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A bayesian semiparametric analysis for additive Hazard models with censored observations

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Abstract

The hazard function, also called the risk function or intensity function, is usually used to model survival data or other waiting times, such as unemployment times. In contrast to the proportional hazard model, the additive risk model assumes that the hazard function is the sum of rather than the product of, the baseline hazard function and a non-negative function of covariates. We propose to introduce the covariates into the model through a Gamma hazard function, while the baseline hazard function is left unspecified. Following the Bayesian paradigm, we obtain an approximation to the posterior distribution using Markov Chain Monte Carlo techniques. The subject-specific survival estimation is also studied. A real example using unemployment data is provided.

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References

  • Aalen, O. O. (1980).A Model for Nonparametric Regression Analysis of Counting Processes, Springer-Verlag, New York.

    Google Scholar 

  • Aalen, O. O. (1989). A linear regression model for the analysis of life times.Statistics in Medicine, 8:907–925.

    Google Scholar 

  • Beamonte, E. (1998).Aportaciones al análisis bayesiano semiparamétrico de datos de supervivencia. Ph.D. thesis, Departmento de Estadística e Investigación Operativa, Universidad de Valencia.

  • Beenstock, M. (1996). Training and the time to find a job in Israel.Applied Economics, 28:935–946.

    Article  Google Scholar 

  • Best, N. G., Cowles, M. K., andVines, S. K. (1995).CODA manual version 0.30. MRC Biostatistics Unit, Cambridge.

    Google Scholar 

  • Buckley, J. (1984). Additive and multiplicative models for relative survival rates.Biometrics, 40:51–62.

    Article  Google Scholar 

  • Casella, G. andGeorge, E. I. (1992). Explaining the Gibbs sampler.The American Statistican, 46:167–174.

    Article  MathSciNet  Google Scholar 

  • Chib, S. andGreenberg, E. (1996). Markov Chain Monte Carlo simulation methods in Econometrics.Econometric Theory, 12:409–431.

    MathSciNet  Google Scholar 

  • Cox, D. R. (1972). Regression models and life tables (with discussion).Journal of the Royal Statistical Society, 34:187–220.

    MATH  Google Scholar 

  • Cox, D. R. (1975). Partial likelihood.Biometrika, 62:269–276.

    Article  MATH  MathSciNet  Google Scholar 

  • Cox, D. R. andOakes, D. A. (1984).Analysis of Survival Data. Chapman & Hall, London.

    Google Scholar 

  • DeGroot, M. H. (1970).Optimal Statistical Decisions. McGraw-Hill, New York.

    MATH  Google Scholar 

  • Follmann, D. A., Goldberg, M. S., andMay, L. (1990). Personal characteristics, unemployment insurance, and the duration of unemployment.Journal of Econometrics, 45:351–366.

    Article  Google Scholar 

  • Gamerman, D. (1991). Dynamic Bayesian models for survival data.Applied Statistics, 40:63–79.

    Article  MATH  Google Scholar 

  • Gelfand, A. E. andSmith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities.Journal of the American Statistical Association, 85:398–409.

    Article  MATH  MathSciNet  Google Scholar 

  • Geman, S. andGeman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images.IEEE Transactions on Pattern Analysis and Machine Intelligence, 6:721–741.

    Article  MATH  Google Scholar 

  • Geweke, J., Keane, M. P., andRunkle, D. E. (1998). Statistical inference in the multinomial multiperiod probit model.Journal of Econometrics, 80:125–165.

    Article  MathSciNet  Google Scholar 

  • Gilks, W. R., Richardson, S., andSpiegelhalter, D. J., eds. (1996).Markov Chain Monte Carlo in Practice. Chapman & Hall, London.

    MATH  Google Scholar 

  • Jaggia, S. andThosar, S. (1995). Contested tender offers: an estimate of the hazard function.Journal of Business & Economic Statistics 13:113–119.

    Article  Google Scholar 

  • Kim, J. andLee, S. Y. (1998). Two-sample goodness-of-fit tests for additive risk models with censored observations.Biometrika, 85:593–603.

    Article  MATH  MathSciNet  Google Scholar 

  • Lin, D., Oakes, D., andYing, Z. (1998). Additive hazards regression with current status data.Biometrika, 85:289–298.

    Article  MATH  MathSciNet  Google Scholar 

  • Lin, D. andYing, Z. (1994). Semiparametric analysis of the additive risk model.Biometrika, 81:61–71.

    Article  MATH  MathSciNet  Google Scholar 

  • McKeague, I. andSasieni, P. (1994). A partly parametric additive risk model.Biometrika, 81:501–514.

    Article  MATH  MathSciNet  Google Scholar 

  • Sinha, D. andDey, D. K. (1997). Semiparametric Bayesian analysis of survival data.Journal of the American Statistical Association, 92:1195–1212.

    Article  MATH  MathSciNet  Google Scholar 

  • Smith, A. F. M. andRoberts, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov Chain Monte Carlo methods.Journal of the Royal Statistical Society, 55:3–23.

    MATH  MathSciNet  Google Scholar 

  • Tierney, L. (1994). Markov Chains for exploring posterior distributions (with discussion).Annals of Statistics, 22:1701–1762.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Economics, Valencia University, Av. Naranjos s/n, 46022, Valencia, Spain

    Eduardo Beamonte

  2. Department of Statistics and Operational Research, Valencia University, Av. Naranjos s/n, 46022, Valencia, Spain

    José D. Bermúdez

Authors
  1. Eduardo Beamonte
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  2. José D. Bermúdez
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Corresponding author

Correspondence to Eduardo Beamonte.

Additional information

This work was partially supported by the Spanish Education and Science Council Project PB96-0776.

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Beamonte, E., Bermúdez, J.D. A bayesian semiparametric analysis for additive Hazard models with censored observations. Test 12, 347–363 (2003). https://doi.org/10.1007/BF02595719

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  • DOI: https://doi.org/10.1007/BF02595719

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