March 2023 A new class of bivariate Sushila distributions in presence of right-censored and cure fraction
Ricardo Puziol de Oliveira, Marcos Vinicius de Oliveira Peres, Jorge Alberto Achcar, Edson Z. Martinez
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Braz. J. Probab. Stat. 37(1): 55-72 (March 2023). DOI: 10.1214/22-BJPS560

Abstract

The present study introduces a new bivariate distribution based on the Sushila distribution to model bivariate lifetime data in presence of a cure fraction, right- censored data and covariates. The new bivariate probability distribution was obtained using a methodology used in the reliability theory based on fatal shocks, usually used to build new bivariate models. Additionally, the cure rate was introduced in the model based on a generalization of standard mixture models extensively used for the univariate lifetime case. The inferences of interest for the model parameters are obtained under a Bayesian approach using MCMC (Markov Chain Monte Carlo) simulation methods to generate samples of the joint posterior distribution for all parameters of the model. A simulation study was developed to study the inferential properties of the new methodology.The proposed methodology also was applied to analyze a set of real medical data obtained from a retrospective cohort study that aimed to assess specific clinical conditions that affect the lives of patients with diabetic retinopathy. For the discrimination of the proposed model with other usual models used in the analysis of bivariate survival data, some Bayesian techniques of model discrimination were used and the model validation was verified from usual Cox-Snell residuals, which allowed us to identify the adequacy of the proposed bivariate cure rate model.

Acknowledgments

The authors would like to thank the anonymous referees for the careful reading and thoughtful suggestions for improving this work’s content.

Citation

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Ricardo Puziol de Oliveira. Marcos Vinicius de Oliveira Peres. Jorge Alberto Achcar. Edson Z. Martinez. "A new class of bivariate Sushila distributions in presence of right-censored and cure fraction." Braz. J. Probab. Stat. 37 (1) 55 - 72, March 2023. https://doi.org/10.1214/22-BJPS560

Information

Received: 1 December 2021; Accepted: 1 December 2022; Published: March 2023
First available in Project Euclid: 27 April 2023

MathSciNet: MR4580884
zbMATH: 07692849
Digital Object Identifier: 10.1214/22-BJPS560

Keywords: Bayesian inference , correlation coefficient , Marshall and Olkin approach , Sushila distribution

Rights: Copyright © 2023 Brazilian Statistical Association

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Vol.37 • No. 1 • March 2023
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