Several Common Models Of The Bayesian Estimation In Surival Analysis

Since the1970s survival analysis has been rapid development and usefulin biology, medicine and other areas of survival analysis.With the theory ofBayesian integration, the survival analysis theory can efectively deal with thesmall sample model, incomplete data and the complex operating environmentproblem.Especially the MCMC method in the application of Bayesian analysismakes the very complex numerical of problem to solve easy.It makes the simula-tion of the parameters posterior distribution more convenient.It greatly promotesthe Bayesian theory and its applications development unprecedented.The projectis mainly to establish Bayesian model with missing covariates based on multivari-ate longitudinal data. We will further study this situation that this model willbe extended to multivariate longitudinal data based on the values of covariateschange over time.Mainly for the survival time for right censored, we use the likelihood functionof right censored data to construct the the likelihood function of the exponen-tial regression model and Weibull regression model.We used Bayesian survivalanalysis theory to obtain the posterior distribution of the parameters and use theMCMC method and the Gibbs sampling to simulate the posterior distribution ofthe parameters. We use the WinBUGS data simulation software to calculate theposterior distribution.When the prior information is insufcient, using Bayesian regression modelto estimate will produce deviation. In view of this situation, we have to buildthe Cox proportional hazards regression model. The Cox proportional hazardsregression model have the nature of parametric and non-parametric. Under thecovariates along with the change of time change condition, we constructed thelikelihood function for the Cox proportional hazards model and use the WinBUGSdata simulation software to calculate the posterior distribution.