The relationship between EQ-5D, HAQ and pain in patients with rheumatoid arthritis: further validation and development of the limited dependent variable, mixture model approach

Objective: To provide robust estimates of EQ-5D as a function of the Health Assessment Questionnaire (HAQ) and pain in patients with rheumatoid arthritis. Method: Repeated observations of patients diagnosed with RA in a US observational cohort (n=100,398 observations) who provided data on HAQ, pain on a visual analogue scale and the EQ-5D questionnaire. We use a bespoke mixture modelling approach to appropriately reflect the characteristics of the EQ-5D instrument and compare this to results from linear regression. Results: The addition of pain alongside HAQ as an explanatory variable substantially improves explanatory power. The preferred model is a four component mixture. Unlike the linear regression it exhibits very good fit to the data, does not suffer from problems of bias or predict values outside the feasible range. Conclusions: It is appropriate to model the relationship between HAQ and EQ-5D but only if suitable statistical methods are applied. Linear models underestimate the QALY benefits, and therefore the cost effectiveness, of therapies. The bespoke mixture model approach outlined here overcomes this problem. The addition of pain as an explanatory variable greatly improves the estimates