Scale mixtures log-Birnbaum–Saunders regression models with censored data: a Bayesian approach

ABSTRACT

The main objective of this paper is to develop a full Bayesian analysis for the Birnbaum–Saunders (BS) regression model based on scale mixtures of the normal (SMN) distribution with right-censored survival data. The BS distributions based on SMN models are a very general approach for analysing lifetime data, which has as special cases the Student-t-BS, slash-BS and the contaminated normal-BS distributions, being a flexible alternative to the use of the corresponding BS distribution or any other well-known compatible model, such as the log-normal distribution. A Gibbs sample algorithm with Metropolis–Hastings algorithm is used to obtain the Bayesian estimates of the parameters. Moreover, some discussions on the model selection to compare the fitted models are given and case-deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback–Leibler divergence. The newly developed procedures are illustrated on a real data set previously analysed under BS regression models.

KEYWORDS:

• Generalized Birnbaum–Saunders distributions
• influential observations
• Kullback–Leibler divergence
• sinh-spherical distribution
• survival analysis

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors researches are partially funded by the Brazilian Institutions CNPq and FAPESP.