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

Author

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  • Chi Hyun Lee

    (The University of Texas MD Anderson Cancer Center)

  • Jing Ning

    (The University of Texas MD Anderson Cancer Center)

  • Yu Shen

    (The University of Texas MD Anderson Cancer Center)

Abstract

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.

Suggested Citation

  • Chi Hyun Lee & Jing Ning & Yu Shen, 2019. "Model diagnostics for the proportional hazards model with length-biased data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 79-96, January.
    • Handle: RePEc:spr:lifeda:v:25:y:2019:i:1:d:10.1007_s10985-018-9422-y
    DOI: 10.1007/s10985-018-9422-y
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    References listed on IDEAS

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    1. Kwun Chuen Gary Chan & Ying Qing Chen & Chong-Zhi Di, 2012. "Proportional mean residual life model for right-censored length-biased data," Biometrika, Biometrika Trust, vol. 99(4), pages 995-1000.
    2. Chiung-yu Huang & Jing Qin, 2012. "Composite Partial Likelihood Estimation Under Length-Biased Sampling, With Application to a Prevalent Cohort Study of Dementia," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 946-957, September.
    3. Wei Yann Tsai, 2009. "Pseudo-partial likelihood for proportional hazards models with biased-sampling data," Biometrika, Biometrika Trust, vol. 96(3), pages 601-615.
    4. Wenbin Lu & Mengling Liu & Yi-Hau Chen, 2014. "Testing goodness-of-fit for the proportional hazards model based on nested case–control data," Biometrics, The International Biometric Society, vol. 70(4), pages 845-851, December.
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    6. Jing Qin & Yu Shen, 2010. "Statistical Methods for Analyzing Right-Censored Length-Biased Data under Cox Model," Biometrics, The International Biometric Society, vol. 66(2), pages 382-392, June.
    7. Shen, Yu & Ning, Jing & Qin, Jing, 2009. "Analyzing Length-Biased Data With Semiparametric Transformation and Accelerated Failure Time Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1192-1202.
    8. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
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