EuroQol · Maths in Health
The Scaling Factor Approach for bolt-on valuation
Overview
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.
The model
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:
CALE (Cross-Attribute Level Effects) specification
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.
Additive (20-parameter) specification
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.
How to use the app
- Settings — upload data (or load the bundled test set)
and configure data type, bolt-on dimensions, base model, fixed
parameters, dummy coding, intercept, censoring, and random effects.
- Generated Code — view and download the complete
analysis script, the xreg2 snippet, or an nlme/OLS equivalent.
- Run Model — execute the model on loaded data
and view coefficients, the implied value-set format, and the
disutility chart.
- Report — view and download a self-contained HTML
report.
Data format
TTO Data
- One row per respondent-state observation
- Outcome column: disutility (0 to 2), utility (-1 to 1), or years in full health (0 to 20)
- Respondent ID column
- EQ-5D dimension columns (levels 1-5) or dummy variables
- Bolt-on dimension column(s) (levels 1-5)
DCE Data
- Two rows per choice pair (one per alternative)
- Alternative indicator column (e.g., "A"/"B")
- Pair ID column to match alternatives
- Binary choice column (0/1)
- EQ-5D and bolt-on dimension columns for each alternative
Dummy Variable Types
- Regular/standard: xdj = 1 if dimension d is at level j.
Suitable for TTO analysis.
- Incremental/cumulative: xdj = 1 if dimension d is at level ≥ j.
Required for CALE specification; recommended for DCE (better convergence).
References
- Yang Z, Rand K, Luo N. "Valuation of Multidimensional Health States With a
Bolt-On: Is There a Shortcut?" Value in Health 2024;27(11):1544-1552.
doi:10.1016/j.jval.2024.06.018
- Yang Z, Rand K, Finch A, Luo N. "Valuation of EQ-5D-5L With Two Bolt-On Items:
Further Evaluation of the Scaling Factor Model." Value in Health 2026.
doi:10.1016/j.jval.2026.02.012