EQ-5D is used in cost-e ectiveness studies underlying many important health policy decisions. It comprises a survey instrument generating a description of health states across ve domains, and a system of utility values for each state. The original 3-level version of EQ-5D is being replaced with a more sensitive 5-level version but little is known about the consequences of this change. We develop a multi-equation ordinal response model incorporating a copula specification with normal mixture marginals to analyse the joint responses to EQ- 5D-3L and EQ-5D-5L in a survey of people a ected by rheumatoid disease, and use it to generate mappings between the 3-level and 5-level descriptive systems. We find significant conflicts between the two, which would imply the reversal of an important conclusion in a real-world evaluation of drug therapies.