Statistics and Computing

, Volume 15, Issue 3, pp 231–239 | Cite as

Tree-structured subgroup analysis for censored survival data: Validation of computationally inexpensive model selection criteria

  • Abdissa NegassaEmail author
  • Antonio Ciampi
  • Michal Abrahamowicz
  • Stanley Shapiro
  • Jean-François Boivin


The performance of computationally inexpensive model selection criteria in the context of tree-structured subgroup analysis is investigated. It is shown through simulation that no single model selection criterion exhibits a uniformly superior performance over a wide range of scenarios. Therefore, a two-stage approach for model selection is proposed and shown to perform satisfactorily. Applied example of subgroup analysis is presented. Problems associated with tree-structured subgroup analysis are discussed and practical solutions are suggested.


censored survival data regression tree model selection two-stage approach subgroup analysis 


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  1. Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19: 716–723.CrossRefGoogle Scholar
  2. Breiman L., Friedman J.H., Olshen R.A. and Stone C.J. 1984. Classification and Regression Trees. Wadsworth, Belmont, CA.Google Scholar
  3. Bulpitt C.J. 1988. Subgroup analysis. Lancet 2: 31–34.CrossRefPubMedGoogle Scholar
  4. Ciampi A., Lou Z., Lin Q. and Negassa A. 1991. Recursive partition and amalgamation with the exponential family: Theory and application. Applied Stochastic Models and Data Analysis 7: 121–137.Google Scholar
  5. Ciampi A. 1991. Generalized regression trees. Computational Statistic and Data Analysis 12: 57–78.CrossRefMathSciNetGoogle Scholar
  6. Ciampi A., Negassa A. and Lou Z. 1995. Tree-structured prediction for censored survival data and the cox model. Journal of Clinical Epidemiology 48: 675–689.CrossRefPubMedGoogle Scholar
  7. Cox D.R. 1972. Regression models and life tables (with discussion). Journal of the Royal Statistical Society B 34: 187–220.Google Scholar
  8. Davis R.B. and Anderson J.R. 1989. Exponential survival trees. Statistics in Medicine 8: 947–961.PubMedGoogle Scholar
  9. Efron B. 1983. Estimating the error rate of a prediction rule: Improvement on cross-validation. Journal of the American Statistical Association 78: 316–331.Google Scholar
  10. Gail M. and Simon R. 1985. Testing for qualitative interactions between treatment effects and patient subsets. Biometrics 41: 361–372.PubMedGoogle Scholar
  11. Kalbfleisch J.D. and Prentice R.L. 1980. The Statistical Analysis of Failure Time Data. J. Wiley and Sons, New York.Google Scholar
  12. Krzanowski W.J. and Lai Y.T. 1988. A criterion for determining the number of groups in a data set using sum-of-squares clustering. Biometrics 44: 23–34.MathSciNetGoogle Scholar
  13. LeBlanc M. and Crowley J. 1992. Relative risk tree for survival data. Biometrics 48: 411–425.PubMedGoogle Scholar
  14. LeBlanc M. and Crowley J. 1993. Survival tree by goodness of split. Journal of the American Statistical Association 88: 457–467.Google Scholar
  15. Negassa A., Ciampi A., Abrahamowicz M., Shapiro S. and Boivin J.-F. 2000. Tree-structured prognostic classification for censored survival data: Validation of computationally inexpensive model selection criteria. Journal of Statistical Computation and Simulation 67: 289–318.MathSciNetGoogle Scholar
  16. Schmoor C., Ulm K. and Schumacher. 1993. Comparison of the cox model and the regression tree procedure in analysing a randomized clinical trial. Statistics in Medicine 12: 2351– 2366.PubMedGoogle Scholar
  17. Segal R.M. 1988. Regression tree for censored data. Biometrics 44: 35–47.Google Scholar
  18. Yusuf S., Wittes J., Probstfield J. and Tyroler H.A. 1991. Analysis and interpretation of treatment effects in subgroups of patients in randomized clinical trials. JAMA 266: 93–98.CrossRefPubMedGoogle Scholar
  19. Zhang H. and Singer B. 1999. Recursive Partitioning in the Health Sciences. Springer-Verlag, New York.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Abdissa Negassa
    • 1
    Email author
  • Antonio Ciampi
    • 2
  • Michal Abrahamowicz
    • 2
    • 3
  • Stanley Shapiro
    • 3
  • Jean-François Boivin
    • 3
    • 4
  1. 1.Department of Epidemiology and Population HealthAlbert Einstein College of Medicine of Yeshiva UniversityBronxUSA
  2. 2.Department of Epidemiology and BiostatisticsMcGill UniversityMontrealCanada
  3. 3.Clinical EpidemiologyMontreal General HospitalMontrealCanada
  4. 4.Center for Clinical Epidemiology and Community studiesThe Sir Mortimer B. Davis Jewish General HospitalMontrealCanada

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