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Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data

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  • Lynn M. Johnson
  • Robert L. Strawderman

Abstract

This paper extends the induced smoothing procedure of Brown & Wang (2006) for the semiparametric accelerated failure time model to the case of clustered failure time data. The resulting procedure permits fast and accurate computation of regression parameter estimates and standard errors using simple and widely available numerical methods, such as the Newton--Raphson algorithm. The regression parameter estimates are shown to be strongly consistent and asymptotically normal; in addition, we prove that the asymptotic distribution of the smoothed estimator coincides with that obtained without the use of smoothing. This establishes a key claim of Brown & Wang (2006) for the case of independent failure time data and also extends such results to the case of clustered data. Simulation results show that these smoothed estimates perform as well as those obtained using the best available methods at a fraction of the computational cost. Copyright 2009, Oxford University Press.

Suggested Citation

  • Lynn M. Johnson & Robert L. Strawderman, 2009. "Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data," Biometrika, Biometrika Trust, vol. 96(3), pages 577-590.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:3:p:577-590
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    File URL: http://hdl.handle.net/10.1093/biomet/asp025
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    Cited by:

    1. Li, Haifen & Zhang, Jiajia & Tang, Yincai, 2012. "Induced smoothing for the semiparametric accelerated hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4312-4319.
    2. 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.
    3. Ritesh Ramchandani & Dianne M. Finkelstein & David A. Schoenfeld, 2020. "Estimation for an accelerated failure time model with intermediate states as auxiliary information," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 1-20, January.
    4. Byungtae Seo & Sangwook Kang, 2023. "Accelerated failure time modeling via nonparametric mixtures," Biometrics, The International Biometric Society, vol. 79(1), pages 165-177, March.
    5. Kyu Hyun Kim & Daniel J. Caplan & Sangwook Kang, 2023. "Smoothed quantile regression for censored residual life," Computational Statistics, Springer, vol. 38(2), pages 1001-1022, June.
    6. Chiou, Sy Han & Kang, Sangwook & Yan, Jun, 2014. "Fitting Accelerated Failure Time Models in Routine Survival Analysis with R Package aftgee," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i11).
    7. Liya Fu & Zhuoran Yang & Yan Zhou & You-Gan Wang, 2021. "An efficient Gehan-type estimation for the accelerated failure time model with clustered and censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 679-709, October.
    8. 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.
    9. Fu, Liya & Wang, You-Gan & Bai, Zhidong, 2010. "Rank regression for analysis of clustered data: A natural induced smoothing approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1036-1050, April.
    10. Zexi Cai & Tony Sit, 2023. "On interquantile smoothness of censored quantile regression with induced smoothing," Biometrics, The International Biometric Society, vol. 79(4), pages 3549-3563, December.
    11. Xue Yu & Yichuan Zhao, 2019. "Jackknife empirical likelihood inference for the accelerated failure time model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 269-288, March.
    12. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.
    13. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.
    14. 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.
    15. Wang, You-Gan & Fu, Liya, 2011. "Rank regression for accelerated failure time model with clustered and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2334-2343, July.

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