Skip to main content
Log in

Dynamic Random Effects Models for Times Between Repeated Events

Lifetime Data Analysis Aims and scope Submit manuscript

Abstract

We consider recurrent event data when the duration or gap times between successive event occurrences are of intrinsic interest. Subject heterogeneity not attributed to observed covariates is usually handled by random effects which result in an exchangeable correlation structure for the gap times of a subject. Recently, efforts have been put into relaxing this restriction to allow non-exchangeable correlation. Here we consider dynamic models where random effects can vary stochastically over the gap times. We extend the traditional Gaussian variance components models and evaluate a previously proposed proportional hazards model through a simulation study and some examples. Besides, semiparametric estimation of the proportional hazards models is considered. Both models are easily used. The Gaussian models are easily interpreted in terms of the variance structure. On the other hand, the proportional hazards models would be more appropriate in the context of survival analysis, particularly in the interpretation of the regression parameters. They can be sensitive to the choice of model for random effects but not to the choice of the baseline hazard function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • O. O. Aalen and E. Husebye, “Statistical analysis of repeated events forming renewal processes,” Statistics in Medicine vol. 10 pp. 1227–1240, 1991.

    Google Scholar 

  • P. K. Andersen, J. P. Klein, K. M. Knudsen, and R. Tabanera-Palacios, “Estimation of the variance in a Cox's regression model with shared frailties,” Biometrics vol. 53 pp. 1475–1484, 1997.

    Google Scholar 

  • D. P. Byar, “Why data bases should not replace randomized clinical trials,” Biometrics vol. 36 pp. 337–342, 1980.

    Google Scholar 

  • B. P. Carlin, N. G. Polson, and D. S. Stoffer, “A Monte Carlo approach to nonnormal and nonlinear state-space modeling,” Journal of American Statistical Association vol. 87 pp. 493–500, 1992.

    Google Scholar 

  • D. G. Clayton, “Some approaches to the analysis of recurrent event data,” Statistical Methods in Medical Research vol. 3 pp. 244–262, 1994.

    Google Scholar 

  • A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood estimation with incomplete data via the EM algorithm (with discussion),” Journal of the Royal Statistical Society B vol. 39 pp. 1–38, 1977.

    Google Scholar 

  • L. Fahrmeir, “Dynamic modelling and penalized likelihood estimation for discrete time survival data,” Biometrika pp. 317–330, 1994.

  • D. A. Follmann and M. S. Goldberg, “Distinguishing heterogeneity from decreasing hazard rates,” Technometrics vol. 30 pp. 389–396, 1988.

    Google Scholar 

  • M. H. Gail, T. J. Santner, and C. C. Brown, “An analysis of comparative carcinogenesis experiments based on multiple times to tumor,” Biometrics vol. 36 pp. 255–266, 1980.

    Google Scholar 

  • A. C. Harvey, Forecasting, structural time series models and the Kalman filter, Cambridge University Press: New York, 1989.

    Google Scholar 

  • A. C. Harvey and C. Fernandes, “Time series models for count or qualitative observations,” Journal of Business and Economic Statistics vol. 7 pp. 407–423, 1989.

    Google Scholar 

  • R. H. Jones, Longitudinal data with serial correlation: A state-space approach, Chapman and Hall: London, 1993.

    Google Scholar 

  • B. Jørgensen, S. Lundbye-Christensen, X. Song, and L. Sun, “A longitudinal study of emergency room visits and air pollution for Prince George, British Columbia,” Statistics in Medicine vol. 15 pp. 823–836, 1996.

    Google Scholar 

  • J. P. Klein, “Semiparametric estimation of random effects using the Cox model based on the EM algorithm,” Biometrics vol. 48 pp. 795–806, 1992.

    Google Scholar 

  • P. Lambert, “Modeling of nonlinear growth curve on series of correlated count data measured at unequally spaced times: A full likelihood based approach,” Biometrics vol. 52 pp. 50–55, 1996a.

    Google Scholar 

  • P. Lambert, “Modelling of repeated series of count data measured at unequally spaced times,” Applied Statistics vol. 45 pp. 31–38, 1996b.

    Google Scholar 

  • J. F. Lawless, “The analysis of recurrent events for multiple subjects,” Applied Statistics vol. 44 pp. 487–498, 1995.

    Google Scholar 

  • J. F. Lawless and D. Y. T. Fong, “State duration models in clinical and observational studies,” Statistics in Medicine vol. 18 pp. 2365–2376, 1999.

    Google Scholar 

  • J. H. Petersen, P. K. Andersen, and R. D. Gill, “Variance components models for survival data,” Statistica Neerlandica vol. 50 pp. 193–211, 1996.

    Google Scholar 

  • A. Pickles and R. Crouchley, “Generalization and applications of frailty models for survival and event data,” Statistical Methods in Medical Research vol. 3 pp. 263–278, 1994.

    Google Scholar 

  • R. L. Prentice, B. J. Williams, and A. V. Peterson, “On the regression analysis of multivariate failure time data,” Biometrika vol. 68 pp. 373–379, 1981.

    Google Scholar 

  • N. Shephard and M. K. Pitt, “Likelihood analysis of non-gaussian measurement time series,” Biometrika vol. 84 pp. 653–667, 1997.

    Google Scholar 

  • J. H. Shih and T. A. Louis, “Tests of independence for bivariate survival data,” Biometrics vol. 52 pp. 1440–1449, 1996.

    Google Scholar 

  • R. L. Smith and J. E. Miller, “A non-gaussian state space model and application to prediction of records,” Journal of Royal Statistical Society B vol. 48 pp. 79–88, 1986.

    Google Scholar 

  • M. K. P. So, “Time series with additive noise,” Biometrika vol. 86 pp. 474–482, 1999.

    Google Scholar 

  • X. Xue and R. Brookmeyer, “Bivariate frailty model for the analysis of multivariate failure time,” Lifetime Data Analysis vol. 2 pp. 277–289, 1996.

    Google Scholar 

  • H. Yue and K. S. Chan, “A dynamic frailty model for multivariate survival data,” Biometrics vol. 53 pp. 785–793, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fong, D.Y., Lam, K., Lawless, J. et al. Dynamic Random Effects Models for Times Between Repeated Events. Lifetime Data Anal 7, 345–362 (2001). https://doi.org/10.1023/A:1012544714667

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012544714667

Navigation