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Maximum likelihood estimation for the proportional hazards model with partly interval‐censored data

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  • Jong S. Kim

Abstract

Summary. The maximum likelihood estimator (MLE) for the proportional hazards model with partly interval‐censored data is studied. Under appropriate regularity conditions, the MLEs of the regression parameter and the cumulative hazard function are shown to be consistent and asymptotically normal. Two methods to estimate the variance–covariance matrix of the MLE of the regression parameter are considered, based on a generalized missing information principle and on a generalized profile information procedure. Simulation studies show that both methods work well in terms of the bias and variance for samples of moderate size. An example illustrates the methods.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:2:p:489-502
    DOI: 10.1111/1467-9868.00398
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    Cited by:

    1. Yanqing Sun & Qingning Zhou & Peter B. Gilbert, 2023. "Analysis of the Cox Model with Longitudinal Covariates with Measurement Errors and Partly Interval Censored Failure Times, with Application to an AIDS Clinical Trial," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 430-454, July.
    2. Audrey Boruvka & Richard J. Cook, 2015. "A Cox-Aalen Model for Interval-censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 414-426, June.
    3. Tomoyuki Sugimoto, 2013. "Asymptotic distribution of the nonparametric distribution estimator based on a martingale approach in doubly censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 859-888, October.
    4. 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.
    5. Li, Jinqing & Ma, Jun, 2019. "Maximum penalized likelihood estimation of additive hazards models with partly interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 170-180.
    6. Li‐Pang Chen & Bangxu Qiu, 2023. "Analysis of length‐biased and partly interval‐censored survival data with mismeasured covariates," Biometrics, The International Biometric Society, vol. 79(4), pages 3929-3940, December.
    7. 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.
    8. Fei Gao & Donglin Zeng & Dan‐Yu Lin, 2017. "Semiparametric estimation of the accelerated failure time model with partly interval‐censored data," Biometrics, The International Biometric Society, vol. 73(4), pages 1161-1168, December.
    9. Mongoué-Tchokoté, Solange & Kim, Jong-Sung, 2008. "New statistical software for the proportional hazards model with current status data," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4272-4286, May.
    10. Valentin Patilea & Jean-Marc Rolin, 2004. "Product-limit Estimators of the Survival Function with Left or Right Censored Data," Working Papers 2004-36, Center for Research in Economics and Statistics.

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