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Asymptotic properties of the maximum likelihood estimator for the proportional hazards model with doubly censored data

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  • Kim, Yongdai
  • Kim, Bumsoo
  • Jang, Woncheol

Abstract

Doubly censored data, which include left as well as right censored observations, are frequently met in practice. Though estimation of the distribution function with doubly censored data has seen much study, relatively little is known about the inference of regression coefficients in the proportional hazards model for doubly censored data. In particular, theoretical properties of the maximum likelihood estimator of the regression coefficients in the proportional hazards model have not been proved yet. In this paper, we show the consistency and asymptotic normality of the maximum likelihood estimator and prove its semiparametric efficiency. The proposed methods are illustrated with simulation studies and analysis of an application from a medical study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:6:p:1339-1351
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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. Zeng, Donglin & Lin, D.Y. & Yin, Guosheng, 2005. "Maximum Likelihood Estimation for the Proportional Odds Model With Random Effects," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 470-483, June.
    3. T. Cai, 2004. "Semiparametric regression analysis for doubly censored data," Biometrika, Biometrika Trust, vol. 91(2), pages 277-290, June.
    4. Hong‐Bin Fang & Gang Li & Jianguo Sun, 2005. "Maximum Likelihood Estimation in a Semiparametric Logistic/Proportional‐Hazards Mixture Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 59-75, March.
    5. Khan, Shakeeb & Tamer, Elie, 2007. "Partial rank estimation of duration models with general forms of censoring," Journal of Econometrics, Elsevier, vol. 136(1), pages 251-280, January.
    6. anonymous, 1991. "Fed upgrades functional cost analysis program," Financial Update, Federal Reserve Bank of Atlanta, issue Win, pages 1-2,6.
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    Cited by:

    1. Kenichi Hayashi & Yasutaka Shimizu, 2018. "Estimation of a Concordance Probability for Doubly Censored Time-to-Event Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 546-567, December.
    2. 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.
    3. 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).

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