【作者】 叶英；

【导师】 刘焕彬；

【作者基本信息】 上海师范大学 ， 概率论与数理统计， 2010， 硕士

【摘要】 复发事件数据常常出现在生物学、医学、经济学、社会学等领域。由于复发事件数据结构复杂,对它的统计分析已经受到学者们广泛重视,其相应研究结果不仅丰富了生存分析,医学与生物统计的研究内容,而且为各交叉学科研究提供理论依据和实际指导。自二十世纪八十年代开始,对复发事件数据的分析研究已经取得了丰富的成果。对复发事件数据的研究主要集中在对复发时间和间隔时间的分析。对复发事数据分析的模型包含两个方面：一方面,基于强度过程,对强度函数和危险率函数进行建模。另一方面,对复发事件数据而言,由于复发事件的均值函数比强度函数更具有解释意义,因此学者们对均值函数或比率函数进行了建模。本文在复发事件间隔时间数据下,首先回顾了可乘危险率模型和可加危险率模型,利用估计方程的思想得到参数和基准危险率函数的估计,以及所得估计的渐近性质。接着讨论了可加可乘危险率模型,对于此危险率模型中参数和基准危险率函数,同样采用估计方程的思想将其估计出来,然后证明了估计量的大样本性质。更多还原

【Abstract】 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.更多还原