Utility scores for the Health Utilities Index Mark 2: an empirical assessment of alternative mapping functions

The Health Utilities Index is one of the most widely used generic health status classification systems. The valuation algorithm rests upon a power transformation between visual analog scale (VAS) and standard gamble (SG) data. This transformation has been the subject of much debate. To date, the literature has concentrated upon the mapping functions themselves. We examine whether alternative mapping functions produce more accurate utility predictions.

We undertook valuation interviews with 201 members of the UK general population, following the methods of the original Health Utilities Index-2 valuation survey. We estimated a cubic and a power mapping function using the mean VAS and SG data from the survey and calculated 2 alternative Multiplicative Multi Attribute Utility Functions (MAUFs). Using a validation sample, we assessed the predictive precision of the models in terms of accuracy (root mean square error and mean absolute error); clinical importance of the prediction error (% states with prediction error greater than 0.03); bias (t test); and whether the prediction error was related to the health state severity (Ljung Box Q statistic).

The power MAUF was an extremely poor predictive model, mean absolute error = 0.18, root mean square error = 0.206. The predictions were biased (t = -12.92). The errors were not related to the severity of the health state, (Liung Box = 10.87). The Cubic MAUF was a better predictive model than the Power MAUF (mean absolute error = 0.084, root mean square error = 0.101). The Cubic MAUF also produced biased predictions (t = -3.57). The prediction errors were not related to the severity of the health state (Liung Box = 5.242).

The Power MAUF is considerably worse than the Cubic MAUF. Our results suggest that the problems with the power function can translate into significant problems with predictive performance of the MAUF.