Marginal regression of recurrent gap times based on semiparametric transformation cure model

References

• Andrews, D. F., and A. M. Herzberg. 1985. Data: A collection of problems from many fields for the student and research worker. New York: Springer-Verlag.
   Google Scholar
• Bennett, S. 1983. Analysis of survival data by the proportional odds model. Statistics in Medicine 2 (2):273–7.
   PubMedGoogle Scholar
• Byar, D. P. 1980. The Veterans Administration study of chemoprophylaxis of recurrent stage I bladder tumors:comparisons of placebo, pyridoxine, and topical thiotepa, in Bladder tumors and other topic in urological oncology, eds. M. Pavone-Macaluso, P.H. Smith, and F. Edsmyn, 363–370. New York: Plenum.
   Google Scholar
• Chang, S. H. 2004. Estimating marginal effects in accelerated failure time models for serial sojourn times among repeated events. Lifetime Data Analysis 10 (2):175–90.
   PubMed Web of Science ®Google Scholar
• Chang, S.-H. and M.-C. Wang. 1999. Conditional regression analysis for recurrent time data. Journal of the American Statistical Association 94:1221–1300.
   Google Scholar
• Chen, K., Z. Jin, and Z. Ying. 2002. Semiparametric analysis of transformation models with censored data. Biometrika 89 (3):659–68. doi: 10.1093/biomet/89.3.659.
   Web of Science ®Google Scholar
• Chen, C.-M., and T.-F. Lu. 2012. Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models. Computational Statistics and Data Analysis 56 (3):645–55. doi: 10.1016/j.csda.2011.09.013.
   Web of Science ®Google Scholar
• Cheng, S. C., L. J. Wei, and Z. Ying. 1995. Analysis of transformation models with censored data. Biometrika 82 (4):835–45. doi: 10.1093/biomet/82.4.835.
   Web of Science ®Google Scholar
• Clayton, D. G. 1978. A model for association in bivariate life tables and its applications in epidemiological studies of familial tendency in chronic disease incident. Biometrika 65 (1):141–51. doi: 10.1093/biomet/65.1.141.
   Web of Science ®Google Scholar
• Cook, R. J., and J. F. Lawless. 2007. The statistical analysis of recurrent events. New York: Springer.
   Google Scholar
• Cox, D. 1972. Regression models and life tables (with discussion). Journal of the Royal Statistical Society. Series B 34 :187–220. doi: 10.1111/j.2517-6161.1972.tb00899.x.
   Web of Science ®Google Scholar
• Darlington, G. A., and S. N. Dixon. 2013. Event-weighted proportional hazards modelling for recurrent gap time data. Statistics in Medicine 32 (1):124–30. doi: 10.1002/sim.5522.
   PubMed Web of Science ®Google Scholar
• Farewell, V. T. 1982. The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 38 (4):1041–6.
   PubMed Web of Science ®Google Scholar
• Gail, M. H., T. J. Santner, and C. C. Brown. 1980. An analysis of comparative carcinogenisis experiments based on multiple times to tumor. Biometrics 36 (2):255–66. doi: 10.2307/2529977.
   PubMed Web of Science ®Google Scholar
• Huang, Y. J., and Y. Q. Chen. 2003. Marginal regression of gaps between recurrent events. Lifetime Data Analysis 9 (3):293–303. doi: 10.1023/A:1025892922453.
   PubMed Web of Science ®Google Scholar
• Kang, F., L. Sun, and X. Zhao. 2015. A class of transformed hazards models for recurrent gap times. Computational Statistics and Data Analysis 83 :151–67. doi: 10.1016/j.csda.2014.10.005.
   Web of Science ®Google Scholar
• Kuk, A. Y. C., and C.-H. Chen. 1992. A mixture model combing logistic regression with proportional hazards regression. Biometrika 79 (3):531–41. doi: 10.1093/biomet/79.3.531.
   Web of Science ®Google Scholar
• Louzada, F., and J. Cobre. 2012. A multiple time scale survival model with a cure fraction. Test 21 (2):355–68. doi: 10.1007/s11749-011-0247-1.
   Web of Science ®Google Scholar
• Lu, W., and Z. Ying. 2004. On semiparametric transformation cure models. Biometrika 91 (2):331–43. doi: 10.1093/biomet/91.2.331.
   Web of Science ®Google Scholar
• Lu, W. 2005. Marginal regression of multivariate event times based on linear transformation models. Lifetime Data Analysis 11 (3):389–404. doi: 10.1007/s10985-005-2969-4.
   PubMed Web of Science ®Google Scholar
• Maller, R. A., and S. Zhou. 1996. Survival analysis with long term survivors. New York: Wiley.
   Google Scholar
• Murphy, S. A., A. J. Rossini, and A. W. van der Vaart. 1997. Maximum likelihood estimation in the proportional odds model. Journal of the American Statistical Association 92 (439):968–76. doi: 10.1080/01621459.1997.10474051.
   Web of Science ®Google Scholar
• Peng, Y., and K. B. G. Dear. 2000. A nonparametric mixture model for cure rate estimation. Biometrics 56 (1):237–43.
   PubMed Web of Science ®Google Scholar
• Pollard, D. 1990. Empirical Processes: Theory and Applications, NSF-CBMS. Regional Conference Series in Probability and Statistics, 2, Hayward, CA: IMS.
   Google Scholar
• Reinhard, H. 1987. Differential equations: Foundations and applications. New York: Macmillan.
   Google Scholar
• Rondeau, V. 2010. Statistical models for recurrent events and death: Application to cancer events. Mathematical and Computer Modelling 52 (7–8):949–55. doi: 10.1016/j.mcm.2010.02.002.
   Google Scholar
• Shen, H., and R. J. Cook. 2014. A dynamic Mover-Stayer model for recurrent event processes subject to resolution. Lifetime Data Analysis 20 (3):404–23. doi: 10.1007/s10985-013-9271-7.
   PubMed Web of Science ®Google Scholar
• Strawderman, R. L. 2005. The accelerated gap times model. Biometrika 92 (3):647–66. doi: 10.1093/biomet/92.3.647.
   Web of Science ®Google Scholar
• Sun, L. Q., D. H. Park, and J. G. Sun. 2006. The additive hazards model for recurrent gap times. Statistica Sinica 16 :919–32.
   Web of Science ®Google Scholar
• Sy, J. P., and J. M. G. Taylor. 2000. Estimation in a cox proportional hazards cure model. Biometrics 56(1):227–36.
   PubMed Web of Science ®Google Scholar
• Yang, S., and R. Prentice. 1999. Semiparametric inference in the proportional odds regression model. Journal of the American Statistical Association 94 (445):125–36. doi: 10.1080/01621459.1999.10473829.
   Web of Science ®Google Scholar
• Wang, M. C., and S. H. Chang. 1999. Nonparametric estimation of a recurrent survival function. Journal of the American Statistical Association 94 (445):146–53. doi: 10.1080/01621459.1999.10473831.
   PubMed Web of Science ®Google Scholar
• Wei, L. J., D. Y. Lin, and L. Weissfeld. 1989. Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American Statistical Association 84 (408):1065–73. doi: 10.1080/01621459.1989.10478873.
   Web of Science ®Google Scholar
• Yu, B. 2008. A frailty mixture cure model with application to hospital readmission cata. Biometrical Journal 50 (3):386–94.
   PubMed Web of Science ®Google Scholar
• Zeng, D., and D. Y. Lin. 2006. Efficient estimation of semiparametric transformation models for counting processes. Biometrika 93 (3):627–40. doi: 10.1093/biomet/93.3.627.
   Web of Science ®Google Scholar
• Zhao, X. B., and X. Zhou. 2008. Discrete-time survival models with long-term survivors. Statistics in Medicine 27 (8):1261–81. doi: 10.1002/sim.3018.
   PubMed Web of Science ®Google Scholar
• Zeng, D., and D. Y. Lin. 2010. A general theory for maximum likelihood estimation in semiparametric regression models with censored data. Statistica Sinica 20 :871–910.
   PubMed Web of Science ®Google Scholar
• Zhao, X., and X. Zhou. 2012. Modeling gap times between recurrent events by marginal rate function. Computational Statistics and Data Analysis 56 (2):370–83. doi: 10.1016/j.csda.2011.07.015.
   Web of Science ®Google Scholar