Methods: Using data from the Health Survey for England (HSE) and the National Health Measurement Study (NHMS) we develop a multivariate ordered probit (MVOP) model for the analysis of the EQ-5D responses and compare its performance against other approaches proposed in the literature, such as response mapping (eg. multinomial logit, ML) and univariate regression models (applied directly on the EQ-5D index score). Models goodness‑of-fit assessment is carried out using the Deviance Information Criteria (DIC), while their in-sample and out-of-sample predictive abilities (crucial when developing mapping algorithms) are assessed using Bayesian proper scoring rules. Departing from the use of measures based on the predicted mean such as the (root) mean squared error, scoring rules exploit instead the whole posterior predictive distribution of the parameters of the model, thus reflecting both central tendency and uncertainty in the prediction. The analysis is implemented within a Bayesian framework.
Results : The MVOP fits the two independent datasets better (DIC: 15,145 for the NHMS and 45,550 HSE) than the ML (DIC: 15,703 for the NHMS and 47,140 HSE) and of the independent ordered probit for each dimensions (DIC: 15,720 for the NHMS and 45,550 HSE). Assessment of their predictive posterior distribution shows that the MVOP has better coverage of the central tendency measure (in-sample validation), and better out-of-sample predictive ability (0.531 for the MVOP vs 0.513 for the independent univariate ordered probit vs 0.481 for the ML).
Conclusions: Explicit modelling of both correlation between the responses on each of the five dimensions of the EQ‑5D and the natural ordering of the severity levels within each dimension yields more accurate predictions. Modelling at the response level, rather than at the index score, facilitates a more generalisable assessment of the EQ-5D responses which is not confounded by the valuation set used in each country.