Bayesian Meta-Analysis of Health State Utility Values: A Tutorial with a Practical Application in Heart Failure

Abstract

Researchers incorporate health state utility values as inputs to inform economic models. However, for a particular health state or condition, multiple utility values derived from different studies typically exist and a single study is often insufficient to represent the best available source of utility needed to inform policy decisions. The purpose of this paper is to provide an introductory guidance for conducting Bayesian meta-analysis of health state utility values to generate a single parameter input for economic evaluation, using R. The tutorial is illustrated using data from a systematic review of health state utilities of patients with heart failure, with 21 studies that reported utilities measured using the EuroQol-5D (EQ-5D). Explanations, key considerations and suggested readings are provided for each step of the tutorial, adhering to a clear workflow for conducting Bayesian meta-analysis: (1) setting-up the data; (2) employing methods to impute missing standard deviations; (3) defining the priors; (4) fitting the model; (5) diagnosing model convergence; (6) interpreting the results; and (7) performing sensitivity analyses. The posterior distributions for the pooled effect size (i.e. mean health state utility) and between-study heterogeneity are discussed and interpreted in light of the data, priors and models used. We hope that this tutorial will foster interest in Bayesian methods and their applications in the meta-analysis of utilities.

Fig. 1

Prior predictive check. The black line represents the observed data, while the blue lines represent the simulated data based on the prior distributions specified for the model parameters.

Fig. 2

Posterior predictive check. The black line represents the observed data, while the blue lines show the simulated data based on the posterior distribution of utility (which takes into account both the observed data and the prior distributions of the model parameters).

Fig. 3

Forest plot showing the posterior distribution of effect sizes for each study and the pooled effect size