Impact of Transformation of Negative Values and Regression Models on Differences Between the UK and US EQ-5D Time Trade-Off Value Sets

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National EQ-5D value sets are developed because preferences for health may vary in different populations. UK values are lower than US values for most of the 243 possible EQ-5D health states. Although similar protocols were used for data collection, analytic choices regarding how to model values from the collected data may also influence national value sets. Participants in the UK and US studies assessed the same subset of 42 EQ-5D health states using the time trade-off (TTO) method. However, different methods were used to transform negative values to a range bounded by 0 and -1, and values for all 243 health states were estimated using two different regression models. The transformation of negative values is inconsistent with expected utility theory, and the choice of which transformation method to use lacks a theoretical foundation.


Our objectives were to assess how much of the observed difference between the UK and US EQ-5D value sets may be explained by the choice of transformation method for negative values relative to the choice of regression model and the differences between elicited TTO values in the respective national studies (datasets).


We applied both transformation methods and both regression models to each of the two datasets, resulting in eight comparable value sets. We arranged these value sets in pairs in which one source of difference (transformation method, regression model or dataset) was varied. For each of these paired value sets, we calculated the mean difference between the two matching values for each of the 243 health states. Finally, we calculated the mean utility gain for all possible transitions between pairs of EQ-5D health states within each value set and used the difference in transition scores as a measure of impact from changing transformation method, regression model or dataset.


The mean absolute difference in values was 1.5 times larger when changing the transformation method than when using different datasets. The choice of transformation method had a 3.2 times larger effect on the mean health gain (transition score) than the choice of dataset. The mean health gain in the UK value set was 0.09 higher than in the US value set. Using the UK transformation method on the US dataset reduced this absolute difference to 0.02. The choice of regression model had little overall impact on the differences between the value sets.


Most of the observed differences between the UK and US value sets were caused by the use of different transformation methods for negative values, rather than differences between the two study populations as reflected in the datasets. Changing the regression model had little impact on the differences between the value sets.

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