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Lifetime Data Analysis

, Volume 9, Issue 2, pp 195–210 | Cite as

Mixed Discrete and Continuous Cox Regression Model

  • Ross L. Prentice
  • John D. Kalbfleisch
Article

Abstract

The Cox (1972) regression model is extended to include discrete and mixed continuous/discrete failure time data by retaining the multiplicative hazard rate form of the absolutely continuous model. Application of martingale arguments to the regression parameter estimating function show the Breslow (1974) estimator to be consistent and asymptotically Gaussian under this model. A computationally convenient estimator of the variance of the score function can be developed, again using martingale arguments. This estimator reduces to the usual hypergeometric form in the special case of testing equality of several survival curves, and it leads more generally to a convenient consistent variance estimator for the regression parameter. A small simulation study is carried out to study the regression parameter estimator and its variance estimator under the discrete Cox model special case and an application to a bladder cancer recurrence dataset is provided.

Cox regression counting process martingale tied failure times 

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References

  1. P. K. Andersen and R. D. Gill, “Cox's regression model for counting processes: a large sample study,” Ann. Statist. vol. 10 pp. 1100–1120, 1982.Google Scholar
  2. P. K. Andersen, O. Borgan, R. D. Gill, and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag: New York, 1993.Google Scholar
  3. D. F. Andrews and A. M. Herzberg, Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer-Verlag: New York, 1985.Google Scholar
  4. N. E. Breslow, “Covariance analysis of censored survival data,” Biometrics vol. 30 pp. 89–99, 1974.Google Scholar
  5. D. P. Byar, “The Veteran's Administration study of chemoprophylaxis of recurrent stage I bladder tumors: comparisons of placebo, pyridoxine, and topical thiotepa,” in Bladder Tumors and Other Topics in Urological Oncology, (M. Pavone-Macaluso, P. H. Smith, and F. Edsmyn, eds.) Plenum: New York, pp. 363–370, 1980.Google Scholar
  6. D. R. Cox, “Regression models and life tables (with discussion),” J. R. Statist. Soc. vol. B-34 pp. 187–220, 1972.Google Scholar
  7. D. R. Cox, “Partial likelihood,” Biometrika vol. 62 pp. 269–276, 1975.Google Scholar
  8. D. M. Delong, G. H. Guirguis, and Y. C. So, “Efficient computation of subset selection probabilities with application to Cox regression,” Biometrika vol. 81 pp. 607–611, 1994.Google Scholar
  9. B. Efron, “Efficiency of Cox's likelihood function for censored data,” J. Amer. Statist. Assoc. vol. 72 pp. 557–565, 1977.Google Scholar
  10. M. H. Gail, J. H. Lubin, and L. V. Rubinstein, “Likelihood calculations for matched case-control studies and survival studies with matched death times,” Biometrika vol. 68 pp. 703–707, 1981.Google Scholar
  11. J. D. Kalbfleisch and R. L. Prentice, “Marginal likelihoods based on Cox's regression and life model,” Biometrika vol. 60 pp. 267–278, 1973.Google Scholar
  12. J. D. Kalbfleisch and R. L. Prentice, The Statistical Analysis of Failure Time Data, Wiley: New York, 1980.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Ross L. Prentice
    • 1
  • John D. Kalbfleisch
    • 2
  1. 1.Division of Public Health SciencesFred Hutchinson Cancer Research CenterSeattleUSA
  2. 2.Department of BiostatisticsUniversity of MichiganAnn ArborUSA

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