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Composite Partial Likelihood Estimation Under Length-Biased Sampling, With Application to a Prevalent Cohort Study of Dementia

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  • Chiung-yu Huang
  • Jing Qin

Abstract

The Canadian Study of Health and Aging (CSHA) employed a prevalent cohort design to study survival after onset of dementia, where patients with dementia were sampled and the onset time of dementia was determined retrospectively. The prevalent cohort sampling scheme favors individuals who survive longer. Thus, the observed survival times are subject to length bias. In recent years, there has been a rising interest in developing estimation procedures for prevalent cohort survival data that not only account for length bias but also actually exploit the incidence distribution of the disease to improve efficiency. This article considers semiparametric estimation of the Cox model for the time from dementia onset to death under a stationarity assumption with respect to the disease incidence. Under the stationarity condition, the semiparametric maximum likelihood estimation is expected to be fully efficient yet difficult to perform for statistical practitioners, as the likelihood depends on the baseline hazard function in a complicated way. Moreover, the asymptotic properties of the semiparametric maximum likelihood estimator are not well-studied. Motivated by the composite likelihood method (Besag 1974), we develop a composite partial likelihood method that retains the simplicity of the popular partial likelihood estimator and can be easily performed using standard statistical software. When applied to the CSHA data, the proposed method estimates a significant difference in survival between the vascular dementia group and the possible Alzheimer's disease group, while the partial likelihood method for left-truncated and right-censored data yields a greater standard error and a 95% confidence interval covering 0, thus highlighting the practical value of employing a more efficient methodology. To check the assumption of stable disease for the CSHA data, we also present new graphical and numerical tests in the article. The R code used to obtain the maximum composite partial likelihood estimator for the CSHA data is available in the online Supplementary Material, posted on the journal web site.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:946-957
    DOI: 10.1080/01621459.2012.682544
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    Citations

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    Cited by:

    1. 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.
    2. Yifan He & Yong Zhou, 2020. "Nonparametric and semiparametric estimators of restricted mean survival time under length-biased sampling," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 761-788, October.
    3. Yu Shen & Jing Ning & Jing Qin, 2017. "Nonparametric and semiparametric regression estimation for length-biased survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 3-24, January.
    4. Fei Gao & Kwun Chuen Gary Chan, 2019. "Semiparametric regression analysis of length‐biased interval‐censored data," Biometrics, The International Biometric Society, vol. 75(1), pages 121-132, March.
    5. Ma, Huijuan & Zhang, Feipeng & Zhou, Yong, 2015. "Composite estimating equation approach for additive risk model with length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 45-53.
    6. Chengbo Li & Yong Zhou, 2021. "The estimation for the general additive–multiplicative hazard model using the length-biased survival data," Statistical Papers, Springer, vol. 62(1), pages 53-74, February.
    7. Yifei Sun & Kwun Chuen Gary Chan & Jing Qin, 2018. "Simple and fast overidentified rank estimation for right†censored length†biased data and backward recurrence time," Biometrics, The International Biometric Society, vol. 74(1), pages 77-85, March.
    8. Shi, Jianhua & Ma, Huijuan & Zhou, Yong, 2018. "The nonparametric quantile estimation for length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 150-158.
    9. Fan Wu & Sehee Kim & Jing Qin & Rajiv Saran & Yi Li, 2018. "A pairwise likelihood augmented Cox estimator for left†truncated data," Biometrics, The International Biometric Society, vol. 74(1), pages 100-108, March.
    10. Wu, Hongping & Cao, Xiaomin & Du, Caifeng, 2019. "Estimating equations of additive mean residual life model with censored length-biased data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    11. Yu-Jen Cheng & Chiung-Yu Huang, 2014. "Combined estimating equation approaches for semiparametric transformation models with length-biased survival data," Biometrics, The International Biometric Society, vol. 70(3), pages 608-618, September.
    12. Zhang, Feipeng & Peng, Heng & Zhou, Yong, 2016. "Composite partial likelihood estimation for length-biased and right-censored data with competing risks," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 160-176.
    13. Peijie Wang & Danning Li & Jianguo Sun, 2021. "A pairwise pseudo‐likelihood approach for left‐truncated and interval‐censored data under the Cox model," Biometrics, The International Biometric Society, vol. 77(4), pages 1303-1314, December.
    14. Zhang, Qiaozhen & Dai, Hongsheng & Fu, Bo, 2016. "A proportional hazards model for time-to-event data with epidemiological bias," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 224-236.
    15. Gongjun Xu & Tony Sit & Lan Wang & Chiung-Yu Huang, 2017. "Estimation and Inference of Quantile Regression for Survival Data Under Biased Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1571-1586, October.
    16. James H. McVittie & Ana F. Best & David B. Wolfson & David A. Stephens & Julian Wolfson & David L. Buckeridge & Shahinaz M. Gadalla, 2023. "Survival Modelling for Data From Combined Cohorts: Opening the Door to Meta Survival Analyses and Survival Analysis Using Electronic Health Records," International Statistical Review, International Statistical Institute, vol. 91(1), pages 72-87, April.
    17. Zhiping Qiu & Jing Qin & Yong Zhou, 2016. "Composite Estimating Equation Method for the Accelerated Failure Time Model with Length-biased Sampling Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 396-415, June.
    18. Na Hu & Xuerong Chen & Jianguo Sun, 2015. "Regression Analysis of Length-biased and Right-censored Failure Time Data with Missing Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 438-452, June.

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