Modelling a preference-based index for EQ-5D-3L and EQ-5D-3L + Sleep using a Bayesian framework

Background Conventionally, frequentist approach has been used to model health state valuation data. Recently, researchers started to explore the use of Bayesian methods in this area.

Objectives This paper presents an alternative approach to modelling health state valuation data of the EQ-5D-3L and EQ-5D-3L + Sleep descriptive systems, using a Bayesian framework, and demonstrates its superiority to conventional frequentist methods.

Methods The valuation study is composed of 18 EQ-5D-3L health states and 18 EQ-5D-3L + Sleep health states valued by 160 members of the general public in South Yorkshire, UK, using the time tradeo-ff technique. Three different models were developed for EQ-5D-3L and EQ-5D-3L + Sleep accordingly using Bayesian Markov chain Monte Carlo simulation methods. Bayesian methods were applied to models fitted included a linear regression, random effect and random effect with covariates. The models are compared based on their predictive performance using mean predictions, root mean squared error (RMSE) and deviance information criterion (DIC). All analyses were performed using Bayesian Markov chain Monte Carlo simulation methods.

Results The random effects with covariates model performs best under all criterions for the two preference-based measures, with RMSE (0.037) and DIC (637.5) for EQ-5D-3L and RMSE (0.019), DIC (416.4) for EQ-5D + Sleep. Compared with models previously estimated using frequentist approach, the Bayesian models reported in this paper provided better predictions of observed values.

Conclusion Bayesian methods provide a better way to model EQ-5D-3L valuation data with and without a sleep ‘bolt-on’ and provide a more flexible in characterizing the full range of uncertainty inherent in these estimates.