Variable Selection In Log-Birnbaum-Saunders Regression Models

The log-Birnbaum-Saunders(log-BS)regression model has a wide range of ap-plications in the fields of medicine and engineering,etc.Which is often used to de-scribe the patient's survival time and product's life.In addition,in practical problems,a large number of variables are often involved,but non-information variables will re-duce the efficiency of estimation and the accuracy of prediction.In order to choose a more reasonable modelling,under the framework of frequency and Bayesian,this paper studies the variable selection problem based on different penalty functions in the log-BS regression model with censored.First of all,this paper introduces a log-BS regression model with censored,and various penalty functions are discussed,including LASSO,adaptive LASSO,elas-tic network,adaptive elastic network and SCAD,etc.At the same time,under the framework of frequency,the coordinate descent method with higher computational efficiency is studied,and the GCV and BIC methods are used to realize the selection of adjustment parameters.Secondly,the paper also introduces a Bayesian hierarchi-cal model under the Bayesian framework,combined with various penalty functions,and uses the Gibbs sampling combined with the MH algorithm to achieve variable selection from the posterior distribution,and introduce the new Bayesian LASSO hi-erarchical model proposed by Mallick and Yi[1]in 2014,and compare it with the classical Bayesian hierarchical model,due to the particularity of Bayesian variable selection,the coefficients of unimportant variables cannot directly shrink to 0,this pa-per adopts three auxiliary methods:credible interval criterion,double likelihood ratio selection,substitution selection method to select variables.Finally,to illustrate the ef-fectiveness of the variable selection method in the frequency and Bayesian framework of the log-BS regression model,this paper carried out a series of simulation studies under different proportions of censored data,At the same time,the paper also applied the proposed variable selection method to VA lung cancer survival data and primary biliary cirrhosis data,and obtained some reasonable conclusions.