| With the continuous improvement of medical technology,many complex diseases can be diagnosed and treated,leading to the existence of cured individuals.In survival analysis,mixed cure model is often used to describe this kind of survival function.Studying the semiparametric healing model has certain practical significance.Currently,Spike-and-Slab Lasso(SSL)variable selection has become a highly concerned method.In this paper,the SSL method is used in the semiparametric mixed cure model for complex censored data,and the effectiveness of this method is explored by establishing a Bayesian hierarchical database model to estimate parameters and select variables.The first part of this article is based on the SSL method to estimate and select variables for the proportional hazard part of the proportional hazards cure model under right censored data,the cure part uses the Logit model.Different from Bayesian adaptive Lasso,the SSL prior under the Bayesian framework uses a mixed Laplace distribution function and considers variable selection from the perspective of probability.SSL adaptively mixes the "deviation" terms of two Lasso,which contrasts with adaptive Lasso and other similar penalties,which assign fixed coefficient specific penalties and therefore do not push coefficient specific shrinkage to extreme values.In the simulation study,different sample sizes were compared,and the results showed that as the sample size increased,the results of variable selection gradually improved.We also compared the simulation results under different hyperparameters,and as the size of the hyperparameters was adjusted,the results also changed.Finally,the superiority of this method in variable selection and parameter estimation was verified through comparison with Bayesian adaptive Lasso.Empirical analysis selected liver cirrhosis data,and clinical research results fully verified the correctness and effectiveness of the results.The second part of this paper reconstructs the proportional hazards mixed cure model under the right censored data on the basis of the previous chapter.The cure part uses the Probit model,the Logit model uses the Logistic distribution function to connect the relationship between the independent variable and the binary response variable,it’s a discrete selection model,while the Probit model uses the Normal distribution function,it is a linear model.This chapter uses the Spike and Slab Lasso method to establish a Bayesian framework hierarchical database model,and estimates parameters and selects variables.In the simulation study,the estimated results under different sample sizes were compared,and compared the results under different deletion ratios and different cure rates to verify the effectiveness of this method when using the Probit model for the cure part.The empirical analysis applied SSL method to the case of breast cancer data in Germany(GBSG2),and the clinical research results fully verified the effectiveness of the results.The third part of this paper estimates the parameters and variable selection under the Bayesian proportional hazards cure model based on case II interval-censored data,the cure part uses the Logit model.For the model under case II interval-censored data,both the proportional hazards model regression coefficient and the cure rate regression coefficient are penalized simultaneously.A Bayesian hierarchical model is constructed for prior distributions with different parameters,and sampling is completed according to posterior inference.The accuracy of the proposed method was verified by comparing simulation studies under different sample sizes and different settings.And by comparing it with Bayesian adaptive Lasso under case II interval-censored data,the superiority of SSL method is obtained.Finally,an empirical analysis of child mortality data in Nigeria is conducted. |
