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Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model

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  • Wen, Chi-Chung
  • Chen, Yi-Hau

Abstract

The Cox model with frailties has been popular for regression analysis of clustered event time data under right censoring. However, due to the lack of reliable computation algorithms, the frailty Cox model has been rarely applied to clustered current status data, where the clustered event times are subject to a special type of interval censoring such that we only observe for each event time whether it exceeds an examination (censoring) time or not. Motivated by the cataract dataset from a cross-sectional study, where bivariate current status data were observed for the occurrence of cataracts in the right and left eyes of each study subject, we develop a very efficient and stable computation algorithm for nonparametric maximum likelihood estimation of gamma-frailty Cox models with clustered current status data. The algorithm proposed is based on a set of self-consistency equations and the contraction principle. A convenient profile-likelihood approach is proposed for variance estimation. Simulation and real data analysis exhibit the nice performance of our proposal.

Suggested Citation

  • Wen, Chi-Chung & Chen, Yi-Hau, 2011. "Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1053-1060, February.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:1053-1060
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    References listed on IDEAS

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    1. 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.
    2. C. P. Farrington & M. N. Kanaan & N. J. Gay, 2001. "Estimation of the basic reproduction number for infectious diseases from age‐stratified serological survey data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 251-292.
    3. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
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    Cited by:

    1. Gamage, Prabhashi W. Withana & McMahan, Christopher S. & Wang, Lianming & Tu, Wanzhu, 2018. "A Gamma-frailty proportional hazards model for bivariate interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 354-366.
    2. Qingning Zhou & Tao Hu & Jianguo Sun, 2017. "A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 664-672, April.
    3. Huazhen Yu & Rui Zhang & Lixin Zhang, 2024. "Copula-based analysis of dependent current status data with semiparametric linear transformation model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 742-775, October.
    4. Wang, Naichen & Wang, Lianming & McMahan, Christopher S., 2015. "Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 140-150.
    5. Jialiang Li & Tonghui Yu & Jing Lv & Mei‐Ling Ting Lee, 2021. "Semiparametric model averaging prediction for lifetime data via hazards regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1187-1209, November.
    6. Donglin Zeng & Fei Gao & D. Y. Lin, 2017. "Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data," Biometrika, Biometrika Trust, vol. 104(3), pages 505-525.
    7. Shuwei Li & Jianguo Sun & Tian Tian & Xia Cui, 2020. "Semiparametric regression analysis of doubly censored failure time data from cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 315-338, April.
    8. Du, Mingyue & Li, Huiqiong & Sun, Jianguo, 2021. "Regression analysis of censored data with nonignorable missing covariates and application to Alzheimer Disease," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    9. Li, Shuwei & Hu, Tao & Wang, Peijie & Sun, Jianguo, 2017. "Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 75-86.

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