A Weibull Regression Model with Gamma Frailties for Multivariate Survival Data

Lifetime Data Analysis

Volumn 3, Issue 2, 1997, Pages 123-137

  Sahu, Sujit K ^a   Dey, Dipak K ^b   Aslanidou, Helen ^b   Sinha, Debajyoti ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c UNIVERSITY OF NEW HAMPSHIRE   (United States)

Author keywords

Autocorrelated prior process; Conditional predictive ordinate; Frailty; Markov chain Monte Carlo methods; Model determination; Posterior predictive loss; Proportional hazards model; Weibull model

Indexed keywords

ARTICLE; BAYES THEOREM; COMPARATIVE STUDY; HUMAN; KIDNEY DISEASE; LIFE TABLE; MONTE CARLO METHOD; MULTIVARIATE ANALYSIS; PROBABILITY; PROPORTIONAL HAZARDS MODEL; REGRESSION ANALYSIS; STATISTICAL MODEL; SURVIVAL;

BAYES THEOREM; HUMANS; KIDNEY DISEASES; LIFE TABLES; LIKELIHOOD FUNCTIONS; MARKOV CHAINS; MONTE CARLO METHOD; MULTIVARIATE ANALYSIS; PROPORTIONAL HAZARDS MODELS; REGRESSION ANALYSIS; SURVIVAL ANALYSIS;

EID: 0030625005     PISSN: 13807870     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009605117713     Document Type: Article

References (30)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, 1965.
2. E. Arjas and D. Gasbarra, "Nonparametric Bayesian inference for right-censored survival data, using the Gibbs sampler," Statistica Sinica, vol.4, pp. 505-524, 1994.
3. N. E. Breslow, "Covariance analysis of censored survival data," Biometrics, vol.30, pp. 89-99, 1974.
4. D. Clayton, "A model for association in bivariate life tables and its application in epidemiological studies of familiar tendency in chronic disease incidence," Biometrika, vol.65, pp. 141-151, 1978.
5. D. Clayton and J. Cuzick, "Multivariate generalizations of the proportional hazards model (with discussion)," J. Roy. Statist. Soc., A vol.148, pp. 82-117, 1985.
6. D. R. Cox and D. Oakes, Analysis of Survival Data, London: Chapman & Hall, 1984.
7. D. Gamerman, "Dynamic Bayesian models for survival data," Appl. Statist., vol.40, pp. 63-79, 1991.
8. A. E. Gelfand, "Model determination using sampling based methods," in Markov Chain Monte Carlo in Practice, (Eds. W. R. Gilks, S. Richardson and D. J. Spiegelhalter), London: Chapman and Hall, 1996, pp. 145-161.
9. A. E. Gelfand and D. K. Dey, "Bayesian model choice: asymptotics and exact calculations," J. Roy. Statist. Soc., B vol.56, pp. 501-514, 1994.
10. A. E. Gelfand, D. K. Dey and H. Chang, "Model determination using predictive distributions with implementation via sampling-based methods (with discussion)," in Bayesian Statistics 4, (Eds. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), Oxford: Oxford University Press, 1992, pp. 147-167.
11. A. E. Gelfand and S. K. Ghosh, "Model Choice: A Minimum Posterior Predictive Loss Approach," to appear in Biometrika, 1997.
12. A. E. Gelfand and A. F. M. Smith, "Sampling based approaches to calculating marginal densities," J. Amer. Statist. Assoc., vol.85, pp. 398-409, 1990.
13. J. Geweke, "Evaluating the accuracy of the sampling-based approaches to the calculation of the posterior moments," in Bayesian Statistics 4, (Eds. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), Oxford: Oxford University Press, 1992, pp. 169-194.
14. S. K. Ghosh, "Modeling and Analysis of Multiple Event Survival Data." Ph. D. thesis, Department of Statistics, University of Connecticut, Storrs, Connecticut, 1996.
15. W. R. Gilks, S. Richardson and D. G. Spiegelhalter, Markov Chain Monte Carlo In Practice. London: Chapman and Hall 1996.
16. W. R. Gilks and P. Wild, "Adaptive rejection sampling for Gibbs sampling," Appl. Statist., vol.41, pp. 337-348, 1992.
17. P. J. Green, "Reversible jump Markov chain Monte Carlo computation and Bayesian model determination," Biometrika, vol. 82, pp. 711-732, 1995.
18. P. Hougaard, "A class of multivariate failure time distributions," Biometrika, vol.73, pp. 671-678, 1986.
19. J. D. Kalbfleisch and R. L. Prentice, "Marginal likelihoods based on Cox's regression and life model," Biometrika, vol.60, pp. 267-278, 1973.
20. R. E. Kass and A. E. Raftery, "Bayes factors," J. Amer. Statist. Assoc., vol.90, pp. 773-795, 1995.
21. J. F. Lawless, Statistical Models and Methods for Life Time Data. New York: John Wiley, 1982.
22. T. Leonard, "Density estimation, stochastic processes and prior information," J. Roy. Statist. Soc., B vol.40, pp. 113-146, 1978.
23. C. A. McGilchrist and C. W. Aisbett, "Regression with frailty in survival analysis," Biometrics, vol.47, pp. 461-466, 1991.
24. D. Oakes, "A model for association in bivariate survival data," J. Roy. Statist. Soc., B, vol.44, pp. 414-422, 1982.
25. A. E. Raftery, "Hypothesis testing and model selection," in Markov Chain Monte Carlo in Practice, (Eds. W. R. Gilks, S. Richardson and D. J. Spiegelhalter), London: Chapman and Hall, 1996, pp. 163-187.
26. A. E. Raftery and S. Lewis, "How many iterations in the Gibbs sampler?," in Bayesian Statistics 4, (Eds. J. M. Bernado, J. O. Berger, A. P. Dawid and A. F. M. Smith), Oxford: Oxford University Press, 1992, pp. 765-776.
27. D. Sinha and D. K. Dey, "Semiparametric Bayesian Analysis of Survival Data," to appear in J. Amer. Statist. Assoc., 1997.
28. D. J. Spiegelhalter, A. Thomas, N. G. Best and W. R. Gilks, "BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.50." MRC Biostatistics Unit, Cambridge, England, 1995.
29. M. Tanner and W. Wong, "The Calculation of Posterior Distributions by Data Augmentation (with discussion)," J. Amer. Statist. Assoc., vol.82, pp. 528-550, 1987.
30. G. A. Whitmore and M. L. T. Lee, "A multivariate survival distribution generated by an Inverse Gaussian mixture of exponentials," Technometrics, vol.33, pp. 39-50, 1991.