Bayesian reference analysis for proportional hazards model of random censorship with Weibull distribution

Maria Ajmal; Muhammad Yameen Danish; Ayesha Tahira

Kybernetika (2022)

  • Volume: 58, Issue: 1, page 25-42
  • ISSN: 0023-5954

Abstract

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This article deals with the objective Bayesian analysis of random censorship model with informative censoring using Weibull distribution. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. The reference prior method is based on the Kullback-Leibler divergence between the prior and the corresponding posterior distribution and easy to implement when the information matrix exists in closed-form. We apply this method to Weibull random censorship model and compare it with Jeffreys and maximum likelihood methods. It is observed that the closed-form expressions for the Bayes estimators are not possible; we use importance sampling technique to obtain the approximate Bayes estimates. The behaviour of maximum likelihood and Bayes estimators is observed via extensive numerical simulation. The proposed methodology is used for the analysis of a real-life data for illustration and appropriateness of the model is tested by Henze goodness-of-fit test.

How to cite

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Ajmal, Maria, Danish, Muhammad Yameen, and Tahira, Ayesha. "Bayesian reference analysis for proportional hazards model of random censorship with Weibull distribution." Kybernetika 58.1 (2022): 25-42. <http://eudml.org/doc/297692>.

@article{Ajmal2022,
abstract = {This article deals with the objective Bayesian analysis of random censorship model with informative censoring using Weibull distribution. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. The reference prior method is based on the Kullback-Leibler divergence between the prior and the corresponding posterior distribution and easy to implement when the information matrix exists in closed-form. We apply this method to Weibull random censorship model and compare it with Jeffreys and maximum likelihood methods. It is observed that the closed-form expressions for the Bayes estimators are not possible; we use importance sampling technique to obtain the approximate Bayes estimates. The behaviour of maximum likelihood and Bayes estimators is observed via extensive numerical simulation. The proposed methodology is used for the analysis of a real-life data for illustration and appropriateness of the model is tested by Henze goodness-of-fit test.},
author = {Ajmal, Maria, Danish, Muhammad Yameen, Tahira, Ayesha},
journal = {Kybernetika},
keywords = {Jeffreys prior method; reference prior method; random censorship model; Kaplan–Meier survival estimate; Henze goodness-of-fit test},
language = {eng},
number = {1},
pages = {25-42},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bayesian reference analysis for proportional hazards model of random censorship with Weibull distribution},
url = {http://eudml.org/doc/297692},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Ajmal, Maria
AU - Danish, Muhammad Yameen
AU - Tahira, Ayesha
TI - Bayesian reference analysis for proportional hazards model of random censorship with Weibull distribution
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 1
SP - 25
EP - 42
AB - This article deals with the objective Bayesian analysis of random censorship model with informative censoring using Weibull distribution. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. The reference prior method is based on the Kullback-Leibler divergence between the prior and the corresponding posterior distribution and easy to implement when the information matrix exists in closed-form. We apply this method to Weibull random censorship model and compare it with Jeffreys and maximum likelihood methods. It is observed that the closed-form expressions for the Bayes estimators are not possible; we use importance sampling technique to obtain the approximate Bayes estimates. The behaviour of maximum likelihood and Bayes estimators is observed via extensive numerical simulation. The proposed methodology is used for the analysis of a real-life data for illustration and appropriateness of the model is tested by Henze goodness-of-fit test.
LA - eng
KW - Jeffreys prior method; reference prior method; random censorship model; Kaplan–Meier survival estimate; Henze goodness-of-fit test
UR - http://eudml.org/doc/297692
ER -

References

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