Abstract
Health economic decision models are subject to various forms of uncertainty, including uncertainty about the parameters of the model and about the model structure. These uncertainties can be handled within a Bayesian framework, which also allows evidence from previous studies to be combined with the data. As an example, we consider a Markov model for assessing the cost-effectiveness of implantable cardioverter defibrillators. Using Markov chain Monte Carlo posterior simulation, uncertainty about the parameters of the model is formally incorporated in the estimates of expected cost and effectiveness. We extend these methods to include uncertainty about the choice between plausible model structures. This is accounted for by averaging the posterior distributions from the competing models using weights that are derived from the pseudo-marginal-likelihood and the deviance information criterion, which are measures of expected predictive utility. We also show how these cost-effectiveness calculations can be performed efficiently in the widely used software WinBUGS.
Highlights
We present a Bayesian model for the cost-effectiveness of two strategies for the prevention of cardiac arrhythmia and formally account for both parameter and model uncertainty
We assess the relative plausibility of these scenarios against data by estimating the expected predictive utility of each model by using the cross-validatory ‘pseudo-marginal-likelihood’ (PML) (Geisser and Eddy, 1979; Gelfand and Dey, 1994) and the commonly used deviance information criterion (Spiegelhalter et al, 2002)
The WBDev approach saves the cost of storage and processing the stored samples, which may be expensive if there are large numbers of unknown parameters or if a large Markov chain Monte Carlo (MCMC) sample is required to represent the posterior distribution accurately
Summary
Cost-effectiveness models are routinely used by health policy makers to evaluate medical interventions and to allocate resources. We show how it can be adapted to handle arbitrarily complex model structures at little extra computational cost, by using an extension of WinBUGS (Lunn, 2003) that enables complex functions of parameters to be calculated substantially faster This application involves several choices between plausible model structures, including the choice of covariates for the incidence of clinical events, and different parametric forms for the relationship of mortality to age. We assess the relative plausibility of these scenarios against data by estimating the expected predictive utility of each model by using the cross-validatory ‘pseudo-marginal-likelihood’ (PML) (Geisser and Eddy, 1979; Gelfand and Dey, 1994) and the commonly used deviance information criterion (Spiegelhalter et al, 2002) The differences in these measures between models can be ‘calibrated’ by a Bayesian bootstrap procedure, to produce the probability that each model has the highest expected predictive utility for a replicate data set, among the models being compared. The data that are analysed in the paper and the programs that were used to analyse them can be obtained from http://www.blackwellpublishing.com/rss
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