Statistical Analysis Of Bayesian Empirical Likelihood Based On Interval-Censored Data

In Survival analysis,medical workers and Biostatisticians are most concerned about the survival time of patients.For example,one disease occurs time or Survival time of diseased individuals in clinical studies.Interval-censored data is pretty important in the field of Survival analysis,so it is meaningful to analysis this type of data.Bayesian method is an efficient estimation method which can be applied in parametric and non-parametric models.Due to the prior information,the estimation result of Bayesian method is more accurate.Empirical likelihood method is an important nonparametric method,which can be used to estimate the parameters by constructing the empirical likelihood ratio function.This method has many excellent properties such as domain invariance and deviation correction.Some researches show that Bayesian empirical likelihood method which combined the empirical likelihood with Bayesian theory performs better in terms of coverage probability and confidence interval.This paper based on the Interval-censored data,then applied Bayesian method and Bayesian empirical likelihood method to conduct research.This paper is mainly including the following two parts.In the first part of this paper,we introduce the Bayesian Empirical Likelihood Statistical Analysis of Current status data under the general linear model.Based on the previous research results,we construct an appropriate transformation model and transfer the censored data to uncensored data.So we can obtain the unbiased estimation equation,then combine the empirical likelihood method with Bayesian framework.Putting an appropriate prior on parameter and obtain the posterior distribution.We can obtain the coverage probabilities under different nominal level through the simulation results.Then applied this method to analyze real data,and the result shows that the estimation method is effective.The second part of this paper introduces the study that based on the case ? Interval censored data,and the hazards function satisfies the proportional hazards model.We proposed the Bayesian estimation of regression parameters under generalized exponential distribution.It is assumed that the prior distribution of regression parameter is normal distribution,the prior distribution of shape parameter and scale parameter is gamma distribution.Obtaining the posterior reference by calculating the likelihood function,using R software and MCMC algorithm to conduct simulation study and estimate the parameters.Finally we applied this method to analyze the breast cancer data.