Bayesian Analysis for Hazard Models with Non-constant Shape Parameter

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.