IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i1p874-887.html
   My bibliography  Save this article

Robust accelerated failure time regression

Author

Listed:
  • Locatelli, Isabella
  • Marazzi, Alfio
  • Yohai, Victor J.

Abstract

Robust estimators for accelerated failure time models with asymmetric (or symmetric) error distribution and censored observations are proposed. It is assumed that the error model belongs to a log-location-scale family of distributions and that the mean response is the parameter of interest. Since scale is a main component of mean, scale is not treated as a nuisance parameter. A three steps procedure is proposed. In the first step, an initial high breakdown point S estimate is computed. In the second step, observations that are unlikely under the estimated model are rejected or down weighted. Finally, a weighted maximum likelihood estimate is computed. To define the estimates, functions of censored residuals are replaced by their estimated conditional expectation given that the response is larger than the observed censored value. The rejection rule in the second step is based on an adaptive cut-off that, asymptotically, does not reject any observation when the data are generated according to the model. Therefore, the final estimate attains full efficiency at the model, with respect to the maximum likelihood estimate, while maintaining the breakdown point of the initial estimator. Asymptotic results are provided. The new procedure is evaluated with the help of Monte Carlo simulations. Two examples with real data are discussed.

Suggested Citation

  • Locatelli, Isabella & Marazzi, Alfio & Yohai, Victor J., 2011. "Robust accelerated failure time regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 874-887, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:874-887
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00296-3
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Zeng, Donglin & Lin, D.Y., 2007. "Efficient Estimation for the Accelerated Failure Time Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1387-1396, December.
    2. Kim, Jin Seon & Yum, Bong-Jin, 2008. "Selection between Weibull and lognormal distributions: A comparative simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 477-485, December.
    3. Marazzi, Alfio & Villar, Ana J. & Yohai, Victor J., 2009. "Robust Response Transformations Based on Optimal Prediction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 360-370.
    4. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    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. Jad Beyhum & Ingrid Keilegom, 2023. "Robust censored regression with $$\ell _1$$ ℓ 1 -norm regularization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 146-162, March.
    2. Sanjoy K. Sinha, 2019. "Robust estimation in accelerated failure time models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 52-78, January.

    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. 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.
    2. 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.
    3. 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.
    4. Zhang, Jiajia & Peng, Yingwei, 2009. "Crossing hazard functions in common survival models," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2124-2130, October.
    5. Jon Arni Steingrimsson & Robert L. Strawderman, 2017. "Estimation in the Semiparametric Accelerated Failure Time Model With Missing Covariates: Improving Efficiency Through Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1221-1235, July.
    6. Fan, Caiyun & Lu, Wenbin & Zhou, Yong, 2021. "Testing error heterogeneity in censored linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    7. Ying Ding & Bin Nan, 2015. "Estimating Mean Survival Time: When is it Possible?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 397-413, June.
    8. Yu, Lili & Zhao, Yichuan, 2024. "Laplace approximated quasi-likelihood method for heteroscedastic survival data," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    9. Lili Yu & Liang Liu & Ding-Geng(Din) Chen, 2013. "Weighted Least-Squares Method for Right-Censored Data in Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 69(2), pages 358-365, June.
    10. Jing Ning & Jing Qin & Yu Shen, 2014. "Score Estimating Equations from Embedded Likelihood Functions Under Accelerated Failure Time Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1625-1635, December.
    11. Zou, Yubo & Zhang, Jiajia & Qin, Guoyou, 2011. "A semiparametric accelerated failure time partial linear model and its application to breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1479-1487, March.
    12. Jichang Yu & Haibo Zhou & Jianwen Cai, 2021. "Accelerated failure time model for data from outcome-dependent sampling," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 15-37, January.
    13. Alexander Hanbo Li & Jelena Bradic, 2019. "Censored Quantile Regression Forests," Papers 1902.03327, arXiv.org.
    14. Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.
    15. Yijian Huang, 2013. "Fast Censored Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 789-806, December.
    16. Zhang, Jiajia & Peng, Yingwei & Li, Haifen, 2013. "A new semiparametric estimation method for accelerated hazards mixture cure model," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 95-102.
    17. Rajkumar Bhimgonda Patil & Basavraj S Kothavale & Laxman Yadu Waghmode, 2019. "Selection of time-to-failure model for computerized numerical control turning center based on the assessment of trends in maintenance data," Journal of Risk and Reliability, , vol. 233(2), pages 105-117, April.
    18. 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.
    19. Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2023. "Automatic robust Box–Cox and extended Yeo–Johnson transformations in regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 75-102, March.
    20. Francisco J. Rubio & Yili Hong, 2016. "Survival and lifetime data analysis with a flexible class of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1794-1813, August.

    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:eee:csdana:v:55:y:2011:i:1:p:874-887. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.