A semiparametric additive rate model for recurrent events with an informative terminal event.

We propose a semiparametric additive rate model for modelling recurrent events in the presence of a terminal event. The dependence between recurrent events and terminal event is nonparametric. A general transformation model is used to model the terminal event. We construct an estimating equation for parameter estimation and derive the asymptotic distributions of the proposed estimators. Simulation studies demonstrate that the proposed inference procedure performs well in realistic settings. Application to a medical study is presented.

[1]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[2]  Jianwen Cai,et al.  Some Graphical Displays and Marginal Regression Analyses for Recurrent Failure Times and Time Dependent Covariates , 1993 .

[3]  Debashis Ghosh,et al.  MARGINAL REGRESSION MODELS FOR RECURRENT AND TERMINAL EVENTS , 2002 .

[4]  Jerald F. Lawless,et al.  Some Simple Robust Methods for the Analysis of Recurrent Events , 1995 .

[5]  Ian W. McKeague,et al.  A partly parametric additive risk model , 1994 .

[6]  Mei-Cheng Wang,et al.  Analyzing Recurrent Event Data With Informative Censoring , 2001, Journal of the American Statistical Association.

[7]  Donglin Zeng,et al.  Semiparametric Transformation Models with Random Effects for Joint Analysis of Recurrent and Terminal Events , 2009, Biometrics.

[8]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[9]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[10]  S. Keleş,et al.  Recurrent events analysis in the presence of time‐dependent covariates and dependent censoring , 2004 .

[11]  Debashis Ghosh,et al.  Semiparametric analysis of recurrent events data in the presence of dependent censoring. , 2003, Biometrics.

[12]  R J Cook,et al.  Marginal analysis of recurrent events and a terminating event. , 1997, Statistics in medicine.

[13]  James M. Robins,et al.  Comparing two failure time distributions in the presence of dependent censoring , 1996 .

[14]  Mei-Cheng Wang,et al.  Joint Modeling and Estimation for Recurrent Event Processes and Failure Time Data , 2004, Journal of the American Statistical Association.

[15]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .

[16]  Zhiliang Ying,et al.  Semiparametric regression for the mean and rate functions of recurrent events , 2000 .

[17]  J. Neaton,et al.  Considerations in choice of a clinical endpoint for AIDS clinical trials. Terry Beirn Community Programs for Clinical Research on AIDS (CPCRA). , 1994, Statistics in medicine.

[18]  R. Wolfe,et al.  Shared Frailty Models for Recurrent Events and a Terminal Event , 2004, Biometrics.

[19]  J. Neaton,et al.  A comparative trial of didanosine or zalcitabine after treatment with zidovudine in patients with human immunodeficiency virus infection. The Terry Beirn Community Programs for Clinical Research on AIDS. , 1994, The New England journal of medicine.

[20]  D. Lin,et al.  Nonparametric Analysis of Recurrent Events and Death , 2000, Biometrics.

[21]  A Munoz,et al.  The Alive Study: A Longitudinal Study of HIV-1 Infection in Intravenous Drug Users: Description of Methods , 1991, NIDA research monograph.

[22]  Donglin Zeng,et al.  Efficient estimation of semiparametric transformation models for counting processes , 2006 .

[23]  Donglin Zeng,et al.  A semiparametric additive rates model for recurrent event data , 2006, Lifetime data analysis.

[24]  Zhiliang Ying,et al.  Semiparametric analysis of the additive risk model , 1994 .