OBJECTIVES: Economic evaluations 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 (e.g., hospitals) or the participant (i.e., repeated measurements). Therefore, we develop a flexible Bayesian approach to jointly model costs and effectiveness of two competing interventions with a multilevel structure.

METHODS: We model costs and effectiveness through Gamma and Beta distributions, respectively, and account for the dependency between the two by adding the effects as a predictor for the costs. The varying intercepts for the clusters in the regression equations are modelled through a bivariate normal distribution. We use G-computation to estimate treatment effects on costs and utilities. To compare the performance of our approach to a frequentist alternative (linear mixed model combined with cluster bootstrapping), we simulate 2000 datasets consisting of 400 participants and 40 clusters. Performance of both models is assessed in terms of bias, variance and coverage probability with respect to the effect sizes defined in the simulation.

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

CONCLUSIONS: Our Bayesian approach is able to handle multiple statistical complexities at once and performs better than a comparable frequentist model. Since it very important that economic evaluations in health care produce precise and reliable estimates, we believe that this paper is a valuable addition to the literature. We provide a full implementation in R and Stan.