Regression Analysis Of Multivariate Interval Censored Failure Time Data With Informative Censoring

In recent years,survival data has become widely available in the fields of biomedicine,economic,sociology,and reliability engineering.The variable of interest often refers to the time between the start of an experiment and the occurrence of the event of interest,which is also referred to as the failure time in the text,and the event of interest is often referred to as the failure event.However,for many reasons,the failure time cannot be observed precisely,and this is also known as the censored failure time.The common censored data are left censored,right censored and interval censored.Among them,interval censoring means that the time of failure cannot be observed precisely,but can only be known to fall within a certain time period between two observations.Thus,right censoring is a special case of interval censoring.If the failure event of interest occurs only once for an individual,we often refer to it as interval censored data of one element,which is the most common interval censored data.However,in real life,there are often two similar individuals with the same event,or an individual with multiple failure events of interest,and we often refer to such data as multivariate data.Moreover,if the failure times of interest are not accurately observed,but falling within a certain observation interval,we call it as multivariate interval censored data.However,there may also be a subgroup of cures in an experiment,where some individuals experience the failure event of interest,but there is a small subset of immunizations that never experience the failure event of interest.For example,in the AIDS study,hemophiliacs were infected with HIV,but only a small proportion of them were diagnosed with AIDS;in other words,there was a group of hemophiliacs who were immune to AIDS in general.There are two main approaches to studying cure rates,namely,mixed cure models and non-mixed cure models.In addition,for most of the existing methods,they are only applicable when the censoring is non-informative or the time to failure of interest is independent of the censoring mechanism.However,this is not always the case,and we will discuss the case where we may face interval censoring with information censoring.For information censoring,we usually refer to the case where the censored variable or mechanism is associated with the failure time of interest,or with some information about the failure time(Huang and Wolfe,2002;Sun,2006;Ma et al).This study may be preceded by symptoms before the disease event of interest,so that patients with certain symptoms may have more clinical visits,or may be seen at different times than scheduled.We would like to emphasize that for right-censored lapse time data,the characteristics of censoring can be measured by a single variable,whereas for interval censored data,two variables are usually needed to describe censoring(Wang et al.,2018;Xu et al.,2019;Zhang et al.,2007).In the second chapter of this thesis,we focus on the regression analysis of multivariate interval censored data with information censoring under the additive risk model.Firstly,the correlation between the failure time and the observed process is described using latent variables,and secondly,the unknown parameters of interest are estimated by means of an estimation equation,and the consistency and asymptotic normality of the estimated quantities are demonstrated.In addition,the results of numerical simulations show that the proposed estimation method performs well with limited samples.Finally,we apply the proposed method to a real-world data set on AIDS.In the third chapter of this thesis,we discuss the regression analysis of multivariate interval censored data with information censoring under a semi-parametric transformation model.Although many scholars have studied multivariate interval censored data,they have not considered the case with information censoring.Sometimes there is a correlation between the failure time of the event of interest and the censoring mechanism,and if this correlation is ignored,we may end up with biased or misleading results.For this reason,we use a fragile term or latent variable to represent the correlation between the failure time and the observation process.Assuming that the failure time of the event of interest obeys the semi-parametric transformation model,we first find the latent variable using the observation process and then use the EM algorithm to maximize the pseudo-likelihood function to obtain the parameter estimates.Moreover,the estimators are proved to be consistent and asymptotically normal.Numerical simulations show that the proposed method performs well and is corroborated in real data.In the fourth chapter of this thesis,based on the third chapter,we investigate the regression analysis of cured subgroups for multivariate intervals censoring with informative censoring.We develop a non-mixed cure rate model for the failure time of the event of interest.The latent variable is expressed as the correlation between the failure time and the observed process,and we estimate the unknown parameters of interest using a two-step method and the EM algorithm.In addition,the estimators are shown to be consistent and asymptotically normal,and the numerical simulations demonstrate the good performance of the proposed method with limited samples.Finally,we apply the proposed method to a set of ocular data of age-related macular degeneration.