Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling

Ying Zhou, Liang Wang (), Tzong-Ru Tsai and Yogesh Mani Tripathi
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Ying Zhou: School of Mathematics, Yunnan Normal University, Kunming 650500, China
Liang Wang: School of Mathematics, Yunnan Normal University, Kunming 650500, China
Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251037, Taiwan
Yogesh Mani Tripathi: Department of Mathematics, Indian Institute of Technology Patna, Bihta 801103, India

Mathematics, 2023, vol. 11, issue 6, 1-30

Abstract: The ranked set sampling (RSS) is an efficient and flexible sampling method. Based on a modified RSS named minimum ranked set sampling samples (MinRSSU), inference of a dependent competing risks model is proposed in this paper. Then, Marshall–Olkin bivariate distribution model is used to describe the dependence of competing risks. When the competing risks data follow the proportional hazard rate distribution, a dependent competing risks model based on MinRSSU sampling is constructed. In addition, the model parameters and reliability indices were estimated by the classical and Bayesian method. Maximum likelihood estimators and corresponding asymptotic confidence intervals are constructed by using asymptotic theory. In addition, the Bayesian estimator and highest posterior density credible intervals are established under the general prior. Furthermore, according to E-Bayesian theory, the point and interval estimators of model parameters and reliability indices are obtained by a sampling algorithm. Finally, extensive simulation studies and a real-life example are presented for illustrations.

Keywords: dependent competing risks; bivariate distribution family; maximum likelihood estimation; bayesian estimation; E-Bayesian estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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