate the covariate effects on the survival outcomes arising from such data while properly adjusting for length-biased sampling. Among them, regression methods based on the proportional hazards model have been widely adopted. However, little work has focused on checking the proportional hazards model assumptions with length-biased data, which is essential to ensure the validity of inference. In this article, we propose a statistical tool for testing the assumed functional form of covariates and the proportional hazards assumption graphically and analytically under the setting of length-biased sampling, through a general class of multiparameter stochastic processes. The finite sample performance is examined through simulation studies, and the proposed methods are illustrated with the data from a cohort study of dementia in Canada.


Dementia Length-biased data Model diagnostics Proportional hazards model Stochastic processes 



This work was partially supported by the U.S. National Institutes of Health, Grants CA193878 and CA016672. The authors thank Professor Asgharian and the investigators from the Canadian Study of Health and Aging for generously sharing the dementia data. The data reported in this article were collected as part of the Canadian Study of Health and Aging. The core study was funded by the Seniors Independence Research Program, through the National Health Research and Development Program (NHRDP) of Health Canada Project 6606-3954-MC(S). Additional funding was provided by Pfizer Canada, Incorporated, through the Medical Research Council/Pharmaceutical Manufacturers Association of Canada Health Activity Program, NHRDP Project 6603-1417-302(R), Bayer Incorporated, and the British Columbia Health Research Foundation Projects 38 (93-2) and 34 (96-1). The study was coordinated through the University of Ottawa and the Division of Aging and Seniors, Health Canada. The authors also acknowledge the Texas Advanced Computing Center at The University of Texas at Austin for providing HPC resources that contributed to the research results reported within this paper.

Supplementary material

10985_2018_9422_MOESM1_ESM.pdf (257 kb)
Supplementary material 1 (pdf 256 KB)


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of BiostatisticsThe University of Texas MD Anderson Cancer CenterHoustonUSA

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