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Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution

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  • Feizjavadian, S.H.
  • Hashemi, R.

Abstract

The lifetime of subjects in reliability and survival analysis in the presence of several causes of failure (i.e., competing risks) has attracted attention in the literature. Most studies have simplified the computations by assuming that the causes are independent, though this does not hold. Dependent competing risks under progressively hybrid censoring condition using a Marshall–Olkin bivariate Weibull distribution is investigated. Maximum likelihood and approximated maximum likelihood estimators are developed for estimating the unknown parameters. Asymptotic distributions of the maximum likelihood estimators are used to construct approximate confidence intervals using the observed Fisher information matrix. Based on a simulation and real applications, it is illustrated that when a parametric distributional assumption is nearly true, a close approximation could be achieved by deliberately censoring the number of subjects and the study duration using Type-II progressively hybrid censoring, which might help to save time and money in research studies.

Suggested Citation

  • Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:19-34
    DOI: 10.1016/j.csda.2014.08.002
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    References listed on IDEAS

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    1. Pareek, Bhuvanesh & Kundu, Debasis & Kumar, Sumit, 2009. "On progressively censored competing risks data for Weibull distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4083-4094, October.
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    3. Kundu, Debasis & Dey, Arabin Kumar, 2009. "Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 956-965, February.
    4. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    5. G. Heinrich & U. Jensen, 1995. "Parameter estimation for a bivariate lifetime distribution in reliability with multivariate extensions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 49-65, December.
    6. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
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    Cited by:

    1. Sun, Yanqing & Li, Mei & Gilbert, Peter B., 2016. "Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 348-358.
    2. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    3. Debasis Kundu, 2022. "Bivariate Semi-parametric Singular Family of Distributions and its Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 846-872, November.
    4. Ke Wu & Liang Wang & Li Yan & Yuhlong Lio, 2021. "Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    5. Zhang, Fode & Shi, Yimin, 2016. "Geometry of exponential family with competing risks and censored data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 234-245.
    6. Bee, Marco & Espa, Giuseppe & Giuliani, Diego, 2015. "Approximate maximum likelihood estimation of the autologistic model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 14-26.
    7. Ying Zhou & Liang Wang & Tzong-Ru Tsai & Yogesh Mani Tripathi, 2023. "Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling," Mathematics, MDPI, vol. 11(6), pages 1-30, March.

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