Bayesian Statistical Inference Of Transformation Model Under Partly Interval-Censored Data

Survival analysis is used for data analysis in many fields,especially in the medical and biological sciences.In this case,the event of concern is often death,the onset of disease or the disappearance of disease symptoms.The time at which the event occurs is called the failure time.Partly interval-censored data is a common and complex data type in survival analysis.Some of which are accurately observed,while others are only within a certain interval.Generally speaking,both right censored and interval censored can be regarded as a special case of partly interval-censored.Due to the unique data structure and complex censoring mechanism of partly interval-censored data,the analysis of partly interval-censored data is much more complex.In the existing survival analysis research,most of them focus on right censored data and interval censored data.The analysis of partly interval-censored data is still very limited.Therefore,conducting in-depth research on such data is very meaningful and practical.The linear transformation model is more general and flexible than the other survival models.Most of the research under this model is based on frequency method,while Bayesian method has good characteristics when facing complex models.Therefore,based on the linear transformation model under the Bayesian framework,this paper deeply considers the data structure and different generation mechanisms,and conducts flexible modeling and robust inference for the partly interval-censored data.The research content of this paper consists of three parts,as follows:First,the first part studies the Bayesian estimation of partly interval-censored data under the linear transformation model.The nonparametric parts of the model are approximated by spline,and the corresponding likelihood function is given by observing the data structure and deriving the specific model.However,due to the complexity of the data structure and the model,the calculation of the likelihood function is an enormous task,and it is very difficult to maximize the likelihood directly.A four-stage data augmentation procedure is introduced to tackle the complex model and data structure challenges.We propose a fully Bayesian approach coped with efficient Markov chain Monte Carlo methods.The proposed method is easy to implement.The asymptotic properties of Bayesian estimators are given by Bernstein-von Mises theorem,and the sensitivity analysis of the number of spline nodes and the selection of hyperparameters is carried out simultaneously in the simulation study of limited samples.The rationality of the proposed model and method is further evaluated,indicating that the proposed method performed well.The method is applied to a dental health study.Secondly,in the second part,we study the Bayesian estimation problem of the transformation model with measurement error in the case of independent and dependent partly interval-censoring data,respectively.Based on first part,for cases where the data is independent,consider that covariates are often measured with error in many research settings,their true values being unobservable or latent.Therefore,the covariates affected by the measurement error are characterized by the classical measurement error model,and the transformation model and the measurement error model are used for joint modeling for posterior inference.Furthermore,data dependence is common in survival analysis,and simply ignoring dependency censorship can skew the results.Therefore,this part further considers data dependence,assumes that the failure time is related to the observed interval.A proportional hazards model is established to describe the length of the interval,and the three models are combined through potential error covariates.In order to better carry out posterior inference,multi-stage data augmentation technology is applied,and combined with MH and ARMS sampling algorithms for Bayesian posterior calculations.The simulation studies compare the naive method and Bayesian method,and verify the effectiveness of Bayesian method.Finally,two examples of heart disease data and community atherosclerosis data are given to illustrate the practicability of the proposed model and method.Finally,the third part studies the Bayesian inference of the transformation model with latent variables under the dependent partly interval-censored data.In clinical trials,available methods with partly interval-censored data typically assume that all potential predictors can be fully observable.However,the above assumptions may not be valid in practice.This part considers a new joint modeling approach to simultaneously model the failure and observation times and correlate these two stochastic processes through shared latent factors.The proposed model comprises a factor analysis model for characterization of the latent factors,a transformation model for the failure time of interest,and a proportional hazards model for the length of censoring interval.Further,the identification problem of the joint model is solved by the given constraints.A multi-stage data augmentation procedure is introduced to tackle the challenges posed by the complex model and data structure.Given an appropriate prior distribution,a Bayesian approach coupled with monotone spline approximation and Markov chain Monte Carlo techniques is developed to estimate the unknown parameters and nonparametric functions.Finally,the validity and robustness of the estimated results are illustrated by a large number of simulation studies and sensitivity analysis,and the model is then applied to a Framingham Heart study.