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

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.