158
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A class of partially linear transformation models for recurrent gap times

, &
Pages 739-766 | Received 07 Nov 2016, Accepted 21 Mar 2017, Published online: 14 Sep 2017

References

  • Aalen, O. O., and E. Husebye. 1991. Statistical analysis of repeated events forming renewal processes. Statistics in Medicine 10:1227–40.
  • Andersen, P. K., and R. D. Gill. 1982. Cox's regression model for counting processes: a large sample study. The Annals of Statistics 10:1100–20.
  • Cai, J., J. Fan, J. Jiang, and H. Zhou. 2007a. Partially linear hazard regression for multivariate survival data. Journal of the American Statistical Association 102:538–51.
  • Cai, J., J. Fan, H. Zhou, and Y. Zhou. 2007b. Hazard models with varying coefficients for multivariate failure time data. The Annals of Statistics 35:324–54.
  • Carroll, R. J., J. Fan, I. Gijbels, and M. P. Wand. 1997. Generalized partially linear single-index models. Journal of the American Statistical Association 92:477–89.
  • Chang, S. H. 2004. Estimating marginal effects in accelerated failure time models for serial sojourn among repeated event. Lifetime Data Analysis 10:175–90.
  • Chang, S. H., and M. C. Wang. 1999. Conditional regression analysis for recurrence time data. Journal of the American Statistical Association 94:1221–30.
  • Chen, K., Z. Jin, and Z. Ying. 2002. Semiparametric analysis of transformation models with censored data. Biometrika 89:659–68.
  • Chen, Y. H. 2009. Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models. Biometrika 96:591–600.
  • Cochran, W. G. 1977. Sampling techniques. New York: Wiley.
  • Cook, R. J., and J. F. Lawless. 2007. The statistical analysis of recurrent events. New York: Springer.
  • Cook, R. J., J. F. Lawless, L. Lakhal-Chaieb, and K.-A. Lee. 2009. Robust estimation of mean functions and treatment effects for recurrent events under event dependent censoring and termination: Application to skeletal complications in cancer metastatic to bone. Journal of the American Statistical Association 104:60–75.
  • Darlington, G. A., and S. N. Dixon. 2013. Event-weighted proportional hazards modelling for recurrent gap time data. Statistics in Medicine 32:124–30.
  • Dong, L., and L. Sun. 2015. A flexible semiparametric transformation model for recurrent event data. Lifetime Data Analysis 21:20–41.
  • Du, P. 2009. Nonparametric modeling of the gap time in recurrent event data. Lifetime Data Analysis 15:256–77.
  • Fan, J., I. Gijbels, and M. King. 1997. Local likelihood and local partial likelihood in hazard regression. The Annals of Statistics 25:1661–90.
  • Fleming, T. R., and D. P. Harrington. 1991. Counting processes and survival analysis. New York: Wiley.
  • Ghosh, D., and D. Y. Lin. 2002. Marginal regression models for recurrent and terminal events. Statistica Sinica 12:663–88.
  • Gumbel, E. J. 1960. Bivariate exponential distributions. Journal of the American Statistical Association 55:698–707.
  • Huang, J. 1999. Efficient estimation of the partly linear additive Cox model. The Annals of Statistics 27:1536–63.
  • Huang, X., and L. Liu. 2007. A joint frailty model for survival and gap times between recurrent events. Biometrics 63:389–97.
  • Huang, Y., and Y. Q. Chen. 2003. Marginal regression of gaps between recurrent events. Lifetime Data Analysis 9:293–303.
  • Jin, Z., Z. Ying, and L. J. Wei. 2001. A simple resampling method by perturbing the minimand. Biometrika 88:381–90.
  • Kalbfleisch, J. D., D. E. Schaubel, Y. Ye, and Q. Gong. 2013. An estimating function approach to the analysis of recurrent and terminal events. Biometrics 69:366–74.
  • 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.
  • Lin, D. Y., W. Sun, and Z. Ying. 1999. Nonparametric estimation of the gap time distribution for serial events with censored data. Biometrika 86:59–70.
  • Lin, D. Y., L. J. Wei, I. Yang, and Z. Ying. 2000. Semiparametric regression for the mean and rate functions of recurrent events. Journal of the Royal Statistical Society Series B 62:711–30.
  • Lin, D. Y., L. J. Wei, and Z. Ying. 1998. Accelerated failure time models for counting processes. Biometrika 85:605–18.
  • Lin, D. Y., L. J. Wei, and Z. Ying. 2001. Semiparametric transformation models for point processes. Journal of the American Statistical Association 96:620–8.
  • Liu, B., W. Lu, and J. Zhang. 2014. Accelerated intensity frailty model for recurrent events data. Biometrics 70:579–87.
  • Lu, W. 2005. Marginal regression of multivariate event times based on linear transformation models. Lifetime Data Analysis 11:389–404.
  • Lu, W., and H. H. Zhang. 2010. On estimation of partially linear transformation models. Journal of the American Statistical Association 105:683–91.
  • Luo, X., and C. Y. Huang. 2011. Analysis of recurrent gap time data using the weighted risk-set method and the modified within-cluster resampling method. Statistics in Medicine 30:301–11.
  • Luo, X., C. Y. Huang, and L. Wang. 2013. Quantile regression for recurrent gap time data. Biometrics 69:375–85.
  • Pepe, M. S., and J. Cai. 1993. Some graphical displays and marginal regression analyses for recurrent failure times and time-dependent covariates. Journal of the American Statistical Association 88:811–20.
  • Pollard, D. 1990. Empirical processes: Theory and applications, volume 2 of NSF-CBMS regional conference series in probability and statistics. Hayward, CA: Institute of Mathematical Statistics.
  • Schaubel, D. E., and J. Cai. 2004. Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data. Biometrika 91:291–303.
  • Shorack, G. R., and J. A. Wellner. 1986. Empirical processes with applications to statistics. New York: Wiley.
  • Strawderman, R. L. 2005. The accelerated gap times model. Biometrika 92:647–66.
  • Sun, L., D. Park, and J. Sun. 2006. The additive hazards model for recurrent gap times. Statistica Sinica 16:919–32.
  • Sun, L., X. Zhao, and J. Zhou. 2011. A class of mixed models for recurrent event data. The Canadian Journal of Statistics 39:578–90.
  • Wang, M. C., and S. H. Chang. 1999. Nonparametric estimation of a recurrent survival function. Journal of the American Statistical Association 94:146–53.
  • Zeng, D., and J. Cai. 2010. Semiparametric additive rate model for recurrent events with informative terminal event. Biometrika 97:699–712.
  • Zeng, D., D.Y. Lin. 2006. Efficient estimation of semiparametric transformation models for counting processes. Biometrika 93:627–40.
  • Zeng, D., and D. Y. Lin. 2007. Semiparametric transformation models with random effects for recurrent events. Journal of the American Statistical Association 102:167–80.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.