Semiparametric Regression Analysis Of Interval-Censored And Doubly Censored Data With A Cured Subgroup

Survival data occurs widely in biomedicine,economic and nance,actuarial science of insurance,reliability engineering and other elds.In survival analysis,the variable of interest is the time until some event of interest occurs.Such variable is generically referred to failure time.For many reasons,the censoring may have arisen because the failure time cannot be accurately observed.The necessity of obtaining methods of analysis that accommodate censoring has been a principal motivating factor for the development of specialized models and procedures for failure time data.There are three types of censoring data in practice,right censoring,interval-censored,doubly censored.An observation on failure time is interval-censored if instead of observing failure time exactly,only an interval is observed.In this paper,two types of interval censoring are considered,case I interval-censored data and case II interval-censored data,respectively.Case I interval-censored data occur when each study subject is observed only once and the only observed information for the event of interest is where the event has occurred no later than the observation time.By doubly censored data,we mean that the failure time of interest represents an elapsed time between two related events,an initial event and a subsequent event,and the observation on the occurrences of both events may su er censoring.However it is worth noting that a proportion of subjects under study may never experience the event of interest,and thus we have a cured subgroup in the whole population.For example,In AIDS research,only a small percentage of hemophilia patients who are infected with the HIV virus are diagnosed with AIDS,which indicates that some patients are immune to AIDS.In addition,with the development of modern technology,high-dimensional data can be seen everywhere.Variable selection is fundamental to identify the important risk factors from high-dimensional covariates.In this paper,we discuss regression analysis of both interval-censored and doubly censored data with a cured subgroup and the variable selection under the interval-censored data with a cured subgroup.In the second chapter of this paper,we discuss regression analysis of doubly censored data with a cured subgroup under a wide class of exible transformation cure models.Firstly,we consider marginal likelihood estimation and develop a two-step approach by combing the multiple imputation and a new expectationmaximization(EM)algorithm for its implementation.The resulting estimators are shown to be consistent and asymptotically normal.The nite sample performance of the proposed method is investigated through simulation studies.The proposed method is also applied to a real data set arising from an AIDS cohort study for illustration.In the third chapter of this paper,we discuss regression analysis of misclassi-ed case I interval-censored data with a cured subgroup.case I interval-censored data are also often referred to current status data.In particular,in practice,the misclassi cation data is obtained because the failure status at the observation time is determined by a diagnostic test with imperfect sensitivity and speci city.For this we assume the event time of interest follows mixture cure model,and to obtain the parameter estimators,EM algorithm is developed to maximize the observed data likelihood function with complex form.The resulting estimators are shown to be consistent and asymptotically normal.The numerical results shown in simulation study indicate that the proposed approach performs well and is superior to the method that ignores the misclassi cation.We also apply the proposed methodology to a real data set on chlamydia.In the fourth chapter of this paper,we discuss variable selection problem for interval-censored data with a cured subgroup.We adopt minimum approximated information criterion,and develop a penalized EM algorithm to select the important variables and estimate the parameters simultaneously.One important merit of the proposed method is that we do not need to select the optimal tuning parameter in the variable selection procedure.Through the simulation study,we compare the proposed method with the commonly used regularization methods,such as LASSO,ALASSO and SCAD,and the obtained results show that the proposed method performs well in terms of variable selection accuracy and is much faster than the LASSO,ALASSO and SCAD from the computational aspect.Finally,we apply the proposed approach to a set of interval-censored data from the national children mortality in Nigeria.