ENBIS: European Network for Business and Industrial Statistics

SIG Modelling: A semiparametric Bayesian mixed-effects model for failure time data.

22 September 2009, 14:25 – 14:45

Abstract

Submitted by

Rainer Göb

Authors

Antonio Pievatolo

Affiliation

CNR IMATI, Milano, Italy,Chairman, ISO/TC 69/SC 5 Acceptance sampling schemes ,University of Würzburg

Abstract

We examine the accelerated failure time (AFT) model for univariate failure time data with right censoring. In the parametric context, the AFT model with Weibull error has been commonly fitted to the failure times of Kevlar fibres from different spools, subject to different levels of stress. We propose a less prescriptive modeling by letting the error distribution be a shape-scale mixture of Weibull densities, the mixing measure being modeled non-parametrically as a normalized generalized gamma measure. Besides regression parameters, in the Bayesian framework one may also obtain predictive distributions of failure times under different stress conditions, via MCMC methods, such as the Polya urn Gibbs sampler. Here we sample also the posterior distribution of the random mixing probability, so that we can provide credibility intervals for the predictive distributions and their quantiles. 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. The difference with respect to Bayesian parametric random-effects models is that this number can be inferred from the data. Compared to previous results, we obtain narrower interval estimates of the quantiles and also useful credibility intervals for the predictive survival functions.

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