Bayesian Survival Regression Analysis Models And Variable Selection

In the clinical study of Survival analysis,the failure time is our interesting variable.But it can't evaluate the treatments in a systematical and comprehensive way.In addition,there are a lot of variables related to the survival time,the variables will affect the survival time in different forms and different treatment methods.The ultimate goal of the study is to find an optimal treatment to improve the patient's survival time and so on.On the other hand,high dimensional data is widespread in survival analysis.Therefore,the parameter estimation and variable selection are some of the most important problems in the survival analysis.We introduce the present situation of the research on Bayesian survival analysis,the common data types in the survival analysis and the common Bayesian sampling algorithm.Here we mainly discuss the estimation and variable selection in Bayesian survival regression analysis.The first part,we build the Generalized Exponential scale parameter regression model with right censored data.The maximum likelihood estimation and Bayesian estimation methods are used to estimate the model parameters.The maximum likelihood estimation used the Newton-Raphson algorithm to estimate parameters.Because the posterior distributions of the parameter do not have the standard form in Bayesian estimation method,we use the MCMC sampling algorithm that combined with MH and Gibbs sampling algorithms to estimate the parameters.Some good performances are demonstrated by simulation studies.Finally,we apply the method to the Stanford heart transplantation data as right censored real data and draw a conclusion.Compared with the classic Cox estimation results,the results show that the proposed method is effective and feasible.It shows that the proposed method has a good estimation performance.The second part,we study the Bayesian scale parameter regression model with Case II interval censored data using the Generalized Exponential model.Because the posterior distributions of the parameter do not have the standard form,we use the M-H sampling algorithm to update the estimators.The simulation results show the method has the good property.We also apply the classic Boston breast cancer data as Case II interval censored real data and draw a valid conclusion.The results showed that adjuvant chemotherapy can improve the rate of recurrence and overall survival rate.The last part,we develop the additive hazard model with Case I interval censored data,and we use the Bayesian Adaptive Lasso method to finish simultaneous estimation and variable selection.Based on the regression model,the relationship between the hazard function and the covariate of the influencing factors is established.Because of the baseline hazard function is unknown,we use the cubic spline method to paramete the baseline hazard function.The objective function under the Bayesian adaptive Lasso method is determined.Then,M-H and other algorithms are used to solve the problem.We have successfully applied our method on simulated data sets.Some good performances are demonstrated by simulation studies.Our method is applied to a study concerning the risk factors of heart failure disease for Type 2 diabetic patients.