Application of Cox Regression with a Change Point in Clinical Studies

  • Xiaolong Luo
  • Gang Chen
  • James M. Boyett


Cox regression with an unknown change point and the corresponding large sample theory are discussed. We show how the results of this approach can be applied to computer-simulated data and to failure-time data from a large cohort of children treated at St. Jude Children’s Research Hospital for newly diagnosied acute lymphoblastic leukemia.


Acute Lymphoblastic Leukemia Change Point FORTRAN Subroutine Dental Abnormality Hazard Rate Model 
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. Chernoff, H. & Rubin, H. (1956), “The Estimation of the Location of a Discontinuity in Density,” Proc. 3rd Berkeley Symp. Math. Statist. Prob. 1, 19–37. Univ. California Press.Google Scholar
  2. Cox D. R. (1972), “Regression Models and Life Tables,” J. Roy. Statist. Soc., B 34, 187–220Google Scholar
  3. Cox D. R. & Oakes D. (1984), Analysis of Survival Data,Chapman and Hall, p. 37.Google Scholar
  4. Efron, B. (1981), “Censored Data and the Bootstrap,” J. Am. Statist. Assoc., 76, 312–319.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Efron, B. & Tibshirani, R. (1986), “ Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy,” Statistical Science, 1, 54–77.MathSciNetCrossRefGoogle Scholar
  6. Fleming, T. R. & Harrington, D. P. (1991), Counting Processes and Survival Analysis,Wiley, New York.Google Scholar
  7. George, S. L. (1994), “Statistical Considerations and Modeling of Clinical Utility of Tumor Markers,” Hematology/Oncology Clinics of North America, Vol. 8. No. 3 457–470Google Scholar
  8. Jespersen, N. C. B. (1986), “Dichotomizing a Continuous Covariate in the Cox RegressionGoogle Scholar
  9. Móde1,“ Technical Report, University of Copenhagen, Statistical Research Unit and Institute of Mathematical StatisticsGoogle Scholar
  10. Lai, T. L. & Ying, Z. (1988), “Stochastic Integrals of Empirical-type Processes with Application to Censored Regression,” J. Multivariate Anal. 27 334–358MathSciNetzbMATHCrossRefGoogle Scholar
  11. Loader, C. R. (1991), “Inference for a Hazard Rate Change Point,” Biometrika, 78, 749–757MathSciNetzbMATHCrossRefGoogle Scholar
  12. Lausen, B. & Schumacher, M. (1992), “Maximally Selected Rank Statistics,” Biometrics, 48, 73–85.CrossRefGoogle Scholar
  13. LeBlanc, M. & Crowley, J. (1993), “Survival Trees by Goodness of Split,” JASA, 88, 457–467.MathSciNetzbMATHCrossRefGoogle Scholar
  14. Liang, K. Y., Self, S. & Liu, X. (1990), “The Cox Proportional Hazards Model with Change Point: An Epidemiologic Application,” Biometrics, 46, 783–793.CrossRefGoogle Scholar
  15. Luo, X. & Boyett, J. M. (1993), “Cutoff Point of Continuous Covariate,” Submitted Google Scholar
  16. Luo, X. (1994), “Asymptotic Distribution of a Change Point in a Cox Lifetable Regression Model,” Submitted Google Scholar
  17. Luo, X., Turnbull, B. W., Cai, H. & Clark, L. C. (1994), “Regression For Censored Survival Data With Lag Effects,” Commun. Statist.-Theor. Meth., 23 (12), 3417–3438MathSciNetzbMATHCrossRefGoogle Scholar
  18. Mathews, D. E. & Farewell, V. T. (1982), “On Testing for a Constant Hazard against aGoogle Scholar
  19. Change-point Alternative,“ Biometrics,38 463–468.Google Scholar
  20. Mathews, D. E., Farewell, V. T. & Pyke, R. (1985), “Asymptotic Score-statistic Processes and Tests for Constant Hazard against a Change-point Alternative,” Ann. Statist., 13, 583–591.MathSciNetCrossRefGoogle Scholar
  21. Miller, R. & Siegmund, D. (1982), “Maximally Selected Chi-Squared Statistics,” Biometrics, 38, 1011–1016.MathSciNetzbMATHCrossRefGoogle Scholar
  22. Nguyen, H. T., Rogers, G. S., & Walker, E. A. (1984), “Estimation in Change-point Hazard Rate Models,” Biometrika, 71, 299–304MathSciNetzbMATHCrossRefGoogle Scholar
  23. Siegmund, D. (1986), “Boundary Crossing Probabilities and Statistical Applications,” Ann. Statist., 14, 361–404.MathSciNetzbMATHCrossRefGoogle Scholar
  24. Simon, R. & Altman, D. G. (1994), “Statistical Aspects of Prognostic Factor Studies in Oncology,” Br. J. Cancer, 69 (6), 979–985CrossRefGoogle Scholar
  25. Tsiatis, A. A. (1990), “Estimating Regression Parameters Using Linear Rank Tests for Censored Data,” Ann. Statist., 18, 354–372.MathSciNetzbMATHCrossRefGoogle Scholar
  26. Yao, Y. C. (1986), “Maximum Likelihood Estimation in Hazard Rate Models with a Change-point,” Commun. Statist.-Theor. Meth., 15 (8), 2455–2466zbMATHCrossRefGoogle Scholar
  27. Ying, Z. (1993), “A Large Sample Study of Rank Estimation for Censored Regression Data,” Ann. Statist., 21, 76–89.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Xiaolong Luo
    • 1
  • Gang Chen
    • 1
  • James M. Boyett
    • 1
  1. 1.Department of BiostatisticsSt. Jude Children’s Research HospitalMemphisUSA

Personalised recommendations