Signature
r_Q = dQ_B / dQ_A - 1; r_I = dQ_A / dQ_B - 1
| Inputs | Definition | Unit |
|---|---|---|
dQ_B | Incremental QALYs of the same treatment, model and costs with utilities from value set B | QALYs |
dQ_A | Incremental QALYs of the treatment with utilities from value set A | QALYs |
r_Q | QALY gain under set B as a share of the gain under set A, less 1 | proportion |
|---|---|---|
r_I | ICER under set B as a share of the ICER under set A, less 1, with the incremental cost unchanged | proportion |
Function
Country-specific value set comparison function
Takes one EQ-5D-3L health profile, or the pair of profiles a treatment moves patients between, and the coefficients of two national value sets, and returns the utility gain under each set, the gap between the two gains and the resulting change in the QALY gain and in the incremental cost-effectiveness ratio. The scoring rule itself is live and is not restated here. The main-effects form with a constant and level decrements, which the article writes as U(s) equal to 1 minus c I(s) minus the sum of the level decrements beta_d(l_d), is HE-FM-EQ3L-001 with the N3 decrement set to zero; HE-FM-EQ3L-002 fixes it at the UK MVH tariff, HE-CF-EQ3L-001 scores any constant and N3 set such as the Dutch one, and HE-FM-EQ3L-003 gives the QALY difference between two states under one set. The records here compare sets. HE-FM-CSVS-001 splits the cross-set gap in a utility gain by term, HE-FM-CSVS-002 turns two QALY gains into relative changes in the gain and the ICER (HE-FM-CUA-001), and HE-FM-CSVS-003 gives the count-based D1 form that the US set uses in place of a constant. Five-level value sets belong to the EQ-5D-5L value set concept, and QALYs from different sets are not added (HE-ER-QALY-003). Notation follows the Country-Specific Value Set article.
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Implementations
Excel
Relative QALY and ICER changes from two named QALY gain cells
With the QALY gain under the reference set in QALYGainSetA and under the alternative set in QALYGainSetB, the first formula returns the value held in QALYChangeRel and the second the value held in ICERChangeRel.
=QALYGainSetB/QALYGainSetA-1; =QALYGainSetA/QALYGainSetB-1
Assumptions
Only the value set differs between the two QALY gains
The two gains come from the same model, comparator, time horizon, discounting and incremental cost, and the utilities alone are rescored, the kind of comparison Navega Biz and colleagues make when they map the utility values used in NICE appraisal models to the EQ-5D-5L. If costs also change, r_I has to be computed from the two ICERs directly.
Both QALY gains positive for the ICER change
r_I is a change in the cost per QALY gained only while dQ_A and dQ_B are both above zero. A value of r_Q below minus 1 means the gain changes sign under set B, and the result is then classified with the dominance rule of HE-FM-DOM-001 (ties included) or compared by net health benefit (HE-FM-CET-002), not by the ratio.
Worked examples
Article's illustrative QALY gains of 0.90 and 0.78 under sets A and B
The article's treatment gains 0.90 QALYs under set A and 0.78 under set B over 2 years. The QALY gain falls by 13.33% and the ICER rises by 15.38%, matching the article's GBP 23,333 and GBP 26,923 per QALY for an extra cost of GBP 21,000. Net health benefit at GBP 25,000 per QALY is 0.06 under set A and minus 0.06 under set B, a fall of 0.12 equal to the fall in the QALY gain.
dQ_A = 0.90; dQ_B = 0.78; r_Q = -0.1333; r_I = 0.1538
UK MVH and Zimbabwe sets for 2 years out of 21232 and in 11121
Two years in 11121 in place of 21232 gain 1.416 QALYs under the UK tariff and 0.760 under the Zimbabwe set (HE-FM-CSVS-001 gains of 0.708 and 0.380). Rescoring with the Zimbabwe set cuts the QALY gain by 46.33% and, for an unchanged cost, raises the ICER by 86.32% (computed here).
dQ_A = 1.416; dQ_B = 0.760; r_Q = -0.4633; r_I = 0.8632
Illustrative single appraisal whose QALY gain rises by 12.5% under a new value set
An illustrative decision with 1 incremental QALY under the old set and 1.125 under the new one has its ICER fall by 11.11%. The pair 12.5% and 11.1% matches the mean changes Navega Biz and colleagues report for 17 oncology decisions whose utilities were mapped to the EQ-5D-5L with the new UK value set, but the identity holds exactly only for one decision (derived), and group means need not follow it.
dQ_A = 1; dQ_B = 1.125; r_Q = 0.125; r_I = -0.1111
Common errors
Taking the ICER change as minus the QALY change
A fall in the QALY gain raises the ICER by more than the fall. In the article's example the QALY gain falls 13.3% and the ICER rises 15.4%, not 13.3%, and for the UK and Zimbabwe comparison a fall of 46.3% raises the ICER by 86.3%, not 46.3% (computed here). The gap matters most near a threshold, where the article's two sets put the same treatment on opposite sides of GBP 25,000 per QALY.
Reading a mean ICER change from a mean QALY change
The reciprocal identity holds for one decision, not for averages across decisions. Navega Biz and colleagues report a mean fall of 37.5% in incremental QALYs and a mean rise of 61.4% in ICERs for 11 non-oncology decisions without a survival gain, while the identity applied to a single 37.5% fall gives a rise of 60.0% (derived). Each decision's ICER change has to be computed from its own pair of gains before averaging.
Computing an ICER change after the value set reverses the gain
Gerlinger and colleagues report that a change of EQ-5D-5L state 44444 into 55511 is an improvement of 0.679 under the Dutch set and a worsening of 0.169 under the Uruguayan one. Held for one year these are QALY changes of 0.679 and minus 0.169, so r_Q is minus 1.2489 and r_I is minus 5.0178, a number with no meaning as a change in cost per QALY gained (computed here). An r_Q below minus 1 signals the reversal, and the result is then read by dominance or net health benefit.
Sources
Changes in incremental QALYs and ICERs when NICE appraisals are rescored with a new value set
Navega Biz A, Hernández Alava M, Wailoo A. Switching from EQ-5D-3L to EQ-5D-5L in England. The impact in NICE technology appraisals. Value in Health. 2026;29(5):794-801. Methods, which state that the mapped 5L values were applied in the cost-effectiveness models and all remaining model parameters remained unchanged, and Abstract and Results, which report 39 appraisal decisions with utility values mapped to the EQ-5D-5L using the eq5dmap model with a new UK value set, a mean increase of 12.5% in absolute incremental QALYs and a mean decrease of 11.1% in ICERs for 17 oncology decisions, and a decrease of 37.5% in incremental QALYs with an increase of 61.4% in ICERs for 11 non-oncology decisions without a survival gain, given as mean absolute changes over the decisions in each group.
Direction of a health change reversed between two national EQ-5D-5L value sets
Gerlinger C, Bamber L, Leverkus F, Schwenke C, Haberland C, Schmidt G, Endrikat J. Comparing the EQ-5D-5L utility index based on value sets of different countries. Impact on the interpretation of clinical study results. BMC Research Notes. 2019;12:18. Main text, Results, which states that in many cases the direction of a change between two health states differed between countries as well as its size, with the change of 44444 into 55511 valued as an improvement of 0.679 units in the Netherlands and a worsening of 0.169 units in Uruguay, and that 44444 was valued at minus 0.289 in the Netherlands and plus 0.353 in Uruguay. Open access.
Canonical Identity
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