广义治愈率模型的贝叶斯推断  

Bayesian Inference on the Generalized Cure Rate Model

作　　者：杨陈慧 廖雪丽 夏业茂[1] YANG Chenhui;LIAO Xueli;XIA Yemao(College of Science,Nanjing Forestry University,Nanjing 210037,China)

机构地区：[1]南京林业大学理学院,江苏南京210037

出　　处：《应用数学》2024年第3期636-646,共11页Mathematica Applicata

基　　金：国家自然科学基金(114761);江苏省研究生科研与实践创新计划项目(SJCX22−0310)。

摘　　要：广义治愈率模型是将治愈率模型推广到含有潜在变量.潜变量的引入增加了模型的复杂度.本文给出其一个分层表示,通过引入Polya-Gamma变量和广义生存时间,将比例治愈率模型置于分层框架内.分层形式提供了计算上的便利.我们在贝叶斯框架内进行了结果展示.Generalized cure rate model is an extension of traditional cure rate model to the situation where the latent variables are included to characterize the heterogeneity of population.However,the introduction of latent variables complicates the likelihood.In this paper,a hierarchical form of the proposed model is presented to facilitate computations.By taking advantage of Polya-gamma variables,we reformulate the logistic model as the normal-type mixture model.Moreover,the censored problem is addressed via auxiliary latent variable method.Under the Bayesian framework,we implement Markov Chains Monte Carlo sampling method to conduct posterior inference.A simulation study is presented to illustrate the effectiveness of the proposed methodology.

关 键 词：广义治愈率模型 Polya-Gamma表示 MCMC抽样 

分 类 号：O212.8[理学—概率论与数理统计] O212.4[理学—数学]