Bayesian analysis of proportional hazard models. (English) Zbl 1053.62036

Summary: This paper is concerned with Bayesian analysis of the proportional hazard model with left truncated and right censored data. We use a process neutral to the right as the prior of the baseline survival function and a finite-dimensional prior is placed on the regression coefficient. We then obtain the exact form of the joint posterior distribution of the regression coefficient and the baseline cumulative hazard function. As a by-product, we prove the propriety of the posterior distribution with the constant prior on the regression coefficient.


62F15 Bayesian inference
62N99 Survival analysis and censored data
62C10 Bayesian problems; characterization of Bayes procedures
60G51 Processes with independent increments; Lévy processes
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[1] ANDERSON, P. K., BORGAN, Ø., GILL, R. D. and KEIDING, N. (1993). Statistical Methods Based on Counting Processes. Springer, New York.
[2] CLAy TON, D. G. (1991). A Monte Carlo method for Bayesian inference in frailty models. Biometrics 47 467-485.
[3] DOKSUM, K. A. (1974). Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2 183-201. · Zbl 0279.60097 · doi:10.1214/aop/1176996703
[4] FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230. · Zbl 0255.62037 · doi:10.1214/aos/1176342360
[5] FLEMING, T. R. and HARRINGTON, D. P. (1991). Counting Processes and Survival Analy sis. Wiley, New York.
[6] HJORT, N. L. (1990). Nonparametric Bay es estimators based on beta processes in models for life history data. Ann. Statist. 18 1259-1294. · Zbl 0711.62033 · doi:10.1214/aos/1176347749
[7] JACOBSEN, M. (1989). Existence and unicity of MLEs in discrete exponential family distributions. Scand. J. Statist. 16 335-349. · Zbl 0684.62025
[8] JACOD, J. (1975). Multivariate point processes: Predictable projection, Radon-Nikody m derivatives, representation of martingales. Z. Warsch. Verw. Gebiete 31 235-253. · Zbl 0302.60032 · doi:10.1007/BF00536010
[9] JACOD, J. and SHIRy AEV, A. N. (1987). Limit Theorems for Stochastic Processes. Springer, New York.
[10] KALBFLEISCH, J. D. (1978). Nonparametric Bayesian analysis of survival time data. J. Roy. Statist. Soc. Ser. B 40 214-221. JSTOR: · Zbl 0387.62030
[11] KIM, Y. (1999). Nonparametric Bayesian estimators for counting processes. Ann. Statist. 27 562-588. · Zbl 0980.62078 · doi:10.1214/aos/1018031207
[12] KIM, Y. and LEE, J. (2001). On posterior consistency of survival models. Ann. Statist. 29 666-686. · Zbl 1012.62105 · doi:10.1214/aos/1009210685
[13] LAUD, P. W., DAMIEN, P. and SMITH, A. F. M. (1998). Bayesian nonparametric and covariate analysis of failure time data. Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 213-225. · Zbl 0918.62077
[14] LEE, J. and KIM, Y. (2002). A new algorithm to generate beta processes. Unpublished manuscript.
[15] LO, A. Y. (1982). Bayesian nonparametric statistical inference for Poisson point processes. Z. Wahrsch. Verw. Gebiete 59 55-66. · Zbl 0482.62078 · doi:10.1007/BF00575525
[16] UNIVERSITY PARK, PENNSy LVANIA 16802 E-MAIL: leej@stat.psu.edu
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