Posterior propriety and computation for the Cox regression model with applications to missing covariates

Biometrika

Volumn 93, Issue 4, 2006, Pages 791-807

  Chen, Ming Hui ^a   Ibrahim, Joseph G ^b   Shao, Qi Man ^c  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b University of North Carolina at Chapel Hill   (United States)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Gamma process prior; Latent variable; Markov chain Monte Carlo; Missing at random; Necessary and sufficient conditions; Partial likelihood; Proportional hazards model

Indexed keywords

EID: 33845764730     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/93.4.791     Document Type: Article

References (19)

1. BRESLOW, N. E. (1974). Covariance analysis of censored survival data. Biometrics 30, 89-99.
2. CHEN, M.-H. & IBRAHIM, J. G. (2001). Maximum likelihood methods for cure rate models with missing covariates. Biometrics 57, 43-52.
3. CHEN, M.-H. & SHAO, Q.-M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. J. Comp. Graph. Statist. 8, 69-92.
4. CHEN, M.-H. & SHAO, Q.-M. (2001). Propriety of posterior distribution for dichotomous quantal response models with general link functions. Proc. Am. Math. Soc. 129, 293-302.
5. CHEN, M.-H., SHAO, Q.-M. & IBRAHIM, J. G. (2000). Monte Carlo Methods in Bayesian Computation. New York: Springer-Verlag.
6. COX, D. R. (1975). Partial likelihood. Biometrika 62, 269-76.
7. GILKS, W. R. & WILD, P. (1992). Adaptive rejection sampling for Gibbs sampling. Appl. Statist. 41, 337-48.
8. HJORT, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models of life history data. Ann. Statist. 18, 1259-94.
9. IBRAHIM, J. G., CHEN, M.-H. & SINHA, D. (2001). Bayesian Survival Analysis. New York: Springer-Verlag.
10. ISHWARAN, H. & JAMES, L. F. (2004). Computational methods for multiplicative intensity models using weighted gamma processes: proportional hazards, marked point processes, and panel count data. J. Am. Statist. Assoc. 99, 175-90.
11. KALBFLEISCH, J. D. (1978). Nonparametric Bayesian analysis of survival time data. J. R. Statist. Soc. B 40, 214-21.
12. KIRKWOOD, J. M., IBRAHIM, J. G., SONDAK, V. K., RICHARDS, J., FLAHERTY, L. E., ERNSTOFF, M. S., SMITH, T. J., RAO, U., STEELE, M. & BLUM, R. H. (2000). The role of high- and low-dose Interferon Alfa-2b in high-risk melanoma: first analysis of Intergroup Trial E1690/S9111/C9190. J. Clin. Oncol. 18, 2444-58.
13. KLEIN, J. P. & MOESCHBERGER, M. L. (1997). Survival Analysis. New York: Springer-Verlag.
14. LIN, J. S. (1994). The collapsed Gibbs sampler in Bayesian computations with applications to a gene regulation problem. J. Am. Statist. Assoc. 89, 958-66.
15. RAFTERY, A. E., MADIGAN, D. & VOLINSKY, C. T. (1995). Accounting for model uncertainty in survival analysis improves predictive performance. In Bayesian Statistics 5, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 323-50. Oxford: Oxford University Press.
16. ROCKAFELLAR, R. T. (1970). Convex Analysis. Princeton, N.J: Princeton University Press.
17. SARGENT, D. J. (1998). A general framework for random effects survival analysis in the Cox proportional hazards setting. Biometrics 54, 1486-97.
18. SINHA, D., IBRAHIM, J. G. & CHEN, M.-H. (2003). A Bayesian justification of Cox's partial likelihood. Biometrika 90, 629-41.
19. VOLINSKY, C. T., MADIGAN, D., RAFTERY, A. E. & KRONMAL, R. A. (1997). Bayesian model averaging in proportional hazards models: assessing the risk of a stroke. Appl. Statist. 46, 433-48.