Objective Bayesian Survival Analysis Using Shape Mixtures of Log-Normal Distributions

Survival models such as the Weibull 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 modeled 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 density and hazard functions. Bayesian inference under nonsubjective 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. In addition, we propose a method for outlier detection based on the mixture structure. A simulation study illustrates the performance of our methods under different scenarios and an application to a real dataset is provided. Supplementary materials for the article, which include R code, are available online.