Computational Statistics

, Volume 16, Issue 2, pp 243–254

# Bayesian Analysis for Hazard Models with Non-constant Shape Parameter

Article

## Summary

We develop an approximate Bayesian analysis for hazard models with shape parameters dependent on covariates. We consider a general hazard regression model which includes, among others, the proportional hazards and the accelerated failure time models, with the inverse power law and the Arrhenius models as relationship of the scale parameter and a covariate, while preserves flexibility to fit datasets where shape parameter depending on covariates is observed. The advantage of this procedure is that it leads to a single algorithm for fitting hazard-based models, and model comparation is easily done through Bayes factors. We use Laplace’s method to find the marginal posterior densities of interest. As advantage we obtain simple expressions for the posterior densities. The Weibull particular case is studied in detail. The methodology is illustrated with an accelerated lifetime test on an electrical insulation film.

## Keywords

Accelerated Lifetime test Bayesian Analysis Extended Hazard Regression Model Laplace Method Weibull Model

## Notes

### Acknowledgements

The author is very grateful to his supervisors, D.R. Cox, A.C. Davison and D.V. Hinkley, to J. Carpenter, and to an Associate Editor and referees for their comments and suggestions on this work. Part of the research was completed while the author was on leave from the Universidade Federal de São Carlos, studing for his doctorate at the University of Oxford. The work was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil.

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