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An EM algorithm for the proportional hazards model with doubly censored data

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  • Kim, Yongdai
  • Kim, Joungyoun
  • Jang, Woncheol

Abstract

In this paper, we consider a new procedure for estimating parameters in the proportional hazards model with doubly censored data. Computing the maximum likelihood estimator with doubly censored data is often nontrivial and requires a certain constraint optimization procedure, which is computationally unstable and sometimes fails to converge. We propose an approximated likelihood and study the maximum approximated likelihood estimator, which is obtained by maximizing the approximated likelihood. In comparison to the maximum likelihood estimator, this new estimator is stable and always converges with an efficient EM algorithm we develop. The stability of the new estimator even with moderate sample sizes is amply demonstrated through simulated and real data. For theoretical justification of the approximated likelihood, we show the consistency of the maximum approximated likelihood estimator.

Suggested Citation

  • Kim, Yongdai & Kim, Joungyoun & Jang, Woncheol, 2013. "An EM algorithm for the proportional hazards model with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 41-51.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:41-51
    DOI: 10.1016/j.csda.2012.06.001
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    References listed on IDEAS

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    1. Jong S. Kim, 2003. "Maximum likelihood estimation for the proportional hazards model with partly interval‐censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 489-502, May.
    2. Kim, Yongdai & Kim, Bumsoo & Jang, Woncheol, 2010. "Asymptotic properties of the maximum likelihood estimator for the proportional hazards model with doubly censored data," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1339-1351, July.
    3. T. Cai, 2004. "Semiparametric regression analysis for doubly censored data," Biometrika, Biometrika Trust, vol. 91(2), pages 277-290, June.
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    Citations

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    Cited by:

    1. Rafael Weißbach & Yongdai Kim & Achim Dörre & Anne Fink & Gabriele Doblhammer, 2021. "Left-censored dementia incidences in estimating cohort effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 38-63, January.
    2. Choi, Taehwa & Kim, Arlene K.H. & Choi, Sangbum, 2021. "Semiparametric least-squares regression with doubly-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    3. Xu, Wenjing & Pan, Qing & Gastwirth, Joseph L., 2014. "Cox proportional hazards models with frailty for negatively correlated employment processes," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 295-307.

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