A semiparametric Bayesian mixed-effects model for failure time data

We examine the accelerated failure time model for univariate failure time data with right censoring, with application to the failure times of Kevlar fibres from different spools, subject to different stress levels. We propose a semi-parametric modelling by letting the error distribution be a shape-scale mixture of Weibull densities, the mixing measure being a normalized generalized gamma measure. We obtain posterior estimates of the regression parameter and also of credibility intervals for the predictive distributions and their quantiles, by including in the MCMC scheme the posterior distribution of the random mixing probability. The number of components in the nonparametric mixture can be interpreted as the number of random effects, having a prior distribution induced by the nonparametric model, and is inferred from the data. Compared to previous results, we obtain narrower interval estimates of the quantiles of the predictive survival function