Tails from the Peak District: Adjusted Limited Dependent Variable Mixture Models of EQ-5D Questionnaire Health State Utility Values

Objectives: Health utility data generated by using the EuroQol five-dimensional (EQ-5D) questionnaire are right bounded at 1 with a substantial gap to the next set of observations, left bounded, and multimodal. These features present challenges to the estimation of the effect of clinical and socioeconomic characteristics on health utilities. Our objective was to develop and demonstrate an appropriate method for dealing with these features. Methods: We developed a statistical model that incorporates an adjusted limited dependent variable approach to reflect the upper bound and the large gap in feasible EQ-5D questionnaire values. Further flexibility was then gained by adopting a mixture modeling framework to address the multimodality of the EQ-5D questionnaire distribution. We compared the performance of these approaches with that of those frequently adopted in the literature (linear and Tobit models) by using data from a clinical trial of patients with rheumatoid arthritis. Results: We found that three latent classes are appropriate in estimating EQ-5D questionnaire values from function, pain, and sociodemographic factors. Superior performance of the adjusted limited dependent variable mixture model was achieved in terms of Akaike and Bayesian information criteria, root mean square error, and mean absolute error. Unlike other approaches, the adjusted limited dependent variable mixture model fits the data well at high EQ-5D questionnaire levels and cannot predict unfeasible EQ-5D questionnaire values. Conclusions: The distribution of the EQ-5D questionnaire is characterized by features that raise statistical challenges. It is well known that standard approaches do not perform well for this reason. This article developed an appropriate method to reflect these features by combining limited dependent variable and mixture modeling and demonstrated superior performance in a rheumatoid arthritis setting. Further refinement of the general framework and testing in other data sets are warranted. Analysis of utility data should apply methods that recognize the distributional features of the data.