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Inference for A Generalized Family of Distributions Under Partially Observed Left Truncated and Right Censored Competing Risks Data

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  • Prakash Chandra

    (Indian Institute of Technology Patna
    Bihar Mausam Sewa Kendra, Sardar Patel Bhawan)

  • Arvind Kumar Alok

    (Indian Institute of Technology (Indian School of Mines))

  • Yogesh Mani Tripathi

    (Indian Institute of Technology Patna)

  • Liang Wang

    (School of Mathematics, Yunnan Normal University)

Abstract

We make inference for a competing risks model under the assumption that observations are left-truncated and right-censored and failure causes are partially observed. When the latent failure times follow a generalized family of distributions, inference for unknown parameters is provided using classical and Bayesian approaches. Particularly existence-uniqueness properties of maximum likelihood estimators are established. Subsequently interval estimators are constructed based on observed Fisher information matrix. Bayes estimates and associated highest posterior density intervals are developed using gamma-beta prior distributions by considering squared error loss function. We also study estimation problem when parameters are order restricted. The performance of all estimators is evaluated based on an extensive simulation study and comments are obtained. A real data set is also analyzed for illustration purposes.

Suggested Citation

  • Prakash Chandra & Arvind Kumar Alok & Yogesh Mani Tripathi & Liang Wang, 2024. "Inference for A Generalized Family of Distributions Under Partially Observed Left Truncated and Right Censored Competing Risks Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 809-844, November.
    • Handle: RePEc:spr:sankhb:v:86:y:2024:i:2:d:10.1007_s13571-024-00332-0
    DOI: 10.1007/s13571-024-00332-0
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    References listed on IDEAS

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    1. Balakrishnan, N. & Mitra, Debanjan, 2012. "Left truncated and right censored Weibull data and likelihood inference with an illustration," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4011-4025.
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    3. Shuvashree Mondal & Debasis Kundu, 2019. "Point and Interval Estimation of Weibull Parameters Based on Joint Progressively Censored Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-25, June.
    4. 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.
    5. Peng, Mengjiao & Xiang, Liming & Wang, Shanshan, 2018. "Semiparametric regression analysis of clustered survival data with semi-competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 53-70.
    6. 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.
    7. Jia-Han Shih & Takeshi Emura, 2018. "Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula," Computational Statistics, Springer, vol. 33(3), pages 1293-1323, September.
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