Criticism of a hierarchical model using Bayes factors

This paper analyses a data file of heart transplant surgeries performed in the United States over a two-year period. A Poisson/gamma exchangeable model is used to learn about the underlying death rates for 94 hospitals. There are concerns about the suitability of this hierarchical model, including the need for a hierarchical structure, the existence of outliers, the choice of prior hyperparameters, the need for a covariate in the model, and the manner in which exchangeability was modelled. Each concern motivates the construction of alternative models and Bayes factors are used to compare the existing model with the alternative models. Graphical displays are used to check the sensitivity of the posterior analysis with respect to model perturbations and plots of Bayes factors are used to criticize these perturbations.