The Addititive-multiplicative Hazards Model For Recurrent Gap Times

Recurrent event datas often appear in applied research of biology, medical, economics and sociology. Since the structure of the recurrent event data is very complicated. A lot of researchers are interested in the statistical analysis. The corresponding results are not only affludent in the study of survival analysis, but also they provide theoretical and practial guide for the study of interdisciplinary.Since the twentieth century, eighties, there are a large number of the study results on the anal-ysis of recurrent events.The study on the recurrent event data is main concentrated on the analysis of the recurrent time and the gap time. The models about the analysis of recurrent event datas contain two sides. In one side, for intensity process, we construct the model of intensity function and hazards function. In the other side, to recurrent event datas, because the mean function of the recurrent event datas is more significant than the intensity function. The researcher construct the model on the mean function or ratio function.In this paper, the observed datas are the gap time of recurrent event. At first, we review the parametric and the nonparametric estimators of the additive hazards model and the proportional hazards model, which are obtained through the estimating equation approaches. And we look back the asymptotic properties of the proposed estimators. Next, we discuss the additive-multiplicative hazards model, for the the parametric and the nonparametric of the model, we still get the es-timators by the estimating equation approaches. Then we present the proof of the asymptotic properties.