Signature
dQ = (U_a - U_b) * T; s_N3 = gamma * (N3_b - N3_a) / (U_a - U_b)
| Inputs | Definition | Unit |
|---|---|---|
U_a | Value set utility of the better state that patients stay in | utility, no unit |
U_b | Value set utility of the worse state that patients would otherwise move to, below U_a | utility, no unit |
T | Time for which the utility gap applies, undiscounted | years |
gamma | N3 decrement of the value set that scored both states, entered as a positive number | utility, no unit |
N3_b | Equal to 1 when the avoided state has a dimension at level 3 | indicator, 0 or 1 |
N3_a | Equal to 1 when the kept state has a dimension at level 3 | indicator, 0 or 1 |
dQ | QALYs gained by staying in the better state for T years | QALYs |
|---|---|---|
s_N3 | Part of the utility difference between the two states that comes from the N3 term | proportion |
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
QALY difference between two EQ-5D-3L states from named cells
With the utilities of the kept and avoided states in cells named UtilityKept and UtilityAvoided and the years in YearsInState, the formula returns dQ.
=(UtilityKept-UtilityAvoided)*YearsInState
Excel
N3 share of an EQ-5D-3L utility gap from named cells
With the N3 decrement in a cell named Gamma and the two N3 indicators in N3Kept and N3Avoided, the formula returns s_N3.
=Gamma*(N3Avoided-N3Kept)/(UtilityKept-UtilityAvoided)
Assumptions
Both EQ-5D-3L states scored with one value set and held constant
U_a, U_b and gamma come from the same value set, and each utility is constant for the T years without discounting. Discounted gains follow HE-FN-DISC-001, and states scored with different sets, such as a 3L and a 5L set, are not compared with this formula.
N3 share defined only for a positive EQ-5D-3L utility gap
The share needs U_a above U_b. When both states are departures from 11111 the constant cancels, so the gap is the N3 term, when it differs, plus the difference in level decrements.
Worked examples
UK tariff QALY gain from keeping EQ-5D-3L state 21121 instead of 21131
Under the UK tariff 21121 scores 0.727 and 21131 scores 0.195. Keeping patients out of the level 3 pain state for 2 years gains 1.064 QALYs, and the N3 decrement 0.269 accounts for about 51% of the utility gap of 0.532.
U_a = 0.727; U_b = 0.195; T = 2; gamma = 0.269; N3_a = 0; N3_b = 1; dQ = 1.064; s_N3 = 0.5056
UK tariff QALY gain from keeping EQ-5D-3L state 21121 instead of 22221
State 22221 scores 0.587 under the UK tariff. Avoiding two extra level 2 problems for 2 years gains 0.28 QALYs, with no N3 share, so the single step to level 3 in the previous example is worth about 3.8 times as much.
U_a = 0.727; U_b = 0.587; T = 2; gamma = 0.269; N3_a = 0; N3_b = 0; dQ = 0.28; s_N3 = 0
Article's illustrative EQ-5D-3L QALY gain and cost per QALY
With the article's illustrative utilities of 0.73 and 0.20 and gamma of 0.27, two years gain 1.06 QALYs and N3 explains about 51% of the gap. An illustrative extra cost of GBP 10,600 then gives GBP 10,000 per QALY, as in the incremental ratio of HE-FM-CUA-001.
U_a = 0.73; U_b = 0.20; T = 2; gamma = 0.27; N3_a = 0; N3_b = 1; dQ = 1.06; s_N3 = 0.5094
Common errors
Reading a large EQ-5D-3L utility gap as a large difference in health
One step from moderate to extreme pain gains 1.064 QALYs over 2 years under the UK tariff, against 0.28 for avoiding two moderate problems, and about half of the larger gain is the N3 decrement. A modelled QALY gain between states that differ by any level 3 response is worth tracing to N3 before it is read as clinical benefit.
Sources
MVH tariff appendix values for the EQ-5D-3L states compared
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. Appendix TTO tariff, which lists 21121 at 0.727, 21131 at 0.195 and 22221 at 0.587, and the text on the N3 term, an intercept for whether any dimension is at level 3 that reflects the much greater disutility of extreme problems.
Dolan's N3 term for any EQ-5D-3L dimension at its most severe level
Dolan P. Modeling valuations for EuroQol health states. Medical Care. 1997;35(11):1095-1108. Abstract, which describes the term that picks up whether any dimension in the state is at its most severe level, alongside the dimension levels and the intercept for any move away from full health.
Canonical Identity
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