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

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. 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

Semi-parametric modelling for costs of health care technologies

Cost data that arise in the evaluation of health care technologies usually exhibit highly skew, heavy-tailed and, possibly, multi-modal distributions. Distribution-free methods for analysing these data, such as the bootstrap, or those based on the asymptotic normality of sample means, may often lead to inefficient or misleading inferences. On the other hand, parametric models that fit the data (or a transformation of the data) equally well can produce very different answers. We consider a Bayesian approach, and model cost data with a distribution composed of a piecewise constant density up to an unknown endpoint, and a generalized Pareto distribution for the remaining tail. Copyright (C) 2004 John Wiley & Sons, Ltd

A note on Bayesian hypothesis testing for the scalar skew-normal distribution

The skew-normal distribution is a class of densities that preserves some useful properties of the normal distribution while allowing a shape parameter to account for skewness. It has various remarkable properties in terms of mathematical tractability and turned out to be quite useful in modelling real data. However from an inferential point of view its use gives raise to many difficulties, that are intrinsically tied with the shape of the likelihood function. This fact suggests to solve the problem by calibrating the likelihood with a weight function, and perhaps the most intuitive calibration can be obtained in the Bayesian framework, where the prior distribution plays naturally the role of the weight function. Here we consider in details the problem of testing normality in the general skew-normal model, and solve it by means of different tools for hypothesis testing in the Bayesian framework, namely the Bayes factor and the Jeffreys divergence, pointing out benefits and problems of both approaches

A robust Bayesian approach for unit root testing

In this paper we deal with the identification of an autoregressive model for an observed time series, and the detection of a unit root in its characteristic polynomial. This is a big issue concerned with distinguishing stationary time series from time series for which differencing is required to induce stationarity. We consider a Bayesian approach, and particular attention is devoted to the problem of the sensitivity of the standard Bayesian analysis with respect to the choice of the prior distribution for the autoregressive coefficients

Semi-parametric modelling for costs of helt care technologies

Cost data that arise in the evaluation of health care technologies usually exhibit highly skew, heavy-tailed and, possibly, multi-modal distributions. Distribution-free methods for analysing these data, such as the bootstrap, or those based on the asymptotic normality of sample means, may often lead to inefficient or misleading inferences. On the other hand, parametric models that fit the data (or a transformation of the data) equally well can produce very different answers. We consider a Bayesian approach, and model cost data with a distribution composed of a piecewise constant density up to an unknown endpoint, and a generalised Pareto distribution for the remaining tail

An alternative bayes factor for testing for unit autoregressive roots

In this paper we deal with the identification of an autoregressive model for an observed time series, and the detection of a unit root in its characteristic polynomial. This is a big issue concerned with distinguishing stationary time series from time series for which differencing is required to induce stationarity. We consider a Bayesian approach, and particular attention is devoted to the problem of the sensitivity of the standard Bayesian analysis with respect to the choice of the prior distribution for the autoregressive coefficients