Bayesian Semiparametric Cure Models With Clustered Interval-censored Data

Modern statistics is mainly divided into two schools: frequency school and Bayesian school.The main feature of Bayesian statistics is that prior knowledge is often included in Bayesian statistical models and the introduction of prior information reflects our understanding of the objective world,that is,we add our own existing knowledge to the process of modeling.This introduction not only makes models describe the reality better,but also,to some extent,reduces the scope of the solution space.In addition,with the development of data acquisition and high performance computing techniques,more and more data from fields of biomedicine and genetic engineering appear in statistical research.Modern survival analysis is a hot research field that combines the developing statistical methods with biological gene data.Meanwhile,it reflects the significant role of statistics in this ”Big Data” Age.In standard survival analysis,we often assume that all subjects will experience the events we are interested in if they are followed for a sufficiently long time.Nevertheless,in practice,a certain proportion of the group will never experience these events,in other words,the occurrence times of them are assumed to be infinite.And in some situations,like many clinical trials,the events may be only known to have occurred within an interval of the time,that is to say,the occurrence times are interval-censored.Developing the new statistical methodology on intervalcensored data is of high significance.In this thesis,a non-mixture cure model for the clustered interval-censored survival data is proposed.We present the Bayesian estimation approach which is implemented using on the Metropolis-Hastings procedure.We conduct simulation studies to evaluate the performance of the proposed method.An example of smoking cessation is analyzed to illustrate the estimation approach.