Some remarks on semi-Markov processes in medical statistics

  • D. R. Cox


The object of this paper is to give a brief account of potential applications of semi-Markov processes in medical statistics, especially in connection with studies involving “quality of life”.


Failure Time Sojourn Time Nonparametric Estimation Proportional Intensity State Zero 
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. P.K. Andersen, O. Borgan, R. Gill and N. Keiding (1982). Linear non-parametric tests for comparison of counting processes, with applications to censored survival data (with discussion). Int. Statist. Rev. 50, 219–258.MathSciNetzbMATHCrossRefGoogle Scholar
  2. D.R. Cox (1972), The statistical analysis of dependencies in point processes. In stochastic point processes, ed. P.A.W. Lewis, 55–66, New York: Wiley.Google Scholar
  3. D.R. Cox and V. Isham (1980), Point processes. London: Chapman & Hall.zbMATHGoogle Scholar
  4. D.R. Cox and D. Oakes (1984), Analysis of survival data. London: Chapman & Hall.Google Scholar
  5. G.E. Dinse & S.W. Lagakos (1982). Nonparametric estimation of lifetime and disease onset distributions from incomplete observations. Biometrics 38, 921–932.zbMATHCrossRefGoogle Scholar
  6. P.M. Fayers and D.R. Jones (1983). Measuring and analysing quality of life in cancer clinical trials: a review. Statistics in Medicine 2, 429–446.CrossRefGoogle Scholar
  7. E. Fix and J. Neyman (1951). A simple stochastic model of recovery, relapse and loss of patients. Human Biology 23, 205–241.Google Scholar
  8. I.B. Gertsbakh (1984). Asymptotic methods in reliability theory: a review. Adv. Appl. Prob. 16, 147–175.MathSciNetzbMATHCrossRefGoogle Scholar
  9. R.D. Gill (1980). Nonparametric estimates based on censored observations of a Markov renewal process. Z. Wahr. 53, 97–116.zbMATHCrossRefGoogle Scholar
  10. S. Johansen (1983). An extension of Cox’s regression model. Int. Statist. Rev. 51, 165–174.MathSciNetzbMATHCrossRefGoogle Scholar
  11. E.L. Kaplan and P. Meier (1958). Nonparametric estimation from incomplete observations. J. Am. Statist. Assoc. 53, 457–481.MathSciNetzbMATHCrossRefGoogle Scholar
  12. S.W. Lagakos (1976). A stochastic model for censored survival time in the presence of an auxiliary variable. Biometrics 32, 551–560.zbMATHCrossRefGoogle Scholar
  13. S.W. Lagakos (1977). Using auxiliary variables for improved estimates of survival time. Biometrics 33, 399–404.zbMATHCrossRefGoogle Scholar
  14. S.W. Lagakos, C.J. Sommer and M. Zelen (1978). Semi-Markov models for partially censored data. Biometrika 65, 311–317.MathSciNetzbMATHCrossRefGoogle Scholar
  15. N. Temkin (1978). An analysis for transient states with application to tumor shrinkage. Biometrics 34, 571–580.zbMATHCrossRefGoogle Scholar
  16. J.G. Voelkel and J. Crowley (1984). Nonparametric inference for a class of semi-Markov processes with censored observations. Ann. Statist. 12, 142–160.MathSciNetzbMATHCrossRefGoogle Scholar
  17. G.H. Weiss and M. Zelen (1965). A semi-Markov model for clinical trials, J. Appl. Prob. 2, 269–285.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • D. R. Cox
    • 1
  1. 1.Department of MathematicsImperial College of Science and TechnologyLondonEngland

Personalised recommendations