15D score as an additive weighted sum of level values

Multiplies the value of the level reported on each dimension by the importance weight of that dimension at that level, and adds the products over the 15 dimensions. This is the additive multi-attribute utility model of the 15D valuation system, v_H = sum of I_j(x_j) times w_j(x_j), with the level x_j written into I_j and w_j here.

Signature

v_H = sum_(j=1)^15 [I_j * w_j]
Inputs
InputsDefinitionUnit
I_jAverage relative importance people attach to dimension j at the level reported, I_j(x_j); the importance weights sum to 1weight, no unit
w_jAverage 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 0value from 0 to 1, no unit
Output
v_HSingle index value of health state Hutility 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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).

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Canonical Identity

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