Joint Modeling Of Longitudinal Measurements And Accelerated Failure Time With A Cure Fraction

At present the research of proportional hazards model is more extensive,correspondingly,the result is more mature.Accelerated failure time model because of intuitive form,easy to understand,at the same time as a good substitute for proportional hazards model,attract our attention and research.In the semiparametric analysis of the accelerated failure time model,rank estimators and kernel methods have been studied.The researchers find that joint modeling by sharing random effects can effectively reduce the error,when we estimate the model parameters separately with data missing and measurement error,thus joint model begin to attract the attention.Along with the advance of medicine,many incurable disease,through a good treatment and control,begin to be cured,showing that these individuals can live normally without recurrence in a period of time.We need to know the cure rate and the individual survival function of uncured subject,mixed cure model can well solve the problem.In this article,on the basis of predecessors’ research,survive model of joint modelling of accelerated failure time and longitudinal data is expanded into mixed cure model,making the use of the model wider.Due to the expression of the posterior distribution of the random effect extremely complex,we use Monte Carlo integration approximate conditional expectation of likelihood function,the maximum conditional expectation of likelihood function,get all the unknown parameters estimation.For cure rate parameters,when the covariate values are 0 or1,we can derive the conditional expectation about two parameters respectively,then we can get the results by simultaneous equations,which is a small innovation.For baseline hazard function parameter estimates,we consider two cases,one case the baseline hazard function is constant,the baseline function survival time obey the exponential distribution,this model is a parameter model,another case for baseline hazard function we use piecewise constant.Then we need to know the baseline survival time,using empirical bayes and the parameter estimation can get baseline survival time estimation.In simulations we carry out above two cases.We can’t derive conditional expectation of likelihood function about parameter of accelerated failure time model β and can’t get accurate information matrix,so the estimates of variance we adopt bootstrap technique.In the case analysis,we analysis data of liver cirrhosis patient with prednisone treatment or not,from the R language packages.Our model can well capture the information contained in the data.