Cost-effectiveness analyses of empirical participant data are frequently complicated by irregularly distributed and correlated observations, which are not well approximated by normal distributions. Things get even more difficult when observations are clustered within higher level units (for example, hospitals) or the participant (that is, multiple measurements at different timepoints). Therefore, we developed a flexible Bayesian approach to jointly model costs and effects of two competing interventions with a multilevel structure.

Our new model is presented in mathematical form and discussed in detail. We model costs and Quality-Adjusted Life-Years effects through Gamma and Beta distributions, and account for the dependency between costs and effects by adding the effects as a predictor for the costs. We further include hurdle models to account for costs of for the presence of zero costs and perfect health scores.

The full model is implemented in the probabilistic programming language Stan. To compare the performance of our Bayesian model to a frequentist approach (linear mixed model combined with bootstrapping), we simulate 1000 datasets consisting of 400 participants and 20 clusters. Performance of both models is assessed in terms of variance, bias and coverage probability with respect to the costs and effects defined in the simulation.

We ran a preliminary simulation with high intraclass correlation, strong negative correlation for patient-level costs and effects, and positive correlation of cluster effects on both outcomes. The analysis shows that the Bayesian model exhibits a slightly larger bias for estimated costs, but smaller errors and higher coverage probability compared to the frequentist alternative. We will explore different scenarios where we vary the parameters of the simulations and assess whether the results are robust to change.

It is very important that economic evaluations in health care produce precise and reliable results. Our Bayesian approach is able to handle multiple statistical complexities at once and performs better than a comparable frequentist model. Whether this conclusion holds for different simulation scenarios will be explored in further stages of this study.