A Bayesian model averaging approach with non-informative priors for cost-effectiveness analyses in health economics

We consider the problem of assessing new and existing technologies for their cost-effectiveness in the case where data on both costs and effects are available from a clinical trial, and we address it by means of the cost-effectiveness acceptability curve. The main difficulty in these analyses is that cost data usually exhibit highly skew and heavy-tailed distributions, so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution, and in particular to model accurately the tail of the distribution, which is highly influential in estimating the population mean. Here, in order to integrate the uncertainty about the model into the analysis of cost data and into cost-effectiveness analyses, we consider an approach based on Bayesian model averaging in the particular case of weak prior informations about the unknown parameters of the different models involved in the procedure. The main consequence of this assumption is that the marginal densities required by Bayesian model averaging are undetermined. However in accordance with the theory of partial Bayes factors and in particular of fractional Bayes factors, we suggest replacing each marginal density with a ratio of integrals, that can be efficiently computed via Path Sampling. The results in terms of cost-effectiveness are compared with those obtained with a semi-parametric approach that does not require any assumption about the distribution of costs.