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Paper No. 13-01

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CA Vallejos and MFJ Steel

Objective Bayesian Survival Analysing using Shape Mixtures of Log-Normal Distributions

Abstract: Survival models such as theWeibull or log-normal lead to inference that is not robust to the presence of outliers. They also assume that all heterogeneity between individuals can be modelled through covariates. This article considers the use of infinite mixtures of lifetime distributions as a solution for these two issues. This can be interpreted as the introduction of a random effect in the survival distribution. We introduce the family of Shape Mixtures of Log-Normal distributions, which covers a wide range of shapes. Bayesian inference under non-subjective priors based on the Jeffreys rule is examined and conditions for posterior propriety are established. The existence of the posterior distribution on the basis of a sample of point observations is not always guaranteed and a solution through set observations is implemented. This also accounts for censored observations. In addition, a method for outlier detection based on the mixture structure is proposed. Finally, the analysis is illustrated using a real dataset.

Keywords: Jeffreys prior; Outlier detection; Posterior existence; Set observations.