Signature
ICER_w = Delta_C / (w * Delta_E); lambda_w = w * lambda
| Inputs | Definition | Unit |
|---|---|---|
Delta_C | Cost of the programme minus that of the comparator, unweighted | currency per patient |
w | Weight applied to every QALY gained in the group, greater than zero | multiplier, dimensionless |
Delta_E | QALYs under the programme minus those under the comparator, greater than zero | QALYs per patient |
lambda | Cost per QALY the decision maker uses, for example GBP 25,000 or GBP 35,000 in the NICE range | currency per QALY |
ICER_w | Incremental cost divided by the weighted QALY gain | currency per weighted QALY |
|---|---|---|
lambda_w | Threshold against which the unweighted ICER gives the same decision as the weighted ICER against lambda | currency per QALY |
Function
Equity-weighted QALY gain, ICER, net health benefit and switching weight function
Maps the incremental QALY gain of a programme in each population group, an equity weight for each group, the incremental cost and the value placed on a QALY to the equity-weighted QALY gain, the equity-weighted ICER, the equity-weighted net health benefit and the weight at which the programme would break even. The weights act on the incremental QALYs only, while costs and the health displaced elsewhere stay unweighted, and with every weight equal to 1 the outputs reduce to the unweighted ICER (HE-FM-ICER-001) and incremental net health benefit (HE-FM-CET-002). The weights come from outside the function, for example the NICE severity weight from absolute and proportional shortfall (HE-FM-ASF-001 and HE-FM-ASF-003) or the weight implied by an Atkinson inequality aversion parameter (HE-FM-ATK-004), and neither is redrafted here. The break-even weight differs from the switching weight between two options in the weighted two-group social welfare formula of the Welfare Economics package, because it compares one programme with the health displaced by its cost. Notation follows the Equity-Weighted Analysis article.
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Implementations
Excel
Equity-weighted ICER and equivalent threshold from named cells
With the incremental cost in IncrementalCost, the incremental QALYs in IncrementalQALYs, the weight in QALYWeight and the value of a QALY in QALYValue, the first formula returns the weighted ICER and the second the equivalent threshold for the unweighted ICER.
=IncrementalCost/(QALYWeight*IncrementalQALYs); =QALYWeight*QALYValue
Assumptions
Positive QALY gain and cost for the equity-weighted ICER
The formula applies when the programme gains QALYs at extra cost. With a QALY loss or a saving, the ratio changes meaning, and net health benefit (HE-FM-EQWA-003) is the safer comparison.
One weight for the whole group in the equity-weighted ICER
Everyone in the group carries the same weight, so dividing the ICER by w and multiplying the threshold by w give the same decision. With several weights in one population the weighted gain comes from HE-FM-EQWA-001 and the equivalence holds only for each group taken alone.
Equity weighting leaves cost and displaced care unchanged
The weighted ICER is used for the decision only and does not change the cost of a QALY. The real cost of the programme and the care displaced to pay for it are the same as in the unweighted analysis, and PMG36 asks for net health benefit with and without the weighting to show the effect on opportunity costs (section 6.3.2).
Worked examples
Severe subgroup with a 1.7 weight judged at GBP 35,000 per QALY
In the article's illustrative subgroup A the medicine costs GBP 30,000 more per patient and gains 0.6 QALYs, an unweighted ICER of GBP 50,000 per QALY. With the weight of 1.7 the weighted gain is 1.7 × 0.6 = 1.02 QALYs and the weighted ICER is about GBP 29,412 per QALY, below GBP 35,000. The same decision follows from comparing GBP 50,000 with the equivalent threshold of GBP 59,500.
Delta_C = 30000; w = 1.7; Delta_E = 0.6; lambda = 35000; ICER_w = 29411.76; lambda_w = 59500
Severe subgroup with a 1.7 weight judged at GBP 25,000 per QALY
At the lower end of the NICE range the weighted ICER of about GBP 29,412 is above GBP 25,000, and the equivalent threshold for the unweighted ICER is GBP 42,500 per QALY (1.7 × 25,000), still below GBP 50,000.
Delta_C = 30000; w = 1.7; Delta_E = 0.6; lambda = 25000; ICER_w = 29411.76; lambda_w = 42500
Subgroup with a weight of 1 where the weighted ICER is unchanged
Subgroup B gains 0.8 QALYs per patient at an extra GBP 24,000 and carries a weight of 1, so the weighted and unweighted ICERs are both GBP 30,000 per QALY and the equivalent threshold is lambda itself.
Delta_C = 24000; w = 1; Delta_E = 0.8; lambda = 35000; ICER_w = 30000; lambda_w = 35000
Common errors
Applying the equity weight to the ICER and to the threshold together
Comparing the weighted ICER of GBP 29,412 with the raised threshold of GBP 59,500 applies the weight twice. It is the same as a weight of 2.89 on the unweighted ICER (1.7 × 1.7 = 2.89), well above the largest NICE severity weight. Either the ICER or the threshold carries the weight, not both.
Reading the equity-weighted ICER as the cost per QALY gained
The weight moves subgroup A from GBP 50,000 to about GBP 29,412 per weighted QALY, but each QALY gained still costs GBP 50,000 and displaces the same care. Reporting GBP 29,412 as the cost per QALY hides the health given up to act on the severity judgement.
Sources
NICE range of acceptable ICERs and QALY weighting
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Chapter 6 Committee recommendations, section 6.3.7 (ICERs in the range of GBP 25,000 to GBP 35,000 per QALY gained), section 6.2.11 (modifiers applied through QALY weighting) and section 6.3.2 (net health benefit with and without the QALY weighting).
Cookson and colleagues on differential threshold ranges by severity
Cookson R, Mirelman AJ, Griffin S, Asaria M, Dawkins B, Norheim OF, Verguet S, Culyer AJ. Using cost-effectiveness analysis to address health equity concerns. Value in Health. 2017;20(2):206-212. Discussion section, which reports that in 2014 the third Norwegian Committee on Priority Setting in the Health Sector proposed three categories of disease severity with differential cost-effectiveness threshold ranges.
Wailoo and colleagues on weights applied to the incremental QALYs of the assessment
Wailoo A, Bell Gorrod H, Dunning L, Kenny J, Leckenby E, Shah K. The NICE experience of designing and utilising severity weights. Health Policy OPEN. 2026;10:100156. Section 1 Background, which states that the severity weights are applied to the health benefits, the incremental QALYs, estimated in the cost-effectiveness assessment.
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