The transformation of utilities for health states worse than death - Consequences for the estimation of EQ-SD value sets

Background: Utilities for health are measured on an interval scale, where I refers to full health and 0 refers to death. No theoretical lower boundary on the utilities for states worse than death exists. As a consequence, negative values receive greater weight in the calculation of mean utilities. To avoid this, negative values often are bound at -1. Objective: The objective of this study was to compare the effect of 3 methods to bound negative values at -1 on the estimation of EQ-5D value sets: truncation, monotonic, and linear transformation. Method: Data of the Dutch EQ-5D valuation study were used. A total of 298 respondents directly valued 17 EQ-5D health states using the time trade-off (TTO) method. Random effects regression analysis was used to interpolate TTO values for all possible EQ-5D states. In the regression analysis the dependent variable is 1 minus the TTO value and the independent variables describe the health state. Two widely used models to estimate EQ-5D value were applied after truncation of negative values and monotonic and linear transformation of negative values. Both models also were estimated on medians. Results: Truncation of negative values gave the largest mean absolute error (MAE); the linear transformation resulted in the smallest MAE. When medians were used for estimation, the MAEs were comparable with the estimation on means. Conclusion: The choice of a method to bound negative values is arbitrary and affects the resulting value set. For the estimation of EQ-5D value sets from a societal perspective the use of medians should be considered.