逐步Ⅰ型混合截尾竞争失效模型的贝叶斯分析（英文）

逐步Ⅰ型混合截尾竞争失效模型的贝叶斯分析（英文）Title: Bayesian Analysis of the Stepwise Type I Truncated Mixture Competing

Ⅰ 逐步型混合截尾竞争失效模型的贝叶斯分析（英 文） Title: Bayesian Analysis of the Stepwise Type ITruncated Mixture Competing Risks Failure Model Abstract: The stepwise type Itruncated mixture competing risks failure model is widely used in survival analysis to study the effect of different competing risks on the failure time. In this paper, we present a Bayesian analysis of this model using Markov Chain Monte Carlo (MCMC) methods. We start by providing abrief introduction to the stepwise type Itruncated mixture competing risks failure model and its statistical properties. Then, we discuss the implementation of the Bayesian analysis, including the specification of prior distributions, derivation of the posterior distribution, and the sampling algorithms for MCMC. Finally, we present asimulation study to assess the performance of the Bayesian analysis and apply the method to areal data example. 1. Introduction Survival analysis has become an essential tool in many fields such as medical research, engineering, and finance. Competing risks failure models are commonly used to consider the presence of multiple causes of failure in survival data. The stepwise type Itruncated mixture model allows for the analysis of competing risks while accounting for the potential truncation of the failure time. In this section, we provide an introduction to the model, its mathematical formulation, and its statistical properties. 2. Bayesian Analysis of the Stepwise Type ITruncated Mixture Competing Risks Failure Model 2.1 Specification of Prior Distributions: We discuss the selection and specification of prior distributions for the model parameters, including the baseline hazard functions, mixing proportions, and covariate effects. We consider informative and non-informative priors and discuss their implications on the posterior inference. 2.2 Derivation of the Posterior Distribution: We derive the posterior distribution of the model parameters given the observed data. We discuss the use of data augmentation techniques to handle the