A Bayesian semiparametric transformation model incorporating frailties

Journal of Statistical Planning and Inference

Volumn 112, Issue 1-2, 2003, Pages 159-174

  Mallick, Bani K ^a   Walker, Stephen ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b University of Bath   (United Kingdom)

Author keywords

Frailty model; Mixtures of incomplete beta functions; P lya trees; Proportional hazards model

Indexed keywords

EID: 0037336497     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(02)00330-0     Document Type: Article

References (35)

1. Andersen, P.K., Gill, R.D., 1982. Cox's regression model for counting process: a large sample study. Ann. Statist. 10, 1100-1120.
2. Aslanidou, H., Dey, D., Sinha, D., 1998. Bayesian analysis of multivariate survival data using Monte Carlo methods. Canad. J. Statist. 26, 33-48.
3. Bennett, S., 1983. Log-logistic regression models for survival data. Appl. Statist. 32, 165-171.
4. Blackwell, D., 1973. Discreteness of Ferguson selections. Ann. Statist. 1, 356-358.
5. Box, G.E.P., Cox, D.R., 1964. An analysis of transformations (with discussion). J. Roy. Statist. Soc. Ser. B 26, 211-252.
6. Cheng, S.C., Wei, L.J., Ying, Z., 1995. Analysis of transformation models with censored data. Biometrika 82, 835-845.
7. Clayton, D.G., Cuzick, J., 1985. Multivariate generalizations of the proportional hazards model (with discussion). J. Roy. Statist. Soc. Ser. A 148, 82-117.
8. Cox, D.R., 1972. Regression models and life tables (with discussion). J. Roy. Statist. Soc. Ser. B 34, 187-220.
9. Cuzick, J., 1988. Rank regression. Ann. Statist. 16, 1369-1389.
10. Diaconis, P., Ylvisaker, D., 1985. Quantifying prior opinion. In: Bernardo, J.M. et al. (Eds.), Bayesian Statistics, Vol. 2, North-Holland, Amsterdam, pp. 133-156.
11. Feigl, P., Zelen, M., 1965. Estimation of exponential probabilities with concomitant information. Biometrics 21, 826-838.
12. Ferguson, T.S., 1974. Prior distributions on spaces of probability measures. Ann. Statist. 2, 615-629.
13. Gelfand, A.E., 1997. Approaches for semiparametric Bayesian regression. In: Ghosh, S. (Ed.), Asymptotics, Nonparametrics and Time Series. Marcel Dekker, Inc., New York, pp. 615-638.
14. Gray, R., 2000. Estimation of regression parameters and the hazard function in transformed linear survival models. Biometrics 56, 571-576.
15. Green, P.J., 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
16. Kalbfleisch, J.D., 1978. Likelihood methods and nonparametric tests. J. Amer. Statist. Assoc. 73, 167-170.
17. Kalbfleisch, J.D., Prentice, R.L., 1980. The Statistical Analysis of Failure Time Data. Wiley, Chichester.
18. Kullback, S., 1959. Information Theory and Statistics. Wiley, New York.
19. Kuo, L., Mallick, B.K., 1997. Bayesian semiparametric inference for the accelerated failure-time model. Canad. J. Statist. 25, 457-472.
20. Lavine, M., 1992. Some aspects of Pólya tree distributions for statistical modelling. Ann. Statist. 20, 1222-1235.
21. Lavine, M., 1994. More aspects of Pólya tree distributions for statistical modelling. Ann. Statist. 22, 1161-1176.
22. Laud, P.W., Ibrahim, J.G., 1995. Predictive model selection. J. Roy. Statist. Soc. Ser. B 57, 247-262.
23. Mallick, B.K., 1994. Bayesian modelling incorporating unknown monotone functions. Ph.D. Thesis, University of Connecticut.
24. Mallick, B.K., Gelfand, A.E., 1994. Generalised linear models with unknown link functions. Biometrika 81, 237-245.
25. McGilchrist, C.A., Aisbett, C.W., 1991. Regression with frailty in survival analysis. Biometrics 47, 461-466.
26. Prentice, R.L., 1973. Exponential survivals with censoring and explanatory variables. Biometrika 60, 279-288.
27. Prentice, R.L., 1978. Linear rank tests with censored data. Biometrika 65, 167-179.
28. Richardson, S., Green, P., 1997. On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. Roy. Statist. Soc. B 59, 731-792.
29. Sinha, D., Dey, D., 1997. Semiparametric Bayesian analysis of Survival Data. J. Amer. Statist. Assoc. 92, 1195-1212.
30. Tierney, L., 1994. Markov chains for exploring posterior distributions. Ann. Statist. 22, 1701-1762.
31. Wakefield, J.C., Smith, A.F.M., Racine-Poon, A., Gelfand, A.E., 1994. Bayesian analysis of linear and non-linear population models using the Gibbs sampler. Appl. Statist. 43, 201-221.
32. Walker, S.G., Mallick, B.K., 1996. Hierarchical generalised linear models and frailty models with Bayesian nonparametric mixing. J. Roy. Statist. Soc. Ser. B 59, 845-860.
33. Walker, S., Mallick, B.K., 1999. Semiparametric accelarated life time model. Biometrics 55, 477-483.
34. Walker, S.G., Wakefield, J.C., 1996. Bayesian semiparametric approaches to the population modelling of a monotone dose-response relation. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, Vol. 5. Oxford University Press, Oxford, pp. 789-790.
35. Ying, Z., Jung, S.H., Wei, L.J., 1995. Survival analysis with median regression models. J. Amer. Statist. Assoc. 90, 178-184.