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Regression Analysis of Interval-Censored Data with Informative Observation Times Under the Accelerated Failure Time Model

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Abstract

This paper discusses regression analysis of interval-censored failure time data arising from the accelerated failure time model in the presence of informative censoring. For the problem, a sieve maximum likelihood estimation approach is proposed and in the method, the copula model is employed to describe the relationship between the failure time of interest and the censoring or observation process. Also I-spline functions are used to approximate the unknown functions in the model, and a simulation study is carried out to assess the finite sample performance of the proposed approach and suggests that it works well in practical situations. In addition, an illustrative example is provided.

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References

  1. Chen C, Lu T, Chen M, et al., Semiparametric transformation models for current status data with informative censoring, Biometrical Journal, 2012, 54(5): 641–656.

    Article  MathSciNet  Google Scholar 

  2. Finkelstein D, A proportional hazards model for interval-censored failure time data, Biometrics, 1986, 42: 845–854.

    Article  MathSciNet  Google Scholar 

  3. Huang J, Efficient estimation for the proportional hazards model with interval censoring, The Annals of Statistics, 1996, 24(2): 540–568.

    Article  MathSciNet  Google Scholar 

  4. Sun J, The Statistical Analysis of Interval-Censored Failure Time Data, Springer Science & Business Media, New York, 2006.

    MATH  Google Scholar 

  5. Finkelstein D and Wolfe R, A semiparametric model for regression analysis of interval-censored failure time data, Biometrics, 1985, 41: 933–945.

    Article  MathSciNet  Google Scholar 

  6. Zeng D, Cai J, and Shen Y, Semiparametric additive risks model for interval-censored data, Statistica Sinica, 2006, 16: 287–302.

    MathSciNet  MATH  Google Scholar 

  7. Wang L, McMahan C, Hudgens M, et al., A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data, Biometrics, 2016, 72(1): 222–231.

    Article  MathSciNet  Google Scholar 

  8. Zeng D, Mao L, and Lin D, Maximum likelihood estimation for semiparametric transformation models with interval-censored data, Biometrika, 2016, 103(2): 253–271.

    Article  MathSciNet  Google Scholar 

  9. Zhou Q, Hu T, and Sun J, A sieve semiparametric maximum likelihood approach for regression analysis of bivariate interval-censored failure time data, Journal of the American Statistical Association, 2017, 112(518): 664–672.

    Article  MathSciNet  Google Scholar 

  10. Zeng D, Gao F, and Lin D, Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data, Biometrika, 2017, 104(3): 505–525.

    Article  MathSciNet  Google Scholar 

  11. Huang X and Wolfe R, A frailty model for informative censoring, Biometrics, 2002, 58: 510–520.

    Article  MathSciNet  Google Scholar 

  12. Zhang Z, Sun L, Sun J, et al., Regression analysis of failure time data with informative interval censoring, Statistics in Medicine, 2007, 26: 2533–2546.

    Article  MathSciNet  Google Scholar 

  13. Wang P, Zhao H, and Sun J, Regression analysis of case K interval-censored failure time data in the presence of informative censoring, Biometrics, 2016, 72(4): 1103–1112.

    Article  MathSciNet  Google Scholar 

  14. Ma L, Hu T, and Sun J, Cox regression analysis of dependent interval-censored failure time data, Computational Statistics and Data Analysis, 2016, 103: 79–90.

    Article  MathSciNet  Google Scholar 

  15. Zhao S, Hu T, Ma L, et al., Regression analysis of interval-censored failure time data with the additive hazards model in the presence of informative censoring, Statistics and Its Interface, 2015, 8(3): 367–377.

    Article  MathSciNet  Google Scholar 

  16. Xu D, Zhao S, Hu T, et al., Regression analysis of informatively interval-censored failure time data with semiparametric linear transformation model, Journal of Nonparametric Statistics, 2019, 31(3): 663–679.

    Article  MathSciNet  Google Scholar 

  17. Lin D, Wei L, and Ying Z, Accelerated failure time models for counting processes, Biometrika, 1998, 85(3): 605–618.

    Article  MathSciNet  Google Scholar 

  18. Jin Z, Lin D, Wei L, et al., Rank-based inference for the accelerated failure time model, Biometrika, 2003, 90(2): 341–353.

    Article  MathSciNet  Google Scholar 

  19. Zeng D and Lin D, Efficient estimation for the accelerated failure time model, Journal of the American Statistical Association, 2007, 102(480): 1387–1396.

    Article  MathSciNet  Google Scholar 

  20. Rabinowitz D, Tsiatis A, and Aragon J, Regression with interval-censored data, Biometrika, 1995, 82(3): 501–513.

    Article  MathSciNet  Google Scholar 

  21. Betensky R, Rabinowitz D, and Tsiatis A, Computationally simple accelerated failure time regression for interval censored data, Biometrika, 2001, 88: 703–711.

    Article  MathSciNet  Google Scholar 

  22. Nelsen R, An Introduction to Copulas, Springer Science and Business Media, New York, 2006.

    MATH  Google Scholar 

  23. Lu M, Zhang Y, and Huang J, Estimation of the mean function with panel count data using monotone polynomial splines, Biometrika, 2007, 94(3): 705–718.

    Article  MathSciNet  Google Scholar 

  24. Schumaker L, Spline Functions: Basic Theory, Cambridge University Press, Cambridge, 2007.

    Book  Google Scholar 

  25. Murphy S and Vaart A, On profile likelihood, Journal of the American Statistical Association, 2000, 95(450): 449–465.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun, 130012, China

    Shishun Zhao & Lijian Dong

  2. Department of Statistics, University of Missouri, Columbia, MO, 65211, USA

    Jianguo Sun

Authors
  1. Shishun Zhao
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  2. Lijian Dong
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  3. Jianguo Sun
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Corresponding author

Correspondence to Shishun Zhao.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11671168 and the Science and Technology Developing Plan of Jilin Province under Grant No. 20200201258JC.

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Zhao, S., Dong, L. & Sun, J. Regression Analysis of Interval-Censored Data with Informative Observation Times Under the Accelerated Failure Time Model. J Syst Sci Complex 35, 1520–1534 (2022). https://doi.org/10.1007/s11424-021-0209-y

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  • DOI: https://doi.org/10.1007/s11424-021-0209-y

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