Additive Transformation Models For Multiple Type Recurrent Events

In the research of biology, medicine and economics, individuals experience the same event or failure repeatedly, we call this event as recurrent event. The data arised during the process of events recurrence is defined as recurrent event data. Depending on the type of the object of study, recurrent event data can be divided into two types in general. If we are interested in a recurrent event, the data is called single type recurrent event data. However sometimes the individual may also experience a variety of different types of recurrent events, and there is a correlation among the different categories, this requests us to study all kinds of events at the same time, the resulting data is called a multi-type recurrent event data.Recurrent events are common in real applications, but the structure of the recurrent event data is often very complicated. Because there often exits dependency and order among these events. More and more scholars are trying to solve these problems, and they also received many meaningful results.For recurrent events, we are often interested in researching the effects of the covariates on the recurrent events. In fact, many scholars have put forward various regression models to study the effect of covariates on single type recurrent events. In traditional research, we always care about the relative ratio of the average functions under two different treatments. So we usually establish models based on the the ratio model. But in some practical problems, we also need to consider the absolute difference of the mean functions under two different processes. It is to say, we need to consider the effects of the covariates on the mean baseline function. This paper mainly discusses the additive transformation models for multi-type recurrent events under the effects of the covariates, and estimating equation approaches are developed for the model parameters.The structure of this article is as follows:Chapter 1 introduces the recurrent events data first, and then gives the Andersen-Gill model, and discusses the back-ground and the practical significance of the additive model for the multiple type recurrent events. Chapter 2 introduces two additive models for the single type re-current events:simple additive model and additive transformation model. Chapter 3 first gives a multi-type additive transformation model for the multiple type recur-rent events, and then estimating equation approaches are developed for the model parameters, the asymptotic properties of estimators are also given at last. Chapter 4 presents a model checking procedure to asess the adequacy of the model, and the fi-nite sample performance of the proposed estimators is examined through simulation study. Chapter 5 gives some summary and discussion about the future research.