Capturing Valuation Study Sampling Uncertainty in the Estimation of Health State Utility Values Using the EQ-5D-3L

Utility scores associated with preference-based health-related quality-of-life instruments such as the EQ-5D-3L are reported as point estimates. In this study, we develop methods for capturing the uncertainty associated with the valuation study of the UK EQ-5D-3L that arises from the variability inherent in the underlying data, which is tacitly ignored by point estimates. We derive a new tariff that properly accounts for this and assigns a specific closed-form distribution to the utility of each of the 243 health states of the EQ-5D-3L.

Using the UK EQ-5D-3L valuation study, we used a Bayesian approach to obtain the posterior distributions of the derived utility scores. We constructed a hierarchical model that accounts for model misspecification and the responses of the survey participants to obtain Markov chain Monte Carlo (MCMC) samples from the posteriors. The posterior distributions were approximated by mixtures of normal distributions under the Kullback-Leibler (KL) divergence as the criterion for the assessment of the approximation. We considered the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to estimate the parameters of the mixture distributions.

We derived an MCMC sample of total size 4,000 × 243. No evidence of nonconvergence was found. Our model was robust to changes in priors and starting values. The posterior utility distributions of the EQ-5D-3L states were summarized as 3-component mixtures of normal distributions, and the corresponding KL divergence values were low.

Our method accounts for layers of uncertainty in valuation studies, which are otherwise ignored. Our techniques can be applied to other instruments and countries' populations.

Guidelines for health technology assessments typically require that uncertainty be accounted for in economic evaluations, but the parameter uncertainty of the regression model used in the valuation study of the health instrument is often tacitly ignored.We consider the UK valuation study of the EQ-5D-3L and construct a Bayesian model that accounts for layers of uncertainty that would otherwise be disregarded, and we derive closed-form utility distributions.The derived tariff can be used by researchers in economic evaluations, as it allows analysts to directly sample a utility value from its corresponding distribution, which reflects the associated uncertainty of the utility score.