Statistical Analysis Of Time - Dependent Recurrence Event Data With Time - Of - Term And Covariates

Recurrent events data refers to the observation of individuals, which contain the recurrentevent time data of interestJn recent years, with biological, medical and economic development,the study of recurrent event data has made great progress. Many important statistical modelsare established. But in this ifeld there are still some important and difficult statistical problems,especially deal with recurrent event dependent on censoirng. At present, many scholars proposedmethods are usually require independent censoring. However, in many cases, the failed time aspart of the censoirng mechanism, it may be related to recurrence process. On the other hand, underthe assumption that recurrent event dependent on censoirng, most scholars proposed approachrequires that covariates independent on time or it depend on some distribution,which makes thetheory is dififcult to use in practice.This paper simply introduces some related knowledge,like the survival function,hazard func?tion, recurrence process, intensity function, frailty model, U-statisties,which are deal with recur?rent event. We consider joint modeling of a recurrent event process and a failure time in which acommon subject-speciifc latent variable is used to model the association between the multiplica?tive intensity of the recurrent event process and the multiplicative hazard of the failure time. Theproposed joint model is flexible in that no parametric assumptions on the distributions of censor?ing times and latent variables are made, and under the model, informative censoring is allowedfor observing both the recurrent events and failure times.Using the order statistics,the PL estima?tion,the pairwise pseudolikelihood function and some relevant statistical methods which are usedto estimate regression parameter.And then we prove its asymptotic properties by Using the Deltamethod, U-statistics methods and some relevant statistical methods.Finally, under the same previ?ous assumptions,considering the actual needs, we consider another joint model which associatingbetween the multiplicative intensity of the recurrent event process and the additive hazard of thefailure time.Properties of the regression parameter estimates and the estimated baseline cumulativehazard functions are also studied.the proportions of the proposed risk function and the intensityof function of sharing vulnerable model, using the similar method and some basic properties ofmartingale, and function estimation of unknown parameters in the model is given and its asymp?totic properties.Using the previous similar method and some basic properties of martingale, wediscusses to estimating the unknown parameters and unknown functions in the model and provingits asymptotic properties.