| The study of clinical data focuses on determining whether the event of interest occurred and the exact timing of the event.However,in clinical trials,the phenomenon of censored data is caused by limitations in trial design,incomplete information on individual observations,and inability to fully observe the exact timing of the event of interest.For example,risk studies of cirrhosis datasets,studies on the prevalence of bile duct hyperplasia in mice,for the analysis of this type of data require us to fit appropriate models for statistical analysis.And when we fit the model,many covariates related to survival time are introduced into the model,and this is where the variable selection technique plays a very important role.For actual clinical data,and when there is grouping information between covariates,simple individual variable selection cannot achieve the effect of selecting group information,so bilevel variable selection,i.e.,bi-level selection technique of within-group and between-group variables,has received more and more attention from scholars.This thesis focuses on the problem of bi-level variable selection for semiparametric transformation models under two types of clinical data.The first part of this thesis focuses on the Bayesian bi-level variable selection problem for the semiparametric transformation model under cirrhosis data.The relevant notation,model assumptions,and data types are first introduced,and the transformation model is specified.The likelihood function of the semiparametric transformation model is derived by fitting the unknown cumulative baseline hazard function by the method of cubic spline.Then the Bayesian Group Bridge method is introduced,and the group prior information of the parameters to be estimated is given and the corresponding posterior likelihood functions are inferred.Next,the MCMC algorithm combining Gibbs and M-H algorithms is used for posterior sampling to verify the effectiveness of the Bayesian bi-level variable selection method for bi-level variable selection under different transformation models through extensive simulation studies.For the application of methods,this thesis selects primary cirrhosis data as a study,primary cirrhosis as a common disease in the clinic,which has an important impact on the survival time of sick patients.Therefore,this thesis is relevant to investigate the primary cirrhosis dataset using a Bayesian bi-level variable selection approach to find out the important group variables and important individual variables that affect the survival time of patients.The second part of this thesis focuses on the Bayesian bi-level variable selection problem for semiparametric transformation models based on mouse bile duct hyperplasia data,and its main approach is similar to the first part,and its main approach is similar to the first part.Firstly,the likelihood function under the semiparametric transformation model is first derived based on the Case I interval censored data.At the same time,the method of cubic spline is selected to fit the cumulative baseline hazard function of the non parametric part.Given a priori information about Group Bridge with grouping,and a posteriori inference is performed.Due to the complexity of the posterior form of the parameters,this thesis utilizes a combination of Gibbs and M-H sampling algorithms for sampling calculations.And the variables were selected by setting different grouping information for multiple model forms under the transformation model,and finally the method of this thesis was applied to the bile duct hyperplasia data of rats for analysis. |
