Regression Survival Analysis For Informative Right Censored Data With PH Model

In survival analysis,most existing approaches for analysing right-censored failure time data assume that the censoring time is independent of the failure time.However,investigators often face problems involving dependent censoring,i.e.,failure time and censoring time are possibly dependent and they may be censored one another,especially in clinical trials.Without accounting for such dependence,survival distributions cannot be estimated consistently.Numerous attempts to model this dependence have been made.Among them,copula function and frailty models are of particular interest because of their simple structure.In survival analysis research,the joint distribution of variables can reflect the depending structure of them.It will reduce the difficulty of research if the joint distribution can be given out accurately.Copula function simplifies the construction of joint distribution as the estimation of the correlation structure between the two marginal distributions,which makes the construction of joint distribution more easily and more accurate.Frailty models consider the variables are independent via introducing a frailty variable.Under this premise,marginal distributions of variables can be obtained,and furthermore,the joint distribution.This article mainly makes research of regression problem about informative right censored data with PH model.The joint distribution function of censoring time and failure time is assumed by the Archimedean copula function and the frailty model separately.In previous studies,the type and parameters of copula are usually assumed to be known by the researcher,and in this paper the joint distribution function of the censored time and the failure time is assumed under the condition that the parameters are unknown.Under the condition that the parameters of the copula function are identifiable,the parameters of copula and PH models,and the maximum likelihood estimation of baseline cumulative hazard function can be obtained,When it comes to frailty models,estimation of the parameters of PH models and baseline cumulative hazard function can be got by using EM algorithm.Finally,the feasibility and effectiveness of the two methods are verified by simulation calculation.