Shared frailty model for recurrent event data with multiple causes

References

• Andersen , P. K. 1982 . Testing goodness of fit of Cox's regression and life model . Biometrics , 38 : 67 – 77 .
   Web of Science ®Google Scholar
• Andersen , P. K. , Borgan , Ø , Gill , R. D. and Keilding , N. 1993 . Statistical Models Based on Counting Processes , New York : Springer .
   Google Scholar
• Balakrishnan , N. and Peng , Y. 2006 . Generalized gamma frailty model . Statist. Med , 25 : 2797 – 2816 .
   PubMed Web of Science ®Google Scholar
• Cook , R. J. and Lawlesss , J. F. 2007 . The Statistical Analysis of Recurrent Events , New York : Springer .
   Google Scholar
• Cox , D. R. 1972 . Regression models and life tables . J. Roy. Statist. Soc. Ser. B , 34 : 187 – 220 .
   Web of Science ®Google Scholar
• Dabrowska , D. M. , Sun , G. and Horowitz , M. M. 1994 . Cox Regression in a Markov renewal model: An application to the analysis of Bone marrow transplant data . J. Amer. Statist. Assoc , 89 : 867 – 877 .
   Web of Science ®Google Scholar
• Gail , M. H. , Santner , T. J. and Brown , C. C. 1980 . An analysis of comparative carcinogenesis experiments based on multiple times to tumor . Biometrics , 36 : 255 – 266 .
   PubMed Web of Science ®Google Scholar
• Ghosh , D. 2004 . Accelerated rates regression models for recurrent failure data . Lifetime Data Anal , 10 : 247 – 261 .
   PubMed Web of Science ®Google Scholar
• Hougaard , P. 2000 . Analysis of Multivariate Survival Data , New York : Springer .
   Google Scholar
• Hu , W. , Li , G. and Li , N. 2009 . A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data . Statist. Med , 28 : 1601 – 1619 .
   PubMed Web of Science ®Google Scholar
• Huang , C. Y. and Wang , M. C. 2004 . Joint modeling and estimation for recurrent event processes and failure time data . J. Amer. Statist. Assoc , 99 : 1153 – 1165 .
   PubMed Web of Science ®Google Scholar
• Huang , C. Y. and Wang , M. C. 2005 . Non-parametric estimation of the bivariate recurrence time distribution . Biometrics , 61 : 392 – 402 .
   PubMed Web of Science ®Google Scholar
• Huang , C. Y. , Wang , M. C. and Zhang , Y. 2006 . Analyzing panel count data with informative observation times . Biometrika , 93 : 763 – 775 .
   PubMed Web of Science ®Google Scholar
• Huang , X. and Liu , L. 2007 . A joint frailty model for survival time and gap times between recurrent events . Biometrics , 63 : 389 – 397 .
   PubMed Web of Science ®Google Scholar
• Kalbfleisch , J. D. and Prentice , R. L. 2002 . The Statistical Analysis of Failure Time Data , New York : Wiley .
   Google Scholar
• Klein , J. P. and Moeschberger , M. L. 2003 . Survival Analysis: Techniques for Censored and Truncated Data , New York : Springer .
   Google Scholar
• Lancaster , T. and Intrator , O. 1998 . Panel data with survival: Hospitalization of HIV-positive patients . J. Amer. Statist. Assoc , 93 : 46 – 53 .
   Web of Science ®Google Scholar
• Lawless , J. F. and Nadeau , C. 1995 . Some simple robust methods for the analysis of recurrent events . Technometrics , 37 : 158 – 168 .
   Web of Science ®Google Scholar
• Lawless , J. F. , Wigg , M. , Tuli , S. , Drake , J. and Lamberti-Pasculli , M. 2001 . Analysis of repeated failures of durations, with application to shunt failures for patients with pediatric hydrocephalus . J. Roy. Statist. Soc. C Appl. Statist , 50 : 449 – 465 .
   Web of Science ®Google Scholar
• Lin , D. Y. , Sun , W. and Ying , Z. 1999 . Nonparametric estimation of gap time distributions for serial events with censored data . Biometrika , 86 : 59 – 70 .
   Web of Science ®Google Scholar
• Lin , D. Y. , Wei , L. J. , Yang , I. and Ying , Z. 2000 . Semi-parametric regression for the mean and rate functions of recurrent events . J. Roy. Statist. Soc. B , 62 : 711 – 730 .
   Google Scholar
• Liu , L. , Wolfe , R. A. and Huang , X. 2004 . Shared frailty models for recurrent events and a terminal event . Biometrics , 60 : 747 – 756 .
   PubMed Web of Science ®Google Scholar
• Louis , T. A. 1982 . Finding the observed information matrix when using the EM algorithm . J. Roy. Statist. Soc. Ser. B , 44 : 226 – 233 .
   Web of Science ®Google Scholar
• Murphy , S. A. 1995 . Asymptotic theory for the frailty model . Ann. Statist , 23 ( 1 ) : 182 – 198 .
   Web of Science ®Google Scholar
• Olesen , A. V. and Parner , E. T. 2005 . Correcting for selection using frailty models . Statist. Med , 25 : 1672 – 1684 .
   Web of Science ®Google Scholar
• Parner , E. 1998 . Asymptotic theory for the correlated gamma frailty . Ann. Statist , 26 : 183 – 214 .
   Web of Science ®Google Scholar
• Pepe , M. S. and Cai , J. 1993 . Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates . J. Amer. Statist. Assoc , 88 : 811 – 820 .
   Web of Science ®Google Scholar
• Rondeau , V. , Mathoulin-Pelissier , S. , Jacqmin-Gadda , H. , Brouste , V. and Soubeyran , P. 2007 . Joint frailty models for recurring events and death using maximum penalized likelihood estimation: Application on cancer events . Biostatistics , 8 : 708 – 721 .
   PubMed Web of Science ®Google Scholar
• Sankaran , P. G. and Anisha , P. Regression methods for gap time hazard functions of recurrent event data with multiple causes (communicated), preprint (2011), submitted for publication
   Google Scholar
• Schaubel , D. E. , Zeng , D. and Cai , J. 2006 . A semiparametric additive rates model for recurrent event data . Lifetime Data Anal , 12 : 389 – 406 .
   PubMed Web of Science ®Google Scholar
• Sun , J. , Tong , X. and He , X. 2007 . Regression analysis of panel count data with dependent observation times . Biometrics , 63 : 1053 – 1059 .
   PubMed Web of Science ®Google Scholar
• Sun , L. and Su , B. 2008 . A class of accelerated means regression models for recurrent event data . Lifetime Data Anal , 14 : 357 – 375 .
   PubMed Web of Science ®Google Scholar
• Wang , M. C. , Qin , J. and Chang , C. T. 2001 . Analyzing recurrent event data with informative censoring . J. Amer. Statist. Assoc , 96 : 1057 – 1065 .
   Web of Science ®Google Scholar
• Wang , W. J. and Wells , M. T. 1998 . Nonparametric estimation of successive duration times under dependent censoring . Biometrika , 86 : 59 – 70 .
   Google Scholar
• Ye , Y. , Kalbfleisch , J. D. and Schaubel , D. E. 2007 . Semi-parametric analysis of correlated recurrent and terminal events . Biometrics , 63 : 78 – 87 .
   PubMed Web of Science ®Google Scholar
• Zeng , D. and Lin , D. Y. 2006 . Efficient estimation of semiparametric transformation models for counting processes . Biometrika , 93 : 627 – 640 .
   Web of Science ®Google Scholar