Challenges in modelling censored health state preference data: Explorations with the EQ-5D and HUI2

Background - There are now a variety of preference based health related quality of life measures available. These instruments describe health in different terms and also use different methods for measuring individual preferences for health. Whilst these instruments have been shown to have acceptable psychometric properties, they have also been shown to be affected by ceiling and/or floor effects. The presence of ceiling effects in the health descriptive system are of particular concern for health state preference modelling as it may impact upon the likelihood of observing censoring and/or compression. Where appropriate methodologies are available to deal with these problems, it is methodologically preferable to use them. In this paper we assess the impact of adopting Tobit models to deal with potential censoring in two datasets – the MVH EQ-5D data and the UK HUI2 health state preference data. In doing so, we will show the impact on estimated values and expected fit. Methods - For each dataset we estimate a generalised least squares model with random effects and a tobit random effects model. The specification of each utility function is equivalent to those in the original publications (Dolan 1997, McCabe et al 2005). For each model we report the estimated coefficients, the Mean Absolute Error (MAE), the Mean Square Error (MSE), the Root Mean Square Error (RMSE), the proportion of states where the absolute prediction error was greater than 0.1 and the correlation between observed and predicted values. Results - Censoring problems were found in the MVH EQ-5D data but not in the UK HUI2 data set. As expected the impact of adjusting for censoring is very different between the two datasets. Conclusion – The impact of taking account of potential censoring is much greater in the EQ-5D data than the HUI2 data. Although the EQ-5D 5 Level (EQ-5D 5L) will reduce the ceiling effect in the EQ-5D 3 Level (EQ-5D 3L), this will not provide a solution to the issue of censoring without a full re-estimation of utilities for all the health states it measures.