Bayesian Inference Of Partial Linear Quantile Regression For Censored Data With Latent Variables

In survival analysis,due to the limits of experimental,the exact time of survival can not be observed every time.So it is necessary to model for the censored time.In general,if the covariate have a linear related to the logarithm of the censored time,the accelerated failure model can be constructed.Partial linear models can be constructed when the covariate and the logarithm of the censored time have both linear and nonlinear relationships.We can also add the quantile regression in partial linear models to analyze the relationship between covariate and censored time at different quantiles.Later,because the Bayesian method can make full use of prior information,it have been widely used in various fields.This paper based on the censored data,being Bayesian inference for partial linear model.The paper is including the following three parts.The first part is Bayesian analysis of the linear model for the right censored data.In view of the right censored data,a partial linear model is established,and the nonlinear part is fitted by Bayesian P-splines method.Numerical simulation verifies the validity of Bayesian P-splines,and the method reduces the influence of knot selection.Finally,it is applied to the case data of ovarian cancer patients,and the conclusion have a practical value to the treatment of ovarian cancer.The second part is Bayesian analysis of partial linear quantile regression with the censored data.First,try to apply Bayesian P-splines estimation method to the quantile regression of partial linear models.Then based on the right censored data,the Bayesian quantile regression model with penalized is studied.Finally,partial linear quantile regression is applied to the censored data.Numerical simulation verifies the validity of the method and eventually applies it to the actual data.The third part is Bayesian analysis of partial linear models with latent variables for the censored data.For the unobservable latent variables,a factor analysis model is established,the observable variables are used to characterize the latent variables,the parameters in the model have appropriate priori structure and posterior distribution,and finally applied to the current data with the partial linear model.The simulation verifies the effectiveness of the method.