In health economics, health-related quality of life (HRQoL) is often assessed by means of preference-based index measurement instruments (e.g. EQ-5D, SF-6D, HUI). Each instrument of this kind consists of (1) a multi-attribute classification system for distinguishing health states and (2) a scoring function which assigns a valuation to each health state distinguished within the classification system. Scoring functions are often produced according to the so-called statistical approach which consists of two steps: (1) the valuations of some of the health states of the classification system are empirically determined and (2) the scoring function values for all health states are estimated from the empirically determined valuations using a theoretical model, i.e. an index model. This approach can run into problems because the empirically determined valuations necessarily contain arbitrary settings. This article is concerned with how these arbitrary settings together with the index model affect the final scoring function values. It is shown that for many conceivable index models the final scoring function values have no empirical meaning. Only additive models with a free additive constant are appropriate for representing the information contained in the empirically determined valuation. Only these models should be used within the statistical approach.
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