Hazards Models For Multiple Type Recurrent Gap Times

In many application areas, subjects may usually experience multiple events or failure over time, which have been termed recurrent events. Recurrent event date often arises in many applica-tion areas, such as, medical science, biology and economics. However, the structure of recurrent event dates is usually complex. Because there exist correlation and sequence between different events. Recently, more and more researchers exert their efforts to solve these difficulties and gain many significant results.The recurrent event dates which record the recurrent time of each event of interest, includes two types. The first type termed single recurrent events is that only one type of recurrent events is of considered. However, in many settings, subjects may experience several types of recurrent events, and these types are dependent on each other. This case is naturally considered, in which dates have been called multiple type recurrent event.For recurrent events, we are interested in assessing the effect of covariates on the recurrent events. There have been many regression models to be proposed. In this thesis, we mainly dis-cussed three models for multiple type recurrent gap times. In Chapter 2, the proportional hazards model has been put forward which is the generalized form of Cox model, methods and asymp-totic properties for inferences on this model are established and some results from simulation are presented. In Chapter 3, we study additive hazards model for multiple type recurrent gap times. Asymptotic properties for estimators of parameter are established. In Chapter 4, the additive-multiplicative hazards model for multiple type recurrent gap times are investigated. Asymptotic properties of the proposed parameter estimators are developed.