Signature
D = min(l_MO + l_SC + l_UA + l_PD + l_AD - 5, 1); N_3 = min(max(l_MO - 2, 0) + max(l_SC - 2, 0) + max(l_UA - 2, 0) + max(l_PD - 2, 0) + max(l_AD - 2, 0), 1); U = 1 - 0.081 * D - 0.069 * (min(l_MO - 1, 1) - max(l_MO - 2, 0)) - 0.314 * max(l_MO - 2, 0) - 0.104 * (min(l_SC - 1, 1) - max(l_SC - 2, 0)) - 0.214 * max(l_SC - 2, 0) - 0.036 * (min(l_UA - 1, 1) - max(l_UA - 2, 0)) - 0.094 * max(l_UA - 2, 0) - 0.123 * (min(l_PD - 1, 1) - max(l_PD - 2, 0)) - 0.386 * max(l_PD - 2, 0) - 0.071 * (min(l_AD - 1, 1) - max(l_AD - 2, 0)) - 0.236 * max(l_AD - 2, 0) - 0.269 * N_3
| Inputs | Definition | Unit |
|---|---|---|
l_MO | Reported mobility level, 1 no problems, 2 some problems, 3 confined to bed | level, whole number 1, 2 or 3 |
l_SC | Reported self-care level, 1 no problems, 2 some problems, 3 unable to wash or dress | level, whole number 1, 2 or 3 |
l_UA | Reported usual activities level, 1 no problems, 2 some problems, 3 unable to perform them | level, whole number 1, 2 or 3 |
l_PD | Reported pain or discomfort level, 1 none, 2 moderate, 3 extreme | level, whole number 1, 2 or 3 |
l_AD | Reported anxiety or depression level, 1 not, 2 moderately, 3 extremely | level, whole number 1, 2 or 3 |
D | Equal to 1 when the levels sum to more than 5 and 0 for state 11111 | indicator, 0 or 1 |
|---|---|---|
N_3 | Equal to 1 when at least one level is 3 and 0 otherwise | indicator, 0 or 1 |
U | Utility of the state under the UK time trade-off tariff, reported to three decimals | utility, no unit |
Function
EQ-5D-3L value set scoring function
Maps an EQ-5D-3L profile, the level from 1 to 3 reported on each of mobility, self-care, usual activities, pain or discomfort and anxiety or depression, to a single utility under the coefficients of a chosen value set. The main-effects form with a constant for any departure from full health and an N3 term for any dimension at level 3 is the one Dolan used for the UK time trade-off tariff, and many of the time trade-off sets tabulated in the EuroQol reference volume follow it. It is the EQ-5D-3L counterpart of the additive 15D score in HE-FM-15D-001, and the utilities it returns are the weights in QALYs from periods of constant utility (HE-FM-QALY-001) and the baselines for utility decrements (HE-FN-DISU-001). Notation follows the EQ-5D-3L Value Set article.
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Implementations
Excel
UK MVH EQ-5D-3L tariff from five named level cells with CHOOSE
With the five levels in cells named Lev_MO, Lev_SC, Lev_UA, Lev_PD and Lev_AD, CHOOSE picks each dimension's decrement for the level reported and the two comparisons set the constant and N3. Rounding the result to 3 decimals with ROUND matches the published tariff.
=1-0.081*(MAX(Lev_MO,Lev_SC,Lev_UA,Lev_PD,Lev_AD)>1)-CHOOSE(Lev_MO,0,0.069,0.314)-CHOOSE(Lev_SC,0,0.104,0.214)-CHOOSE(Lev_UA,0,0.036,0.094)-CHOOSE(Lev_PD,0,0.123,0.386)-CHOOSE(Lev_AD,0,0.071,0.236)-0.269*(MAX(Lev_MO,Lev_SC,Lev_UA,Lev_PD,Lev_AD)=3)
Assumptions
UK tariff coefficients as published by the MVH study
The coefficients are those of the UK time trade-off tariff, 0.081 for the constant, 0.069 and 0.314 for mobility, 0.104 and 0.214 for self-care, 0.036 and 0.094 for usual activities, 0.123 and 0.386 for pain or discomfort, 0.071 and 0.236 for anxiety or depression and 0.269 for N3. They are taken from Table 1 of the Dolan, Gudex, Kind and Williams discussion paper and agree with the UK row of Table 2.2 of the EuroQol reference volume.
Whole-number levels in the order of the EQ-5D-3L profile
The levels are entered as whole numbers 1, 2 or 3 in the profile order mobility, self-care, usual activities, pain or discomfort and anxiety or depression. The min and max indicators are exact only for those values, so a mean level or a missing response has to be resolved before scoring.
Utilities reported to three decimals on a scale anchored at full health and dead
Full health is 1 and dead is 0, and the published tariff lists every state to three decimals, from 1.000 for 11111 down to minus 0.594 for 33333. The value of minus 0.402 that the discussion paper gives for the unconscious state is a mean of observed valuations and does not come from this model.
Worked examples
UK tariff value of EQ-5D-3L full health 11111
With every level at 1 neither indicator is set and no decrement applies, so the UK tariff gives 1, the limiting case at the top of the scale.
l_MO = 1; l_SC = 1; l_UA = 1; l_PD = 1; l_AD = 1; D = 0; N_3 = 0; U = 1
UK tariff value of the mild EQ-5D-3L state 21111
Some problems walking about and nothing else costs the constant 0.081 and the mobility level 2 decrement 0.069, giving 0.850, the value printed in the tariff appendix.
l_MO = 2; l_SC = 1; l_UA = 1; l_PD = 1; l_AD = 1; D = 1; N_3 = 0; U = 0.850
UK tariff value of EQ-5D-3L state 11113 with one dimension at level 3
Extreme anxiety or depression alone costs the constant 0.081, the level 3 decrement 0.236 and the N3 decrement 0.269, giving 0.414. A single level 3 response is enough to bring in N3.
l_MO = 1; l_SC = 1; l_UA = 1; l_PD = 1; l_AD = 3; D = 1; N_3 = 1; U = 0.414
UK tariff value of EQ-5D-3L state 11223 as worked in the MVH paper
The discussion paper's own example subtracts the constant 0.081, the usual activities and pain level 2 decrements 0.036 and 0.123, the anxiety or depression level 3 decrement 0.236 and N3 0.269 from 1, giving 0.255.
l_MO = 1; l_SC = 1; l_UA = 2; l_PD = 2; l_AD = 3; D = 1; N_3 = 1; U = 0.255
UK tariff value of the worst EQ-5D-3L state 33333
Every dimension at level 3 costs the constant, the five level 3 decrements and N3 once, 1.594 in all, giving minus 0.594, the minimum of the UK tariff.
l_MO = 3; l_SC = 3; l_UA = 3; l_PD = 3; l_AD = 3; D = 1; N_3 = 1; U = -0.594
Common errors
Leaving out the UK EQ-5D-3L constant for a mild state
Subtracting only the mobility decrement for 21111 gives 0.931 instead of 0.850. The constant 0.081 is charged for any departure from full health, so omitting it overstates every state other than 11111 by the same amount and inflates utilities most visibly near the top of the scale.
Reading an EQ-5D-3L profile in reverse dimension order
The five digits run mobility, self-care, usual activities, pain or discomfort and anxiety or depression. Reading 11223 backwards scores 32211, 0.196 in the UK tariff instead of 0.255, because the dimensions carry different decrements.
Sources
MVH discussion paper Table 1 coefficients and EQ-5D-3L tariff appendix
Dolan P, Gudex C, Kind P, Williams A. A social tariff for EuroQol. Results from a UK general population survey. Centre for Health Economics Discussion Paper 138. York, University of York, 1995. Table 1, coefficients for TTO tariffs (constant 0.081, mobility 0.069 and 0.314, self-care 0.104 and 0.214, usual activity 0.036 and 0.094, pain or discomfort 0.123 and 0.386, anxiety or depression 0.071 and 0.236, N3 0.269), the worked example for state 11223 giving 0.255 and the appendix TTO tariff for all 243 states, with 33333 at minus 0.594. Scanned text, read from the page images.
UK row of the EuroQol reference volume EQ-5D-3L coefficient table
Janssen B, Szende A, Ramos-Goñi JM. Data and methods. In Szende A, Janssen B, Cabases J, editors. Self-reported population health. An international perspective based on EQ-5D. Dordrecht, Springer, 2014, chapter 2. Table 2.2, UK row (MVH Group 1995, random effects model, mean absolute difference 0.039), which prints the same twelve coefficients as negative values, constant minus 0.081 to N3 minus 0.269.
Canonical Identity
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