The Transformation of Utilities for Health States Worse Than Death

Abstract

Utilities for health are measured on an interval scale, where 1 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. 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. 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. 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. 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.