Bayesian Approach And Variable Selection For The Proportional Odds Model With Interval Censored Data

Interval censored data usually appear in many fields,such as demography,epidemiology and medical research.In this type of research,participants usually make periodic observations or inspections.The observed time of interest failure is accurate,but it is known that it is within a certain interval.For example,the time interval between HIV infection of a participant is usually composed of the time of the last negative test and the time of the first positive test.There are a large number of high-dimensional data in survival analysis.It is significant to use Bayesian theory to select variables.The first part mainly studied the Bayesian variable selection of the proportion odds model under Type I interval censored data.Firstly,the Bayesian proportion odds model was constructed using monotonic spline functions and Poisson process data augmentation,and the posterior distribution was calculated using Gibbs sampling method.As the sample size increased,the estimation performance of the parameters gradually improved.Empirical analysis was conducted on the 1995 Diabetes Registry Study of Prince of Wales Hospital in Hong Kong,with the aim of studying heart failure in type II diabetes patients.The second part mainly studied the Bayesian variable selection of the proportion odds model under Type II interval censored data.Firstly,the Poisson process data augmentation likelihood function of Type II interval censored data was constructed by introducing monotonic spline functions,and the posterior distribution was derived based on the spike-and-slab prior and the Gibbs sampling method was given.The numerical simulation results showed that the parameter estimation performance significantly improved with an increase in sample size.Based on this method,it was applied to the transformation model.In the empirical analysis,the study focused on the factors that have the greatest impact on child mortality using the data on child mortality rates generated by the 2003 Nigeria Demographic and Health Survey.The third part mainly studied the Bayesian variable selection of the proportion odds model under partially interval censored data.Partially interval censored data are more complex than Type II interval censored data because they contain exact time data.It is necessary to introduce new monotonic spline functions to perform Poisson process data augmentation on the likelihood function of exact time.The posterior distribution was given by using the Gibbs sampling method for the augmented function of the full likelihood function in the Bayesian framework.In the numerical simulation,the parameter estimation performance significantly improved with an increase in sample size.In the empirical analysis,the study focused on the factors that affect the condition of tooth 46 by selecting the longitudinal dental data from Belgium in 1989.