Estimating the Relationship Between EQ-5D-5L and EQ-5D-3L: Results from a UK Population Study

Objectives The aim of this study was to estimate the relationship between EQ-5D-3L and EQ-5D-5L, in both directions, using a single model. Methods An online survey containing both variants of EQ-5D, with randomised ordering, was administered to a large UK sample in 2020. A joint statistical model of the ten EQ-5D responses (five at 5L, five at 3L), using a multi-equation ordinal regression framework was estimated. The joint model ensures mappings in either direction are fully consistent with the information in the sample and satisfy Bayes’ rule. Three extensions enhance model flexibility: a copula specification allows differing degrees of correlation between the 3L and 5L responses at the upper and lower extremes of health; a normal mixture residual distribution gives flexibility in the distributional form of responses; and a common factor captures correlations in responses across the five dimensions. Results Almost 50,000 responses were received. Thirty-five percent of respondents reported an existing medical condition. Ninety percent of possible 3L and 43% of possible 5L health states were observed. The preferred model specification includes age, sex and the responses to the EQ-5D instrument. Close alignment to the observed data was observed both in within-sample and out-of-sample comparisons. Conclusion The results from this study provide a means of translating evidence to or from EQ-5D-3L to or from 5L based on a large-scale UK population survey with randomised ordering. Mapping can be performed either using descriptive system responses, individual utility scores or summary statistics.