An Accelerated Rates Model For Recurrent Events Data With A Terminal Event

In many longitudinal studies, the events of interest may recur on the same subject, we called them recurrent events which can be found in many fields such as biology and medicine. In early studies, researchers regard death as censoring and assumed it to be independent of recurrent processes. But it is clear that the recurrence of serious events often elevates the risk of death, that means, the assumption may be unrealistic. In recent years, the concept of terminal event was put forward to distinguish censoring event. But because of the terminal event, some censoring time may be unobservable and the generalized estimating equation cannot be used directly.Marginal model is one of common methods to deal with the terminal events, it does not specify the correlation between the terminal event and the recurrent events. In this article, we consider two modifications: inverse probability of survival weighting(IPSW) technique and inverse probability of censoring weighting(IPCW) technique to deal with the data loss and propose a marginal accelerated rates model. The asymptotic properties of the proposed estimators are proved.In accelerated rates model, the effect of covariates have a clear and intuitive meaning since they act on time directly. Because some of resulting variance estimators are numerically unstable, we use resampling technique to obtain a stable variance and develop a technique for checking the adequacy of the general model.