Signature
v_H = sum_(j=1)^15 [I_j * w_j]
| Inputs | Definition | Unit |
|---|---|---|
I_j | Average relative importance people attach to dimension j at the level reported, I_j(x_j); the importance weights sum to 1 | weight, no unit |
w_j | Average value people place on the level reported on dimension j, w_j(x_j), with the top level valued at 1 and being dead at 0 | value from 0 to 1, no unit |
v_H | Single index value of health state H | utility on a 0 to 1 scale, no unit |
|---|
Function
15D index score function
Maps a respondent's levels on the 15 dimensions of the 15D, each with 5 ordinal levels, to a single index on a 0 to 1 scale, where 0 is being dead and 1 is no problems on any dimension. The index is a preference-based utility that can weight survival in QALY calculations.
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Implementations
Excel
15D score from weight and value rows
With the 15 importance weights at the reported levels in ImportanceWeights and the 15 level values in LevelValues, in ranges of equal shape, Excel returns the score.
=SUMPRODUCT(ImportanceWeights,LevelValues)
Assumptions
Additive independence of dimensions
The value of a level on one dimension does not depend on the levels of the other dimensions, so the index is a sum over dimensions.
Population weights elicited without a duration
Level values and importance weights were elicited from representative population samples by rating scale and magnitude estimation, with the duration of health states left unspecified. The weights are distributed with the scoring algorithm by the instrument's developer on request and are not reproduced on this page.
A response on every dimension
The score is computed only when all 15 dimensions are answered. Missing responses are handled by a separate replacement algorithm, and the score is left missing when more than three dimensions are unanswered.
Worked examples
Illustrative respondent with three problem dimensions
With illustrative importance weights summing to 1 and level values of 0.70 for breathing, 0.80 for sleeping and 0.60 for discomfort and symptoms, and 1 elsewhere, the score is 0.936. The weights and values are not the published 15D weights.
I_j = [0.08,0.07,0.06,0.08,0.06,0.06,0.06,0.07,0.07,0.07,0.07,0.07,0.06,0.07,0.05]; w_j = [1,1,1,0.70,0.80,1,1,1,1,1,0.60,1,1,1,1]; v_H = 0.936
No problems on any dimension
When every dimension is at its top level, each level value is 1 and the score equals the sum of the importance weights, 1.
I_j = [0.08,0.07,0.06,0.08,0.06,0.06,0.06,0.07,0.07,0.07,0.07,0.07,0.06,0.07,0.05]; w_j = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; v_H = 1
Common errors
Summing level codes instead of level values
Adding the questionnaire codes 1 to 5, or averaging them, gives a number that is neither a level value nor a preference weight. The codes are first converted to level values and importance weights by the scoring algorithm.
Treating 15D scores as interchangeable with EQ-5D values
The 15D index stops at 0 and cannot value a state as worse than dead, and it was valued with different methods and samples from EQ-5D value sets. NICE's interim methods statement asks for non-EQ-5D measures to be mapped to utility values based on the UK EQ-5D-5L value set when EQ-5D-5L data are not available.
Reading every change in score as important
Alanne and colleagues estimated the minimum important change in the 15D score at plus or minus 0.015. A mean change of 0.010 falls within the band described by patients as much the same.
Sources
15D valuation system and additive model
Sintonen H. 15D instrument website (www.15d-instrument.net): Valuation system page. Accessed 29 September 2026. The 15D score formula v_H = sum of I_j(x_j) times w_j(x_j), the anchors (0 dead, 0.0162 unconscious or comatose, 1 no problems on any dimension), level values on a 0 to 1 scale and importance weights summing to 1, elicitation by rating scale and magnitude estimation, and unspecified duration.
Properties and applications of the 15D
Sintonen H. The 15D instrument of health-related quality of life: properties and applications. Annals of Medicine. 2001;33(5):328-336. The valuation system is an application of multi-attribute utility theory, and the single index score on a 0 to 1 scale is calculated from the descriptive system with population-based preference weights.
Two-stage additive valuation model of the 15D
Sintonen H. The 15D measure of health related quality of life. II Feasibility, reliability and validity of its valuation system. Working Paper 42. Melbourne: National Centre for Health Program Evaluation; 1995. Section 2 Alternative value components for the 15D, model (2): importance weights that vary by level, summing to 1, and level values with the top level at 1 and being dead at 0, under additive independence.
Minimum important change in the 15D score
Alanne S, Roine RP, Räsänen P, Vainiola T, Sintonen H. Estimating the minimum important change in the 15D scores. Quality of Life Research. 2015;24(3):599-606. Generic minimum important change of plus or minus 0.015, estimated in 4,903 hospital patients.
NICE mapping of non-EQ-5D measures to the EQ-5D-5L value set
National Institute for Health and Care Excellence. Interim methods statement: implementing the EQ-5D-5L value set (PMG51). Published 27 August 2026. Statement sections 1.7 and 1.10 (the EQ-5D-5L and UK value set as the preferred approach for adults; non-EQ-5D measures mapped to utility values based on the UK EQ-5D-5L value set when EQ-5D-5L data are not available).
Canonical Identity
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