Bayesian Adaptive Lasso Variable Selection For Two Regression Models With Interval Censored Data

In the studies of survival analysis,high dimensional data are prevalent.The variable selection under high dimensional variables is one of the main research problems in the survival analysis.In general,the variable selection is implemented in the framework of the regression model.The main research contents of this paper are the Bayesian adaptive Lasso variable selection problem of two kinds of regression models under interval censored data.The variable selection and regression coefficients of Cox model and AFT model are obtained by Bayesian adaptive Lasso variable selection algorithm.The first part mainly studies the variable selection of the Cox proportional hazards regression model based on the Bayesian adaptive Lasso algorithm under the type I interval censored data.Solving unknown baseline risk functions is the key to constructing the Cox proportional hazards model;In this paper,the cubic spline is chosen to approximate the baseline risk function.Then the Bayesian adaptive Lasso under the Cox proportional hazards model is constructed through the hierarchical Bayesian structure,A suitable prior distribution(such as normal distribution,exponential distribution,gamma distribution,etc.),the posterior distribution of the BaLasso variable selection under the Cox proportional hazards model is obtained by posterior estimation.Finally,the MCMC sampling algorithm combined with MH and Gibbs solves the underestimated parameters and performs variable selection.The effect of the method is verified by simulation in many cases.In the second part,we mainly study the variable selection of AFT regression model based on Bayesian adaptive Lasso algorithm under type I interval censored data.The Bayesian adaptive Lasso model of AFT model is constructed by modeling the residual and logarithmic variance of AFT model and hierarchical Bayesian structure.A suitable prior distribution(such as normal distribution,exponential distribution,gamma distribution,etc.)is found in the construction of the model.The posterior distribution of the BaLasso variable selection of AFT regression is obtained by posterior estimation.Finally,the MCMC sampling algorithm combined with MH and Gibbs solves the underestimated parameters and performs variable selection.The effect of the method is verified by simulation in many cases.