Statistical Analysis Of Semi-parametric Model Based On EMVS Algorithm For Complex Censored Data

With the continuous development of the field of survival analysis,we are faced with increasingly complex data types,and statistical analysis of data types such as left-censored data,right-censored data,and interval-censored data can no longer meet the current needs.Therefore,it is necessary to further promote the research related to complex data types.In this paper,two types of complex censored data are considered,namely partly intervalcensored data and doubly censored data.Partly interval-censored data consist of exact and interval observations of the failure time of interest.In the doubly censored data,the failure time of interest is the time interval from the start event to the end event,and both events are censored at their occurrence times.In this paper,the statistical analysis is based on the above two types of complex censored data combined with a semi-parametric model.Semiparametric models are common statistical models,which include both parametric and nonparametric components.In this paper,three kinds of semiparametric models are considered,namely proportional hazards model,proportional hazards with cure model and semiparametric transformation model.In addition,with the development of technology,the data is gradually huge and the data dimension is getting higher.At this time,variable selection is needed to screen out variables with significant impact.Among many variable selection methods,EMVS(EM for Variable Selection)is a variable selection method developed based on the EM algorithm,which has the advantages of high selection accuracy and short operation time.Therefore,this paper considers the statistical analysis of a proportional hazards model under partly interval-censored data,a proportional hazards with cure model and a semi-parametric model under doubly censored data based on the EMVS algorithm.There are three parts as follows.The first part of this paper investigates the statistical analysis of the proportional hazards model under partly interval-censored data based on the EMVS algorithm.The likelihood function is first determined and the spike and slab prior and latent variables are introduced,and then the posterior distributions of the parameters are obtained,followed by the application of the EMVS algorithm to determine the selection rules for variable selection.Numerical simulations verified the validity of the method.Finally,an empirical analysis was performed using data from the heart failure study in type II diabetic patients.The second part of this paper investigates the statistical analysis of the proportional hazards with cure model based on the EMVS algorithm under partly interval-censored data.In the paper,a suitable prior distribution is selected based on the likelihood function,while Poisson latent variables and 0-1 latent variables are introduced to simplify the likelihood and derive the posterior distribution,and then the iterative equations of the unknown parameters are calculated by the EMVS algorithm,and the Bayesian formula is used to obtain the posterior probabilities,and then the selection rules are obtained for variable selection.The numerical simulation part verifies the validity of the research method in this paper.The empirical evidence was selected from the 2003 Nigeria Demographic and Health Survey(NDHS)data for the analysis.The third part of this paper investigates the statistical analysis of the semi-parametric transformation model based on the EMVS algorithm under doubly censored data.Based on the likelihood function of the semi-parametric transformation model of doubly censored data,and then the 0-1 latent variables are introduced by combining the spike and slab prior to derive the posterior distribution of the parameters,and then the EMVS algorithm is used to derive the variable selection rules for variable selection.The numerical simulation part shows that the method is effective.The longitudinal dental data from the bayes Surv package is chosen for the empirical evidence.