Selecting Health States for EQ-5D-3L Valuation Studies: Statistical Considerations Matter

For many countries, the three-level EuroQol five-dimensional questionnaire (EQ-5D-3L) value sets have been established to estimate health state utilities. To generate these value sets, researchers first collect values for a subset of preselected health states from a panel representing the general public, and then use a prediction algorithm to generate values for all 243 states. High prevalence of a health state in daily practice has historically been a key criterion in selecting a subset of health states as the observed set. More recently, other criteria have been suggested, especially approaches based on statistical criteria such as randomization and orthogonality.

To evaluate the validity and accuracy of both the earlier and newer criteria, in terms of prediction of values for all the health states and of the values of common health states in particular.

We used a pre-existing data set that contained visual analogue scale values from 126 students, each of whom valued all 243 EQ-5D-3L states. Then, we generated a series of designs and subsequently modeled the data with respect to each design. Some of these designs were used in the past; for example, the Measurement and Valuation of Health approach was included. Others were newly generated. The performance of different designs was evaluated in terms of the lowest root mean squared error for all health states taken together, and separately for common and rare states. Classification as common or rare was based on the frequency of the states' occurrence in three patient and population data sets pooled together (N = 5269).

The orthogonal design with 54 health states produced the lowest root mean squared errors. Over-representation of common health states in a design did not improve the estimations for these states. The published designs performed the worst, whereas the random selection designs were good on average. Nevertheless, the performance of the random selection designs showed more variance compared with orthogonal designs, because some of the former designs did not display appropriate balance.

The published designs gave rise to large estimation errors for the extrapolated EQ-5D-3L health states. The orthogonal design focusing on statistical efficiency showed its superiority. Overall, when weighing up design properties, increased statistical efficiency outweighs an increased error rate, if any, in rare health states.