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Weighted Lindley Shared Regression Model for Bivariate Left Censored Data

Author

Listed:
  • Shikhar Tyagi

    (Central University of Rajasthan)

  • Arvind Pandey

    (Central University of Rajasthan)

  • Christophe Chesneau

    (Université de Caen Normandie, LMNO)

Abstract

Due to the lack of complete data in biological, epidemiological, and medical studies, analysis of censored data is very common among researchers. But analysis of bivariate censored data is not a regular mechanism. Because it is not necessary to always have independent bivariate data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in data. Ignoring observed and unobserved covariates could have negative consequences. But it is not easy to find out whether there is any effect of unobserved covariate or not. Shared frailty models are the viable choice to counter such a scenario. However, due to certain constraints such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty distribution weighted Lindley for reversed hazard rate setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under reversed hazard rate setup. Generalized exponential and exponential Gumbel baseline distributions are proposed as a useful tool for ensuring the effect of unobserved heterogeneity. The Bayesian paradigm of Markov Chain Monte Carlo methodology with flat and informative prior under different loss functions is used to estimate the model parameters. Subsequently, model comparisons are performed using Bayesian comparison techniques. The popular Australian twin data set is used to illustrate the results and to demonstrate that better models are recommended.

Suggested Citation

  • Shikhar Tyagi & Arvind Pandey & Christophe Chesneau, 2022. "Weighted Lindley Shared Regression Model for Bivariate Left Censored Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 655-682, November.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00278-1
    DOI: 10.1007/s13571-022-00278-1
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    3. David D. Hanagal & Susmita M. Bhambure, 2017. "Shared gamma frailty models based on reversed hazard rate for modeling Australian twin data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 5812-5826, June.
    4. Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
    5. David D. Hanagal & Arvind Pandey, 2017. "Shared frailty models based on reversed hazard rate for modified inverse Weibull distribution as baseline distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 234-246, January.
    6. Hanagal, David D. & Pandey, Arvind, 2014. "Gamma shared frailty model based on reversed hazard rate for bivariate survival data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 190-196.
    7. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
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