Model-Based and/or Marginal Analysis for Multiple Event-Time Data?

  • David Oakes
Part of the Lecture Notes in Statistics book series (LNS, volume 123)


We will explore the relationship between a marginal proportional hazards formulation for ordered failure times, as proposed by Wei, Lin and Weissfeld (1989) and strongly supported by Therneau (1997), and a conditional formulation advocated by, among others, Clayton (1988), Oakes (1992) and Pepe and Cai (1993). We review the derivation given by Oakes (1992) of a conditional proportional hazards model via an underlying frailty structure. Quite generally, we show that a family of absolutely continuous bivariate survivor functions cannot simultaneously satisfy the proportional hazards model both conditionally and unconditionally. We will explore the efficiency loss in using the marginal approach compared with full likelihood procedures in two simple special cases, and find it to be quite small.


Failure Time Marginal Model Failure Time Data Cumulative Hazard Function Asymptotic Relative Efficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andersen, P.K. and Gill, R.D. (1982). Cox’s regression model for counting processes, a large sample study. Ann. Statist., 10, 1100–1120.MathSciNetMATHCrossRefGoogle Scholar
  2. Clayton, D.G. (1988). The analysis of event history data: a review of progress and outstanding problems. Statist. Med., 7, 819–841.CrossRefGoogle Scholar
  3. Cox, D.R. (1972). The statistical analysis of dependencies in point processes. In Lewis, P.A.W. (ed). Symposium on Point Processes, New York, Wiley, pp 55–66.Google Scholar
  4. Dabrowska, D.M., Sun, G.W. and Horowitz, M.H. (1992). Cox regression in a Markov renewal model with an application to the analysis of bone marrow transplant data. J. Amer. Statist. Assoc. 89, 867–877.CrossRefGoogle Scholar
  5. Efron, B. (1977). The efficiency of Cox’s likelihood function for censored data. J. Amer. Statist. Assoc, 72, 557–565.MathSciNetMATHCrossRefGoogle Scholar
  6. Greenwood, M. and Yule, G.U. (1920). An enquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease as repeated accidents. J. R. Statist. Soc, 83, 255–279.CrossRefGoogle Scholar
  7. Hughes, M.D. (1995). Power Considerations for Clinical Trials Using Multivariate Time-to-Event Data. Unpublished Manuscript.Google Scholar
  8. Huster, W.J., Brookmeyer, R. and Self, S.G. (1989). Modelling paired survival data with covariates. Biometrics, 45, 145–156.MathSciNetMATHCrossRefGoogle Scholar
  9. Liang, K.Y. and Zeger, S.L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22.MathSciNetMATHCrossRefGoogle Scholar
  10. Manatunga, A.K. and Oakes, D. (1995). Parametric analysis for matched pair survival data. Unpublished Manuscript.Google Scholar
  11. Oakes, D. (1977). The asymptotic information in censored survival data. Biometrika, 64, 441–448.MathSciNetMATHCrossRefGoogle Scholar
  12. Oakes, D. (1981). Survival times, aspects of partial likelihood. Int. Statist. Rev., 49, 199–233.MathSciNetCrossRefGoogle Scholar
  13. Oakes, D. (1992). Frailty models for multiple event-time data. In Klein, J.P. and Goel P.K. (eds). Survival Analysis: State of the Art. Kluwer, pp 371–380.Google Scholar
  14. Oakes, D. and Cui, L. (1994). On semiparametric inference for modulated renewal processes. Biometrika, 81, 83–90.MathSciNetMATHCrossRefGoogle Scholar
  15. Parkinson Study Group (1989). Effect of deprenyl on the progression of disability in early Parkinson’s disease. New Engl. J. Med., 320, 1364–1371.Google Scholar
  16. Parkinson Study Group (1993). Effects of tocopherol and deprenyl on the progression of disability in early Parkinson’s disease. New Engl. J. Med., 328, 176–183.CrossRefGoogle Scholar
  17. Parkinson Study Group (1996). Impact of deprenyl and tocopherol treatment on Parkinson’s disease in DATATOP patients requiring levodopa. Ann. Neurol., 39, 37–45.CrossRefGoogle Scholar
  18. 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.MATHCrossRefGoogle Scholar
  19. Prentice, R.L., Williams, B.J. and Peterson, A.V. (1981). On the regression analysis of multivariate failure time data. Biometrika, 68, 373–37.MathSciNetMATHCrossRefGoogle Scholar
  20. Therneau, T. (1997). Extending the Cox model. In Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis, Eds. D. Y. Lin and T. R. Fleming, pp. xxx–xxx. New York: Springer-Verlag.Google Scholar
  21. Wei, L.J. and Lachin, J.M. (1984). Two-sample asymptotically distribution-free tests for incomplete multivariate observations. J. Amer. Statist. Assoc. 79, 653–661.MathSciNetMATHCrossRefGoogle Scholar
  22. Wei, L.J., Lin, D.Y., and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modelling of marginal distributions. J. Amer. Statist. Assoc. 84, 1065–1073.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • David Oakes

There are no affiliations available

Personalised recommendations