Bayesian Models with Spatial Correlation Improve the Precision of EQ-5D-5L Value Sets
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Background Health utilities from value sets for the EQ-5D-5L are commonly used in economic evaluations. We examined whether modeling spatial correlation among health states could improve the precision of the value sets. Methods Using data from 7 EQ-5D-5L valuation studies, we compared the predictive precision of the published linear model, a recently proposed cross-attribute level effects (CALE) model, and 2 Bayesian models with spatial correlation. Predictive precision was quantified through the root mean squared error (RMSE) for out-of-sample predictions of state-level mean utilities on omitting individual states, as well as omitting blocks of states. Results In all 7 countries, on omitting single health states, Bayesian models with spatial correlation improved upon the published linear model: the RMSEs for the originally published models, 0.050, 0.051, 0.060, 0.061, 0.039, 0.050, and 0.087 for Canada, China, Germany, Indonesia, Japan, Korea, and the Netherlands, respectively, could be reduced to 0.043, 0.042, 0.051, 0.054, 0.037, 0.037, and 0.085, respectively. On omitting blocks of health states, Bayesian models with spatial correlation led to smaller RMSEs in 3 countries, while the CALE model led to smaller RMSEs in the remaining 4 countries. Discussion: Bayesian models incorporating spatial correlation and CALE models are promising for improving the precision of value sets for the EQ-5D-5L. The differential performance of the Bayesian models on omitting single states versus blocks of states suggests that designing valuation studies to capture more health states may further improve precision. We suggest that Bayesian and CALE models be considered as candidates when creating value sets and that alternative designs be explored; this is vital as the prediction errors in value sets need to be smaller than the minimal important difference of the instrument. Highlights The accuracy of value sets of multi-attribute utility instruments is typically of the same order of magnitude as the instrument’s minimal important difference and would benefit from improvement. Bayesian models with spatial correlation have been shown to improve value set accuracy in isolated cases. We showed that Bayesian approaches with spatial correlation improved predictive precision in 7 EQ-5D-5L valuation studies. We recommend that Bayesian models incorporating spatial correlation be considered when creating value sets and have provided code for fitting them.
