This tool generates R code for the Scaling Factor Approach (SFA) to EQ-5D-5L bolt-on valuation. The SFA allows researchers to estimate disutility weights for new bolt-on dimensions using published EQ-5D-5L value sets as fixed reference parameters.
When a new dimension is added to EQ-5D-5L, health state disutilities are compressed because the descriptive system is richer. The SFA accounts for this by introducing a scaling factor λ < 1:
The 8-parameter CALE model uses dimension weights (β) and level thresholds (γ):
disutility = α + λ · (Σd βd · [xd2γ2 + xd3γ3 + xd4γ4 + xd5] + βBO · [xBO,2γ2 + … + xBO,5]) + ε
Where βd and γj are fixed from the published value set, and only α, λ, and βBO are estimated.
disutility = α + λ · (Σd Σj=2..5 βdj xdj + Σj=2..5 βBO,j xBO,j) + ε
Where βdj are fixed from the value set (20 parameters for 5 dimensions × 4 levels), and only α, λ, and βBO,2 through βBO,5 are estimated.
The SFA assumes that adding the bolt-on compresses every core dimension by the same factor λ. This tab tests that assumption by refitting the model with (a) a user-defined grouping of the dimensions into up to five scale groups and (b) one scale per dimension (S_MO .. S_AD), and comparing the fits by likelihood ratio, AIC and BIC. The flexible models are diagnostics only: with more than one scale the model is no longer an affine transform of the published value set, so they are not candidate value sets.
Run the Full script from the Generated Code tab first (it loads
the data, builds the dummies and defines
fixed_values
); this script then refits the flexible models and prints the
comparison.