Semiparametric Additive Intensity Model with Frailty for Recurrent Events  

作　　者：Yah Yah LIU Yuan Shan WU 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第9期1831-1842,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 10771163） The authors are grateful from the Associate Editor and the referees which article. for the valuable comments and suggestions drastically improved the appearance of this

摘　　要：The seminal Cox＇s proportional intensity model with multiplicative frailty is a popular approach to analyzing the frequently encountered recurrent event data in scientific studies. In the case of violating the proportional intensity assumption, the additive intensity model is a useful alternative. Both the additive and proportional intensity models provide two principal frameworks for studying the association between the risk factors and the disease recurrences. However, methodology devel- opment on the additive intensity model with frailty is lacking, although would be valuable. In this paper, we propose an additive intensity model with additive frailty to formulate the effects of possibly time-dependent covariates on recurrent events as well as to evaluate the intra-class dependence within recurrent events which is captured by the frailty variable. The asymptotic properties for both the regression parameters and the association parameters in frailty distribution are established. Fhrthermore, we also investigate the large-sample properties of the estimator for the cumulative baseline intensity function.The seminal Cox＇s proportional intensity model with multiplicative frailty is a popular approach to analyzing the frequently encountered recurrent event data in scientific studies. In the case of violating the proportional intensity assumption, the additive intensity model is a useful alternative. Both the additive and proportional intensity models provide two principal frameworks for studying the association between the risk factors and the disease recurrences. However, methodology devel- opment on the additive intensity model with frailty is lacking, although would be valuable. In this paper, we propose an additive intensity model with additive frailty to formulate the effects of possibly time-dependent covariates on recurrent events as well as to evaluate the intra-class dependence within recurrent events which is captured by the frailty variable. The asymptotic properties for both the regression parameters and the association parameters in frailty distribution are established. Fhrthermore, we also investigate the large-sample properties of the estimator for the cumulative baseline intensity function.

关 键 词：Additive intensity model counting process Donsker class FRAILTY recurrent events 

分 类 号：O212.1[理学—概率论与数理统计] TU361.01[理学—数学]