Introduction to Cox (1972) Regression Models and Life-Tables

  • Ross L. Prentice
Part of the Springer Series in Statistics book series (SSS)

Abstract

In this paper, Sir David Cox proposed a stimulating and pioneering procedure for the regression analysis of censored failure time data. Within a few years of publication, this procedure became a data analytic standard in a number of application areas, most notably in the biomedical sciences. The procedure has also stimulated considerable related methodologic development.

Keywords

Covariance Kato Toxicology Asbestos 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Anderson. P.K. (1986). Time-dependent covariates and Markov processes, in Modern Statistical Methods in Chronic Disease Epidemiology ( S.H. Moolgavkar. and R.L Prentice. eds.). Wiley. New York. pp. 82–103.Google Scholar
  3. Begun, J.M., Hall. W.J. Huang, W., and Wellner, J.A. (1983). Information and asym¬ptotic efficiency in parametric-nonparametric models, Ann. Statist.. 11, 432–452.MathSciNetMATHCrossRefGoogle Scholar
  4. Breslow, N. (1972). Contribution to the discussion of paper by D.R. Cox, J. Roy. Statist. Soc., Ser. B, 34, 216–217.MathSciNetGoogle Scholar
  5. Clayton. D., and Cuzick, J. (1985). Multivariate generalizations of the proportional hazards model. J. Roy. Statist. Soc., Ser, A, 148, 82–117 (with discussion),MathSciNetMATHCrossRefGoogle Scholar
  6. Cox, D.R. (1972). Regression models and life-tables (with discussion). J. R. Statist. Soc. Ser. B, 34, 187–202.MATHGoogle Scholar
  7. Cox. D.R. (1975). Partial likelihood. Biometrika. 62. 269–276.MathSciNetMATHCrossRefGoogle Scholar
  8. Cox, D.R., and Oakcs, D. (1984). Analysis of Survival Data. Chapman and Hall, New- York.Google Scholar
  9. Crowley, J., and Hu. M. (1977). Covariance analysis of heart transplant survival data, J. Amer. Statist. Assoc., 73. 27–36.CrossRefGoogle Scholar
  10. Efron, B. (1977). The efficiency of Cox’s likelihood function for censored data, J. Amer. Statist. Assoc., 72. 557–565.MathSciNetMATHCrossRefGoogle Scholar
  11. Kalbfleisch, J.D.. and McIntosh. A.A. (1977). Efficiency in survival distributions with time-dependent covariablcs, Biometrika, 64. 47–50.MATHCrossRefGoogle Scholar
  12. Kalbfleisch, J.D., and Prentice. R.L. (1973). Marginal likelihoods based on Cox’s regression and life model, Biometrika, 60, 267–278.MathSciNetMATHCrossRefGoogle Scholar
  13. Kalbfleiseh. J.D., and Prentice. R.L. (1980). The Statistical Analysis of Failure Time Data. Wiley, New York.Google Scholar
  14. Kay, R. (1979). Some further asymptotic efficiency calculations for survival data regression models. Biometrika., 66, 91–96.MathSciNetMATHCrossRefGoogle Scholar
  15. Liang, K.Y., and Zeger. S.L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22.MathSciNetMATHCrossRefGoogle Scholar
  16. Liddell, F.D.K., McDonald. J.C. and Thomas, D.C. (1977). Methods of cohort anal¬ysis. Appraisal by application to asbestos mining. J. Roy. Statist. Soc.. Ser. A, 140. 469–491 (with discussion).CrossRefGoogle Scholar
  17. Lustbader. E.D. (1980). Time-dependent covariates in survival analysis, Biometrika, 67. 697–698.MathSciNetCrossRefGoogle Scholar
  18. Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemother. Rept.. 50, 163–170.Google Scholar
  19. Mehrotra, K.D., Michalek. J.E., and Mihalko, D. (1982). A relationship between two forms of linear rank procedures for ccnsorcd data. Biometrika, 69, 674–676.MathSciNetMATHGoogle Scholar
  20. Oakes, D. (1972). Contribution to discussion of paper by D.R. Cox, J. Roy. Statist. Soc. Ser. B. 34. 208.Google Scholar
  21. Oakes. D. (1977). The asymptotic information in censored survival data, Biometrika. 64, 441–448.MathSciNetMATHCrossRefGoogle Scholar
  22. Peto, R. (1972). Contribution to discussion of paper by D.R. Cox. J. Roy. Statist. Soc.. Ser. B, 34. 205–207.MathSciNetGoogle Scholar
  23. Peto, R. and Peto, J. (1972). Asymptotically efficient rank invariant test procedures, J. Roy. Statist. Soc., Ser. A, 135, 185–206 (with discussion).MathSciNetCrossRefGoogle Scholar
  24. Prentice, R.L. (1978). Linear rank tests with right censored data. Biometrika, 65, 167–179.MathSciNetMATHCrossRefGoogle Scholar
  25. Prentice, R.L. (1986). A case-cohort design for epidemiologic cohort studies and disease prevention trials, Biometrika, 73, 1–11.MathSciNetMATHCrossRefGoogle Scholar
  26. Prentice. R.L., and Breslow, N.E. (1978). Retrospective studies and failure time models. Biometrika. 65. 153–158.MATHCrossRefGoogle Scholar
  27. Prentice, R.L., Williams, B.J. and Peterson A.V. On the regression analysis of multivariate failure time data (1981). Biometrika 68, 373–379.MathSciNetMATHCrossRefGoogle Scholar
  28. Prentice. R.L. Shimizu, Y., Lin. C.H.. Peterson, A.V, Kato, H. Mason. M.W., and Szatrowski, T.P. (1982a). Serial blood pressure measurements and cardiovascular disease in a Japanese cohort. Amer. J. Epid., 116, 1–28.Google Scholar
  29. Prentice, R.L.. Peterson. A.V. and Marek, P. (1982b). Dose mortality relationship in RFM micc following 136Cs gamma irradiation. Radiation Res.. 90. 57–76.CrossRefGoogle Scholar
  30. Sheehe, P.R. (1962). Dynamic risk analysis in retrospective matched pair studies of disease. Biometrics, 18, 323–341.CrossRefGoogle Scholar
  31. Wei. L.J., Lin, D.Y., and Weissfield, L. (1989). Regression analysis of multivariate incomplete failure time data by modelling marginal distributions, J. Amer. Statist. Assoc.. 84. 1065–1073.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Ross L. Prentice
    • 1
  1. 1.Fred Hutchinson Cancer Research CenterUSA

Personalised recommendations