Bayesian Adaptive Lasso Variable Selection Of Proportional Hazard Cure Model Under Complex Medical Data

In the field of biostatistics,it is often assumed that when the observation period is long enough,all subjects will experience the event of interest to the researcher.In practice,nevertheless,there is often a certain percentage of cured individuals within the study subject groups,this group of subjects is completely cured after receiving a specific treatment,in other words,they will never experience the events we are interested.Therefore,it is of great interest to study the cured model.Also,a large number of influencing factors may be encountered in practice,such as patient demographic characteristics,clinical measures,and medical history,which makes variable selection one of the important practical issues to be faced by many scholars.Most extant methods for variable selection in cured models are presented in a frequency framework.In this paper,we apply Bayesian adaptive Lasso method for simultaneous estimation and variable selection based on proportional hazards cure model.The first part focuses on parameter estimation and variable selection for a Bayesian proportional hazards cure model with right-censored data.First,a proportional hazards cure model with right censored data is established and the likelihood function of the proportional hazards cure model is constructed.solving the nonparametric problem in the model is the key,In this paper,a cubic spline approach is used to fit the model of baseline risk function.Then,a Bayesian adaptive lasso for the proportional hazards cure model is constructed using a hierarchical Bayesian framework with an appropriate prior distribution,The posterior distribution of the Bayesian Adaptive Lasso selection variables in the proportional hazards model with cure fraction can be obtained by posterior estimation.Because the posterior distribution of parameters in Bayesian estimation methods does not have a standard form.The parameters are estimated using the MCMC sampling algorithm,which combines the MH and Gibbs sampling algorithms.The simulation results confirm that this method has good characteristics.The second section focuses on parameter estimation and variable selection for a proportional hazards cure model based on Case I interval censored data with a Bayesian framework.Based on the Case I interval censored data,considering the variable selection in two different situations,firstly,a penalty term is imposed on the regression coefficient of the proportional hazards model,and then the cure rate and the regression coefficient of the proportional hazards model are penalized at the same time,and then the two cases are constructed.the objective function.Sampling is done according to a posteriori inference and the MCMC sampling algorithm.The simulation results confirm that this method has good characteristics.