LESS IS MORE – EQ-5D-5L VALUE SETS BASED ON AN 8-PARAMETER NON-LINEAR MODEL PREDICTS LEFT-OUT STATES BETTER THAN A 20-PARAMETER MAIN EFFECTS MODEL

With its recent expansion from having each of its five dimensions described at 3 levels (no, moderate, extreme problems) to 5 levels (no, slight, moderate, severe, extreme problems), the EQ-5D-5L describes a total of 3125 different health states, as opposed to 243 previously. This expansion has complicated the process of value algorithm generation; a main effect regression model requires 20 dummy variables (4 per dimension), and most value algorithms presented for the -5L version so far have had at least one logically inconsistent coefficient. 

Purpose:

The objective of the study was to test the relative merits of a simplified, nonlinear regression model, compared to the "standard" approach, in terms of ability to predict values for left-out states. 

Method:
TTO data from EQ-5D-5L valuation studies in Spain and China (N > 1000 for each) was used, in which 86 of the 3125 possible health states were valued. The base case comparator was an additive model with 20 dummy variables, representing problems at levels 2 through 5 on each of the 5 dimensions. The contender was a model with 5 dimension variables (taking values representing level 5) multiplied by three cross-dimensional level parameters, taking values representing the magnitude of the levels relative to level 5. Models were predicted leaving out all observations of single states 1 by 1, and the value of the left-out states were predicted on the basis of the remaining 85 states. Model performance was compared in terms of MAE, intra-class correlation, and the presence of non-monotonicity.

Result:
The simplified multiplicative model outperformed the 20-parameter additive model in terms of MAE and ICC. While the 20-parameter model often displayed non-monotonicity, this was never observed for the multiplicative model.

Conclusion:

The typical 20-parameter additive model appears to result in over-specification, in addition to often-occurring non-monotonicity. By comparison, the simpler 8-parameter multiplicative model appears to be less susceptible to non-monotonicity, and predicts left-out states better. It appears that imposing a cross-dimensional structure on the model specification improves the predictive ability of the model. If results are reproduced on other EQ-5D-5L datasets, extensions on the 8-parameter multiplicative model should be considered for future value-algorithm generation for the EQ-5D-5L