IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v79y2023i2p1000-1013.html
   My bibliography  Save this article

Nonparametric and semiparametric estimation with sequentially truncated survival data

Author

Listed:
  • Rebecca A. Betensky
  • Jing Qian
  • Jingyao Hou

Abstract

In observational cohort studies with complex sampling schemes, truncation arises when the time to event of interest is observed only when it falls below or exceeds another random time, that is, the truncation time. In more complex settings, observation may require a particular ordering of event times; we refer to this as sequential truncation. Estimators of the event time distribution have been developed for simple left‐truncated or right‐truncated data. However, these estimators may be inconsistent under sequential truncation. We propose nonparametric and semiparametric maximum likelihood estimators for the distribution of the event time of interest in the presence of sequential truncation, under two truncation models. We show the equivalence of an inverse probability weighted estimator and a product limit estimator under one of these models. We study the large sample properties of the proposed estimators and derive their asymptotic variance estimators. We evaluate the proposed methods through simulation studies and apply the methods to an Alzheimer's disease study. We have developed an R package, seqTrun, for implementation of our method.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:1000-1013
    DOI: 10.1111/biom.13678
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13678
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13678?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
    ---><---

    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.
    2. Mandel, Micha, 2007. "Censoring and TruncationHighlighting the Differences," The American Statistician, American Statistical Association, vol. 61, pages 321-324, November.
    3. Pao-sheng Shen, 2010. "Nonparametric analysis of doubly truncated data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 835-853, October.
    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. Lior Rennert & Sharon X. Xie, 2022. "Cox regression model under dependent truncation," Biometrics, The International Biometric Society, vol. 78(2), pages 460-473, June.
    2. 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.
    3. 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.
    4. Shen, Pao-sheng & Hsu, Huichen, 2020. "Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. 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.
    6. 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.
    7. Stephan M. Bischofberger, 2020. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time," Risks, MDPI, vol. 8(1), pages 1-17, January.
    8. Moreira, Carla & de Una-Alvarez, Jacobo & Van Keilegom, Ingrid, 2012. "Goodness-of-fit Tests for a Semiparametric Model under Random Double Truncation," LIDAM Discussion Papers ISBA 2012024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. 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.
    10. 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.
    11. Pao-sheng Shen, 2012. "Analysis of left-truncated right-censored or doubly censored data with linear transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 584-603, September.
    12. Takeshi Emura & Ya-Hsuan Hu & Yoshihiko Konno, 2017. "Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation," Statistical Papers, Springer, vol. 58(3), pages 877-909, September.
    13. Linh Hoang Khanh Dang & Carlo Giovanni Camarda & France Meslé & Nadine Ouellette & Jean-Marie Robine & Jacques Vallin, 2023. "The question of the human mortality plateau: Contrasting insights by longevity pioneers," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 48(11), pages 321-338.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Rafael Weißbach & Dominik Wied, 2022. "Truncating the exponential with a uniform distribution," Statistical Papers, Springer, vol. 63(4), pages 1247-1270, August.
    19. 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.
    20. van den Berg, Gerard J. & Effraimidis, Georgios, 2014. "Dependence Measures in Bivariate Gamma Frailty Models," IZA Discussion Papers 8083, Institute of Labor Economics (IZA).

    More about this item

    Statistics

    Access and download statistics

    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:bla:biomet:v:79:y:2023:i:2:p:1000-1013. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.