An Additive-Multiplicative Rates Model For Recurrent Event Data With A Terminal Event

Recurrent event refers to the event which happens repeatedly in a period,and the corresponding data is called recurrent event data.The data occured frequently in many fields such as biomedicine,pubic health,engineer and so on.Examples include multiple recurrences of bladder cancer,multiple infection of AIDS,recurrent economic recessions,repeated drug use and so on.Usually because of some limitations,we can't observe the recurrent event data completely and only observe them in a certain time,in which there may exist censoring event and terminal events.Censoring event precludes us observing the recurrent event process further,and a terminal event will stop the process.For the study of recurrent event,early studies regard the terminal event as independently censoring,which results in the intensity model.After a while,most literatures assume that recurrent event and the terminal event are uncertainly related and employ the marginal model.However,recently someone proposed a joint model which uses a shared frailty to account for the association between the recurrent event process and the terminal event,so we have partial marginal model.Compared with the first two models,the last one is more sensitive and hence more widely used.In application,covariate may have multiplicative effect or additive effect,but the existing studies usually assume the covariates only have multiplicative effect on the recurrent event and proposed the proportional model or assume the additive effect and use the additive model.Hence,in this thesis,I employ a joint model to study the recurrent event data with a terminal event.The covariates were assumed to have both additive and multiplicative effects on the response process and a shared gamma frailty was used to account for the association between the recurrent events and the terminal event.Specifically,an additive-multiplicative rates frailty model was used to characterize the recurrent event process and the hazards function of the terminal event was assumed to follow the COX proportional hazards frailty model.Martingale theory in counting process and generalized estimating equation are used to create estimation function for estimating the model parameters and asymptotic variance.Finally,Monte-Carlo simulations are constructed to examine the finite sample performance of the proposed estimators.The simulation results show that the proposed method perfects well compared some naive procedures.Also the proposed method is proved to have good robustness when the assumption of a gamma frailty is wrong.