Lifetime Data Analysis

, Volume 11, Issue 3, pp 405–425 | Cite as

Semiparametric Methods for Clustered Recurrent Event Data

  • Douglas E. Schaubel
  • Jianwen Cai


In biomedical studies, the event of interest is often recurrent and within-subject events cannot usually be assumed independent. In addition, individuals within a cluster might not be independent; for example, in multi-center or familial studies, subjects from the same center or family might be correlated. We propose methods of estimating parameters in two semi-parametric proportional rates/means models for clustered recurrent event data. The first model contains a baseline rate function which is common across clusters, while the second model features cluster-specific baseline rates. Dependence structures for patients-within-cluster and events-within-patient are both unspecified. Estimating equations are derived for the regression parameters. For the common baseline model, an estimator of the baseline mean function is proposed. The asymptotic distributions of the model parameters are derived, while finite-sample properties are assessed through a simulation study. Using data from a national organ failure registry, the proposed methods are applied to the analysis of technique failures among Canadian dialysis patients.


clustered failure time data marginal model ordered event times proportional rates robust variance 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aalen, O. O. 1978Nonparametric inference for a family of counting processesThe Annals of Statistics6701726Google Scholar
  2. Bilias, Y., Gu, M., Ying, Z. 1997Towards a general asymptotic theory for the Cox model with staggered entryThe Annals of Statistics25662682CrossRefGoogle Scholar
  3. N. Breslow, “Contribution to the discussion of the paper by D.R. Cox,” Journal of the Royal Statistic al Society, Series B, vol. 34, pp. 187–220, 1972.Google Scholar
  4. Cai, T., Wei, L. J., Wilcox, M. 2000Semiparametric regression analysis for clustered failure time dataBiometrika87867878CrossRefGoogle Scholar
  5. Clegg, L. X., Cai, J., Sen, P. K. 1999A marginal mixed baseline hazards model for multivariate failure time dataBiometrics55805812CrossRefPubMedGoogle Scholar
  6. Cook, R. J., Lawless, J. F. 2002Analysis of repeated eventsStatistical Methods in Medical Research11141166CrossRefPubMedGoogle Scholar
  7. Glidden, D. V., Vittinghoff, E. 2004Modelling clustered survival data from multicentre clinical trialsStatistics in Medicine23369388CrossRefPubMedGoogle Scholar
  8. Jacobsen, M. 1989Existence and unicity of MLEs in discrete exponential family distributionsScandinavian Journal of Statistics16335349Google Scholar
  9. Kalbfleisch, J. D., Prentice, R. L. 2002The Statistical Analysis of Failure Time DataWileyNew York, NYGoogle Scholar
  10. Lawless, J. F. 1987Regression methods for Poisson process dataJournal of the American Statistical Association82808815Google Scholar
  11. Lawless, J. F., Nadeau, C. 1995Some simple robust methods for the analysis of recurrent eventsTechnometrics37158168MathSciNetGoogle Scholar
  12. Lee, E. W., Wei, L. J., Amato, D. A. 1992Cox-type regression analysis for large numbers of small groups of correlated failure time observationsKlein, J. P.Goel, P. K. eds. Survival Analysis: State of the ArtKluwerDordrecht237247Google Scholar
  13. Lin, D. Y., Wei, L. J., Yang, I., Ying, Z. 2000Semiparametric regression for the mean and rate functions of recurrent eventsJournal of the Royal Statistical Society: Series B62711730CrossRefMathSciNetGoogle Scholar
  14. Pepe, M. S., Cai, J. 1993Some graphical displays and marginal regression analyses for recurrent failure times and time-dependent covariatesJournal of the American Statistical Association88811820Google Scholar
  15. Pollard, D. 1990Empirical Processes: Theory and ApplicationsInstitute of Mathematical StatisticsmHayward, CAGoogle Scholar
  16. Rockafellar, R. T. 1970Convex AnalysisPrinceton University PressPrinceton, NJGoogle Scholar
  17. Sen, P. K., Singer, J. M. 1993Large Sample Methods in StatisticsChapman & HallNew York, NYGoogle Scholar
  18. Spiekerman, C. F., Lin, D. Y. 1998Marginal regression models for multivariate failure time dataJournal of American Statistical Association9311641175Google Scholar
  19. Vaart, A. W., Wellner, J. A. 1996Weak Convergence and Empirical ProcessesSpringerNew York, NYGoogle Scholar
  20. Wei, L. J., Lin, D. Y., Weissfeld, L. 1989Regression analysis of multivariate incomplete failure time data by modeling marginal distributionsJournal of American Statistical Association8410651073Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of BiostatisticsUniversity of MichiganAnn ArborUSA
  2. 2.Department of BiostatisticsUniversity of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations