Purpose: An individual patient data (IPD) meta-analysis of five trials that compared the cost-effectiveness of initial endoscopy versus empirical treatment for dyspepsia was carried out. This calculated patient-level net benefits as a linear function of the patients' cost, clinical benefit and a given threshold willingness-to-pay per unit of clinical benefit. It has been proposed that net benefits are normally distributed and that cost-effectiveness analysis can be based on their regression on the treatment arm as a dummy variable. We aimed to test the normality of net benefits and to determine if the skewed density of net-benefits was better modelled by a mixture of normal densities or a single normal density.

Methods: The data had a two-level structure of patients nested within trial centres, and therefore, a multilevel regression model was fitted to account for the two sources of variation. The assumption that patient-level net benefits come from a normal distribution is not always appropriate as they are a function of skew cost data and indeed tend to have densities with long left-hand tails. A model which is robust to outliers is therefore required. Thus, the multilevel model was extended so that the net-benefits were modelled by a mixture of normal densities. All analyses were done under the Bayesian semi-parametric framework.

Results: Preliminary analysis showed no statistically significant (p-value=0.21) difference in clinical benefit between the two treatment arms across the five trials. There was a significant difference (p-value=0.0025) in total costs between the two arms, with initial endoscopy costing more. The multilevel regression model was fitted to net benefits with threshold willingness-to-pay of 0 to 3000 pounds sterling, and it showed that initial endoscopy was not more cost-effective than empirical therapy.

Conclusion: The mixture model performed better than a single normal density model for patient-level net benefits. There was considerable variability in cost-effectiveness between trial centres. Where individual patient trial data can be obtained for both costs and effects, assumptions of normality in the net benefit framework should be formally tested and alternative models applied.

Keywords: Individual patient data meta-analysis, Net benefits, Multilevel model, Mixture distribution