IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v8y2012i1n29.html
   My bibliography  Save this article

Survival Curve Estimation with Dependent Left Truncated Data Using Cox's Model

Author

Listed:
  • Mackenzie Todd

    (Dartmouth College)

Abstract

The Kaplan-Meier and closely related Lynden-Bell estimators are used to provide nonparametric estimation of the distribution of a left-truncated random variable. These estimators assume that the left-truncation variable is independent of the time-to-event. This paper proposes a semiparametric method for estimating the marginal distribution of the time-to-event that does not require independence. It models the conditional distribution of the time-to-event given the truncation variable using Cox's model for left truncated data, and uses inverse probability weighting. We report the results of simulations and illustrate the method using a survival study.

Suggested Citation

  • Mackenzie Todd, 2012. "Survival Curve Estimation with Dependent Left Truncated Data Using Cox's Model," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-20, October.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:29
    DOI: 10.1515/1557-4679.1312
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1557-4679.1312
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/1557-4679.1312?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. Martin, Emily C. & Betensky, Rebecca A., 2005. "Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 484-492, June.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Lior Rennert & Sharon X. Xie, 2022. "Cox regression model under dependent truncation," Biometrics, The International Biometric Society, vol. 78(2), pages 460-473, June.
    3. Moreira, C. & de Uña-Álvarez, J. & Meira-Machado, L., 2016. "Nonparametric regression with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 294-307.
    4. Austin, Matthew D. & Betensky, Rebecca A., 2014. "Eliminating bias due to censoring in Kendall’s tau estimators for quasi-independence of truncation and failure," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 16-26.
    5. van den Berg, Gerard J. & Effraimidis, Georgios, 2014. "Dependence Measures in Bivariate Gamma Frailty Models," IZA Discussion Papers 8083, Institute of Labor Economics (IZA).
    6. Martin Forster & S. D. Smith, 2011. "Surviving slavery: mortality at Mesopotamia, a Jamaican sugar estate, 1762–1832," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(4), pages 907-929, October.
    7. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    8. Lior Rennert & Sharon X. Xie, 2018. "Cox regression model with doubly truncated data," Biometrics, The International Biometric Society, vol. 74(2), pages 725-733, June.
    9. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    10. Stephan M. Bischofberger, 2020. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time," Risks, MDPI, vol. 8(1), pages 1-17, January.
    11. Jing Qian & Sy Han Chiou & Rebecca A. Betensky, 2022. "Transformation model based regression with dependently truncated and independently censored data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 395-416, March.
    12. Emura, Takeshi & Konno, Yoshihiko, 2012. "A goodness-of-fit test for parametric models based on dependently truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2237-2250.
    13. Ying Wu & Richard J. Cook, 2018. "Variable selection and prediction in biased samples with censored outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 72-93, January.
    14. T. Emura & K. Murotani, 2015. "An algorithm for estimating survival under a copula-based dependent truncation model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 734-751, December.
    15. Carla Moreira & Jacobo de Uña-Álvarez & Roel Braekers, 2021. "Nonparametric estimation of a distribution function from doubly truncated data under dependence," Computational Statistics, Springer, vol. 36(3), pages 1693-1720, September.
    16. Chiou, Sy Han & Qian, Jing & Mormino, Elizabeth & Betensky, Rebecca A., 2018. "Permutation tests for general dependent truncation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 308-324.
    17. Rebecca A. Betensky & Jing Qian & Jingyao Hou, 2023. "Nonparametric and semiparametric estimation with sequentially truncated survival data," Biometrics, The International Biometric Society, vol. 79(2), pages 1000-1013, June.
    18. Qian, Jing & Betensky, Rebecca A., 2014. "Assumptions regarding right censoring in the presence of left truncation," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 12-17.
    19. Micha Mandel & Rebecca A. Betensky, 2007. "Testing Goodness of Fit of a Uniform Truncation Model," Biometrics, The International Biometric Society, vol. 63(2), pages 405-412, June.
    20. Emura, Takeshi & Wang, Weijing, 2010. "Testing quasi-independence for truncation data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 223-239, 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:bpj:ijbist:v:8:y:2012:i:1:n:29. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.