Bayesian modelling of positively skewed data with particular application to the cost aspect of medical cost-effectiveness analysis.

The motivation for this research was the study of a medical cost data set from a clinical trial. If a Regulatory Body were to be accept the new intervention that has been proposed then a Health Care provider has to budget for future treatments for some members of the rest of the population. In this Bayesian analysis we want to be able to calculate the expected value for one unobserved member of this finite population from its posterior predictive distribution by firstly establishing the parametric data model that best captures the positive skew characteristics of the costs. We then develop a novel approach to modelling the priors that enable an expert's prior beliefs to be elicited while permitting a limited analytical study of the model. These techniques have been applied to recent medical data sets to establish their comparative efficiency when compared with classical estimators.