Research On Two Kinds Of Joint Modeling Methods With Latent Variable Under Interval-censored Data

In the study of biomedicine and survival analysis,the main variable of interest is the time of the occurrence of interest events.In practical research,it is often influenced by many factors,For example,the survival time of the individual,and the survival time is influenced by many factors such as environment,sex,race,age and other factors.It is the main research task to study these covariate if it affects the variable of interest events.The quantitative analysis of influencing factors is given from the angle of regression model,and then the important factors are found.Accordingly,the better research plans and ideas for the interesting events can be further given.However,in the specific study,many covariables can not be observed directly.It is necessary to describe and depict some latent variable models.Therefore,the research on the latent variable model is one of the main topics of the current survival analysis.In this paper,we firstly introduce the development and research status of latent variable models,common types of censoring data,basic distributions,classical hazards regression models and the likelihood function of the truncated-censored data in survival analysis.Scendly,we mainly discusses two types of survival analysis models,and one is parameter models without latent variables,another is a semi-parametric regression model with latent variables,and which is divided into four parts:The first part,in the left truncated and right censored data,when the time variable T is the generalized exponential distribution,considering whether the scale parameter has been affected by covariates,we can establish two kinds of the model,and get parameter estimation with the maximum likelihood estimation,and the Newton-Raphson algorithm is used to solve the equation.Using the model that hasn't scale regression analysis to analyze the transformer life data set,we can obtain the survival function and hazard function the electric power transformer;and using the model that has regression analysis about the scale parameter to analyze the Channing house data set,we can obtain the survival function and hazard function affected by sex.The second part,in the interval-censored data set,based on the bayesian parameter estimation,we proposed accelerated failure time model of the generalized exponential distribution,established the likelihood function and posterior likelihood function of parameter about our model,and gained the parameters sample by Metropolis-Hasting algorithm,we regard average sample as the parameter estimation and use R software simulation.The model was applied to the hemophilia grouped data,and analyzed the influence of different experimental groups on survival functionThe third part,under the case I interval-censored data,we investigate an additive hazards joint regression model with latent variables,First,the latent variable factor is described by the deterministic factor analysis(CFA)model,and the additive hazards model is built based on latent variables and observed variables.Then,we extended a hybrid estimation process proposed by Pan et al(2015)to our joint model.Under some regularities conditions,the consistency and asymptotic normality of the estimation are proved.R software is used to simulate,and the properties of joint model parameter estimation are verified under different samples and basic hazards functions.The last part,under the case I interval-censored data,we consider a joint modeling approach that incorporates latent variables into a proportional hazards model to examine the observed and latent risk factors of interval-censoring failure time.Based on the third part of latent variable factor estimation,the approximate partial likelihood function of the model under interval I censored data is written out,and the scoring equation is obtained.The latent variable factor is estimated by the latent variable model.The process of use the latent variable can lead to the bias of estimation equation.Therefore,the bias is corrected and the unbiased estimation equation is obtained.The asymptotic variance of the estimator is given by the Taylor expansion method.Under different samples and basic hazards functions,we use R software to simulate and verify the properties of the joint model.