Bayesian Nonparametric and Covariate Analysis of Failure Time Data

  • Purushottam W. Laud
  • Paul Damien
  • Adrian F. M. Smith
Part of the Lecture Notes in Statistics book series (LNS, volume 133)


A Bayesian analysis of the semi-parametric regression model of Cox (1972) is given. The cumulative hazard function is modelled as a beta process. The posterior distribution of the regression parameters and the survival function are obtained using a combination of recent Monte Carlo methods. An illustrative analysis within the context of survival time data is given.


Posterior Distribution Hazard Rate Markov Chain Monte Carlo Method Frailty Model Cumulative Hazard 
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. Andersen, P.K., Borgan, O., Gill, R.D. and Keiding, N. (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag.zbMATHCrossRefGoogle Scholar
  2. Besag, J. and Green, P.J. (1993). Spatial Statistics and Bayesian Computation. J. R. Statist. Soc. B 55, 25–37.MathSciNetzbMATHGoogle Scholar
  3. Breslow, N.E. (1974). Covariate Analysis of Censored Survival Data. Biometrics 30, 89–99.CrossRefGoogle Scholar
  4. Cox, D.R. (1972). Regression Models and Life Tables (with Discussion). J. R. Statist. Soc. B 34, 187–220.zbMATHGoogle Scholar
  5. Damien, P., Laud, P.W., and Smith, A.F.M., (1995). Approximate Random Variate Generation from Infinitely Divisible Distributions with Applications to Bayesian Inference. J. R. Statist. Soc. B 57, 547–563.MathSciNetzbMATHGoogle Scholar
  6. Damien, P., Laud, P.W., and Smith, A.F.M., (1996) Implementation of Bayesian. Nonparametric Inference Based on Beta Processes. Scand. J. Statist. 23, 27–36.MathSciNetzbMATHGoogle Scholar
  7. Dykstra, R. L. and Laud, P. W. (1981). Bayesian Nonparametric Approach Toward Reliability, Ann. Statist. 9, 356–367.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Efron, B. (1977). The Efficiency of Cox’s Likelihood Function for Censored Data. J. Am. Statist. Assoc. 72, 557–565.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Ferguson, T. S. (1973). A Bayesian Analysis of Some Nonparametric Problems, Ann. Statist. 1, 209–230.MathSciNetzbMATHCrossRefGoogle Scholar
  10. Gilks, W.R. and Wild, P. (1992). Adaptive Rejection Sampling for Gibbs Sampling. Appl. Statist. 41, 337–348.zbMATHCrossRefGoogle Scholar
  11. Gill, R.D. and Johansen, S. (1990). A Survey of Product-Integration with a View toward Application in Survival Analysis. Ann. Statist. 18, 1501–1555.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Hjort, N.L. (1990). Nonpararnetric Bayes Estimators Based on Beta Processes in Models for Life History Data. Ann. Statist. 18, pp 1259–1294.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Kalbfleisch, J.D. (1978). Non-parametric Bayesian Analysis of Survival Time Data. J. R. Statist. Soc. B 40, 2, 214–221.MathSciNetzbMATHGoogle Scholar
  14. Kalbfleisch, J.D. and Prentice, R.L. (1980). The Statistical Analysis of Failure Time Data. New York: John Wiley.zbMATHGoogle Scholar
  15. Klein, J.P. and Moeschberger, M.L. (1996). Survival Analysis: Methods for Censored and Truncated Data. New York: Springer-Verlag.Google Scholar
  16. Sinha, D. and Dey, D.K. (1997). J. Am. Statist. Assoc. 92, 1195–1212.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Smith, A.F.M. and Roberts, G.O. (1993). Bayesian Computations via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods. J. R. Statist. Soc. B 55, 3–23.MathSciNetzbMATHGoogle Scholar
  18. Walker, S.G. (1996). Random Variate Generation from an Infinitely Divisible Distribution via Gibbs Sampling. Technical Report, Imperial College, London.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Purushottam W. Laud
  • Paul Damien
  • Adrian F. M. Smith

There are no affiliations available

Personalised recommendations