| Recurrent event data have been increasingly important in longitudinal medical studies. If a subject repeatedly happens some random events, that is the same individuals may experience the same kind of events in some time, such as bladder cancer patients relapse by his treatment, a leukemia patients after bone marrow transplantation repeatedly suffer infection, we treat such data as recurrent event data.Recurrent event data have some characteristics as follows:(1)There is the order of the event;(2)There exists heterogeneity among individuals;(3)The recurrent event data is independence;(4) In practice, recurrent event times are subject to censoring. If censoring is caused by the end of the study or random loss to follow-up, then the censoring time can be regarded as independent or non-informative of the recurrent event times. In many applications, especially in medical studies, the observation on recurrent events may be terminated by the subject’s withdrawal from the study (because of deteriorating health or some other reasons) or the subject’s death. Then the censoring time (i.e., time to the terminal event) is likely to be correlated with the recurrent event times. We call the informative censoring of the recurrent event times. When the recurrent even with a terminal event, data has the independence, and the traditional Cox proportion hazards model has been unable to solve this kind of data. This will force us to find a more suitable replacement model to analysis and explain such data more reasonable. It is of interest to many researchers to study how to select a more suitable model to analysis the recurrent event data.This topic on the basis of recurrent event data’s characteristics, discusses the alternative model which do not satisfy the classic Cox hazard model, and can make the explanation of the medical follow-up study with the recurrent events data reasonable.The first chapter of this paper combined with the actual data to introduce the characteristics and the theory of the model with recurrent event data. We found that these models are suitable for non-informative of the recurrent event data. Using them to analysis the recurrent event with terminal event, they often treat the terminal event as censoring information, then will cause the estimation of parameters biased and cover the information of the terminal event. Chapter two introduced the theory research, and parameter estimation methods of the frailty model and the recurrent event with a terminal event. We proposed a simple parameters estimation method using Gaussian quadrature techniques to estimation in joint frailty model. This estimation method is relatively straightforward and has been implemented in SAS9.2Proc NLMIXED. Thus further confirmed that frailty model was based on Cox proportion hazard model to analysis the recurrent event data. Random effects of the model on one hand explains the heterogeneity between subgroups, on the other hand allows correlation between individual’s survival time. However, simple frailty model can be a good solution to heterogeneity, as the iteration of EM algorithm is slow and PPL algorithm applies only to simple frailty model etc, the parameter estimation method is not perfect and limit its application.Chapter three combined with the example of coronary heart disease, and make comparison with a simple frailty model (shared the gamma frailty model, the conditions shared frailty model and so on) and the joint frailty model of recurrent event and a terminal event. Although the simple frailty model considers the correlation of the survival time and heterogeneity between the individual, they treat the terminal event as censoring information and ignore the information of the terminal event. However, we conduct the shared joint model. The results show that the impact factor on recurrence and death is different of318patients who had the coronary artery disease. The risk of recurrence and death is positively (gamma=1.3614, p=0.0031), which has a statistical significance show that we should consider the recurrent event and the terminal event to conduct the joint model in the actual problems. We also found that the coronary artery disease patients who with the higher risk of relapse will have higher risk of death. Treatment, gender, and the history of hypertension are factors which impact the relapse of the coronary heart disease patients.Treatment and gender are also affect the coronary heart disease patients’death, the woman who has coronary heart disease events with higher risk of death than man, but the risk of recurrence is reversed. The shared joint frailty model of the recurrent event and a terminal event can evaluate different covariates stratification in the process of censoring and relation, and provide new ideas for the application of clinical. In short, frailty model is the effective method to analysis independent and heterogeneity of the recurrent event data. The shared joint frailty model is the optimal model to analysis the recurrent events and a terminal event. Shared joint frailty model can explain the correlation and heterogeneity between individuals. By Gaussian quadrature techniques to parameter estimation, we do not need assumption the specific prior distribution of baseline risk, and only need approximate piecewise constant baseline risk, and can be used SAS9.2Proc NLMIXED process. Further studies indicate that using Gaussian quadrature techniques to estimate parameter is convenient and feasible, not only can be directly obtained the value of standard, but also can expand the application to the complex models. With the informative censoring of the recurrent event times, we have the random effects incorporated into the process of the censoring information to directly produce simple joint frailty model to evaluate different covariates stratification in the process of censoring and relation, not only can describe the correlation and heterogeneity between individual, but also can describe the risk of recurrence and termination. |
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