IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v34y2025i2d10.1007_s10260-025-00781-5.html
   My bibliography  Save this article

Accelerated failure time and additive hazard models for combined right-censored and left-truncated right-censored failure time data

Author

Listed:
  • James McVittie

    (University of Regina)

Abstract

The semiparametric accelerated failure time and additive hazards models are commonly used alternatives to the proportional hazards model. For independent samples of right-censored or left-truncated right-censored failure time data, estimating equation based procedures are used to derive estimators for the unknown model parameters. In various applications, a sample data set can consist of multiple types of partially observed failure time data through the use of multiple sampling schemes or combination of multiple data sets. We propose three different estimation methodologies for estimating the unknown regression parameters in the accelerated failure time and additive hazards models using combined right-censored and left-truncated right-censored failure time data. These three methods are based on averaging the parametric estimators of the two samples, determining the zero-crossing of the summation of the two samples’ estimating equations and determining the zero-crossing of a single estimating equation based on the combination of the two samples. We assess the performance of the estimators through extensive simulation studies and use the estimators to model the factors affecting African lion mortality.

Suggested Citation

  • James McVittie, 2025. "Accelerated failure time and additive hazard models for combined right-censored and left-truncated right-censored failure time data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(2), pages 237-260, May.
    • Handle: RePEc:spr:stmapp:v:34:y:2025:i:2:d:10.1007_s10260-025-00781-5
    DOI: 10.1007/s10260-025-00781-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-025-00781-5
    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/s10260-025-00781-5?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. Bergeron, Pierre-Jerome & Asgharian, Masoud & Wolfson, David B., 2008. "Covariate Bias Induced by Length-Biased Sampling of Failure Times," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 737-742, June.
    2. Hirofumi Michimae & Takeshi Emura, 2022. "Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    3. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    4. James H. McVittie & David B. Wolfson & David A. Stephens, 2023. "A note on the partial likelihood estimator of the proportional hazards model for combined incident and prevalent cohort data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(4), pages 487-497, May.
    5. Gruber, Susan & Laan, Mark van der, 2012. "tmle: An R Package for Targeted Maximum Likelihood Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i13).
    6. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    7. Zheng Wenjing & van der Laan Mark J., 2012. "Targeted Maximum Likelihood Estimation of Natural Direct Effects," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-40, January.
    8. Chiung-Yu Huang & Jing Qin, 2013. "Semiparametric estimation for the additive hazards model with left-truncated and right-censored data," Biometrika, Biometrika Trust, vol. 100(4), pages 877-888.
    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. Iván Díaz & Nima S. Hejazi, 2020. "Causal mediation analysis for stochastic interventions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 661-683, July.
    3. Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression," Papers 2112.14249, arXiv.org, revised May 2025.
    4. Brooks Jordan C. & van der Laan Mark J. & Singer Daniel E. & Go Alan S., 2013. "Targeted Minimum Loss-Based Estimation of Causal Effects in Right-Censored Survival Data with Time-Dependent Covariates: Warfarin, Stroke, and Death in Atrial Fibrillation," Journal of Causal Inference, De Gruyter, vol. 1(2), pages 235-254, November.
    5. Xiang Zhou, 2022. "Semiparametric estimation for causal mediation analysis with multiple causally ordered mediators," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 794-821, July.
    6. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    7. Samuel D. Lendle & Meenakshi S. Subbaraman & Mark J. van der Laan, 2013. "Identification and Efficient Estimation of the Natural Direct Effect among the Untreated," Biometrics, The International Biometric Society, vol. 69(2), pages 310-317, June.
    8. Xu, Linzhi & Zhang, Jiajia, 2010. "An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1467-1474, June.
    9. 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.
    10. 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.
    11. Jun Wang & Yahe Yu, 2024. "Improved estimation of average treatment effects under covariate‐adaptive randomization methods," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(2), pages 310-333, May.
    12. 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.
    13. Martin Gaynor & Nirav Mehta & Seth Richards-Shubik, 2023. "Optimal Contracting with Altruistic Agents: Medicare Payments for Dialysis Drugs," American Economic Review, American Economic Association, vol. 113(6), pages 1530-1571, June.
    14. Kwun Chuen Gary Chan & Mei-Cheng Wang, 2012. "Estimating Incident Population Distribution from Prevalent Data," Biometrics, The International Biometric Society, vol. 68(2), pages 521-531, June.
    15. Xu, Linzhi & Zhang, Jiajia, 2010. "Multiple imputation method for the semiparametric accelerated failure time mixture cure model," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1808-1816, July.
    16. Martin Huber & Michael Lechner & Giovanni Mellace, 2016. "The Finite Sample Performance of Estimators for Mediation Analysis Under Sequential Conditional Independence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 139-160, January.
    17. 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.
    18. Kuhn, Peter J. & Shen, Kailing, 2010. "Gender Discrimination in Job Ads: Theory and Evidence," IZA Discussion Papers 5195, Institute of Labor Economics (IZA).
    19. Ronald Herrera & Ursula Berger & Ondine S. Von Ehrenstein & Iván Díaz & Stella Huber & Daniel Moraga Muñoz & Katja Radon, 2017. "Estimating the Causal Impact of Proximity to Gold and Copper Mines on Respiratory Diseases in Chilean Children: An Application of Targeted Maximum Likelihood Estimation," IJERPH, MDPI, vol. 15(1), pages 1-15, December.
    20. Yu-Jen Cheng & Mei-Cheng Wang, 2012. "Estimating Propensity Scores and Causal Survival Functions Using Prevalent Survival Data," Biometrics, The International Biometric Society, vol. 68(3), pages 707-716, September.

    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:stmapp:v:34:y:2025:i:2:d:10.1007_s10260-025-00781-5. 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.