IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v26y2020i4d10.1007_s10985-020-09498-x.html
   My bibliography  Save this article

Nonparametric and semiparametric estimators of restricted mean survival time under length-biased sampling

Author

Listed:
  • Yifan He

    (Shanghai University of Finance and Economics)

  • Yong Zhou

    (East China Normal University)

Abstract

Restricted mean survival time is often of direct interest in epidemiologic studies involving censored survival time. In this article, we propose the nonparametric and semiparametric estimators of the mean restricted to the preassigned interval with censored length-biased data. Based on the peculiarity of length-biased data, the auxiliary information that truncation time and residual time have the same distribution is taken into account for improving estimation efficiency. For two-sample comparison, we construct two tests which are easy to implement. We also derive the asymptotic properties for the proposed estimators and test statistics. In simulation studies, some simulations are conducted to compare the performances of several approaches to estimate restricted mean and to assess the test statistics. In addition, our methods are applied to a real data example and some interesting results are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:4:d:10.1007_s10985-020-09498-x
    DOI: 10.1007/s10985-020-09498-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-020-09498-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10985-020-09498-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chi Hyun Lee & Jing Ning & Yu Shen, 2018. "Analysis of restricted mean survival time for length†biased data," Biometrics, The International Biometric Society, vol. 74(2), pages 575-583, June.
    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. 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.
    4. Min Zhang & Douglas E. Schaubel, 2011. "Estimating Differences in Restricted Mean Lifetime Using Observational Data Subject to Dependent Censoring," Biometrics, The International Biometric Society, vol. 67(3), pages 740-749, September.
    5. Chiung-Yu Huang & Jing Qin, 2011. "Nonparametric estimation for length-biased and right-censored data," Biometrika, Biometrika Trust, vol. 98(1), pages 177-186.
    6. Lin, Cunjie & Zhou, Yong, 2014. "Inference for the treatment effects in two sample problems with right-censored and length-biased data," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 17-24.
    7. Wei Yann Tsai, 2009. "Pseudo-partial likelihood for proportional hazards models with biased-sampling data," Biometrika, Biometrika Trust, vol. 96(3), pages 601-615.
    8. Wolkewitz, Martin & Allignol, Arthur & Schumacher, Martin & Beyersmann, Jan, 2010. "Two Pitfalls in Survival Analyses of Time-Dependent Exposure: A Case Study in a Cohort of Oscar Nominees," The American Statistician, American Statistical Association, vol. 64(3), pages 205-211.
    9. Min Zhang & Douglas E. Schaubel, 2012. "Double-Robust Semiparametric Estimator for Differences in Restricted Mean Lifetimes in Observational Studies," Biometrics, The International Biometric Society, vol. 68(4), pages 999-1009, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Xiaoran & Du, Junjie & Bai, Fangfang, 2023. "Semiparametric inference of treatment effects on restricted mean survival time in two sample problems from length-biased samples," Statistics & Probability Letters, Elsevier, vol. 193(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chi Hyun Lee & Jing Ning & Yu Shen, 2018. "Analysis of restricted mean survival time for length†biased data," Biometrics, The International Biometric Society, vol. 74(2), pages 575-583, June.
    2. 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.
    3. 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.
    4. 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.
    5. Yang, Xiaoran & Du, Junjie & Bai, Fangfang, 2023. "Semiparametric inference of treatment effects on restricted mean survival time in two sample problems from length-biased samples," Statistics & Probability Letters, Elsevier, vol. 193(C).
    6. Xuerong Chen & Yeqian Liu & Jianguo Sun & Yong Zhou, 2016. "Semiparametric Quantile Regression Analysis of Right-censored and Length-biased Failure Time Data with Partially Linear Varying Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 921-938, December.
    7. 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.
    8. 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.
    9. Zexi Cai & Tony Sit, 2020. "Censored quantile regression model with time‐varying covariates under length‐biased sampling," Biometrics, The International Biometric Society, vol. 76(4), pages 1201-1215, December.
    10. 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.
    11. 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.
    12. Lin, Cunjie & Zhou, Yong, 2016. "Semiparametric varying-coefficient model with right-censored and length-biased data," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 119-144.
    13. Li Xun & Li Tao & Yong Zhou, 2020. "Estimators of quantile difference between two samples with length-biased and right-censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 409-429, June.
    14. 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.
    15. 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.
    16. Chyong-Mei Chen & Pao-sheng Shen & Yi Liu, 2021. "On semiparametric transformation model with LTRC data: pseudo likelihood approach," Statistical Papers, Springer, vol. 62(1), pages 3-30, February.
    17. Micha Mandel & Jacobo de Uña†à lvarez & David K. Simon & Rebecca A. Betensky, 2018. "Inverse probability weighted Cox regression for doubly truncated data," Biometrics, The International Biometric Society, vol. 74(2), pages 481-487, June.
    18. Lin, Cunjie & Zhou, Yong, 2014. "Analyzing right-censored and length-biased data with varying-coefficient transformation model," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 45-63.
    19. 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.
    20. Jieli Ding & Tsui-Shan Lu & Jianwen Cai & Haibo Zhou, 2017. "Recent progresses in outcome-dependent sampling with failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 57-82, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:lifeda:v:26:y:2020:i:4:d:10.1007_s10985-020-09498-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.