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Title: Incorporating Unobserved Heterogeneity in Weibull Survival Models: A Bayesian Approach


We propose flexible classes of distributions for survival modelling that naturally deal with both the presence of outlying observations and unobserved heterogeneity. We present the family of Rate Mixtures of Weibull distributions, for which a random effect is introduced through the rate parameter. This family contains i.a. the well-known Lomax distribution and can accommodate flexible hazard functions. Covariates are introduced through an Accelerated Failure Time model and we explicitly take censoring into account. We construct a weakly informative prior that combines the structure of the Jeffreys prior with a proper (informative) prior. This prior is shown to lead to a proper posterior distribution under mild conditions. Bayesian inference is implemented by means of a Metropolis-within-Gibbs algorithm. The mixing structure is exploited in order to provide an outlier detection method. Our methods are illustrated using two real datasets, one concerning bone marrow transplants and another on cerebral palsy.

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