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Bayesian nonparametric estimation of hazard rate in monotone Aalen model
Kybernetika, Tome 50 (2014) no. 6, pp. 849-868
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This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the method is applicable on small sample size datasets.
This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the method is applicable on small sample size datasets.
DOI : 10.14736/kyb-2014-6-0849
Classification : 62F15, 62G05, 62N02, 62N05
Keywords: monotone Aalen model; Bayesian estimation; Gibbs sampler; small sample size 
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Timková, Jana. Bayesian nonparametric estimation of hazard rate in monotone Aalen model. Kybernetika, Tome 50 (2014) no. 6, pp. 849-868. doi: 10.14736/kyb-2014-6-0849

[1] Aalen, O. O.: A model for nonparametric regression analysis of counting processes. Springer Lect. Notes in Statist. 2 (1980), 1-25. | MR | Zbl

[2] Aalen, O. O.: A linear regression model for the analysis of life times. Statist. Med. 8 (1989), 907-925. | DOI

[3] Andersen, P. K., Borgan, A., Gill, R. D., Kieding, N.: Statistical Models Based on Counting Processes. Springer, New York 1993. | MR

[4] Arjas, E., Gasbarra, D.: Nonparametric bayesian inference from right censored survival data, using Gibbs sampler. Statist. Sinica 4 (1994), 505-524. | MR

[5] Cox, D. R.: Regression models and life-tables. J. Roy. Statist. Soc. 34 (1972), 2, 187-220. | MR | Zbl

[6] Blasi, P. De, Hjort, N. L.: Bayesian survival analysis in proportional hazard models with logistic relative risk. Scand. J. Statist. 34 (2007), 229-257. | DOI | MR | Zbl

[7] Blasi, P. De, Hjort, N. L.: The Bernstein-von Mises theorem in semiparametric competing risks models. J. Statist. Planning Inf. 34 (2009), 1678-1700. | Zbl

[8] Doksum, K.: Tailfree and neutral random probabilities and their posterior distributions. Ann. Statist. 2 (2006), 183-201. | MR | Zbl

[9] Green, P. J.: Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 (1995), 711-732. | DOI | MR | Zbl

[10] Hjort, N. L.: Nonparametric Bayes estimators based on beta processes in models for Life history data. Ann. Stat. 3 (1990), 1259 - 1294. | DOI | MR | Zbl

[11] Huffer, F. W., McKeague, I. W.: Weighted least squares estimation for Aalen's additive risk model. J. Amer. Statist. Assoc. 86 (1991), 114-129. | DOI

[12] Kaplan, E. L., Meier, P.: Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 (1958), 457-481. | DOI | MR | Zbl

[13] Kim, Y.: The Bernstein-von Mises theorem for the proportional hazard model. Ann. Statist. 34 (2006), 1678-1700. | DOI | MR | Zbl

[14] Kim, Y., Lee, J.: A Bernstein-von Mises theorem in the nonparametric right-censoring model. Ann. Statist. 32 (2004), 1492-1512. | DOI | MR | Zbl

[15] Sinha, D., Dipak, K. D.: Semiparametric Bayesian analysis of survival data. J. Amer. Statist. Assoc. 92 (1997), 1195-1212. | DOI | MR | Zbl

[16] Timková, J.: Bayesian nonparametric estimation of hazard rate in survival analysis using Gibbs sampler. In: Proc. WDS 2008, Part I: Mathematics and Computer Sciences, pp. 80-87.

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