Signature
w_star = Delta_C / (lambda * Delta_E)
| Inputs | Definition | Unit |
|---|---|---|
Delta_C | Cost of the programme minus that of the comparator, greater than zero | currency per patient |
lambda | Cost per QALY used to value the displaced health, greater than zero | currency per QALY |
Delta_E | QALYs under the programme minus those under the comparator, greater than zero | QALYs per patient |
w_star | Weight on the QALY gain at which the weighted net health benefit is zero | multiplier, dimensionless |
|---|
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
Break-even equity weight from named cells
With the cells named as for the weighted ICER, the formula returns the weight at which the weighted net health benefit is zero.
=IncrementalCost/(QALYValue*IncrementalQALYs)
Assumptions
Positive cost and QALY gain for a break-even weight
Delta_C and Delta_E are both above zero. A programme that saves money and gains health needs no weight, and one that loses health cannot be rescued by a weight above 1.
Break-even weight depends on the value of a QALY
Because lambda sits in the denominator, the break-even weight is higher at GBP 25,000 than at GBP 35,000 per QALY, so it is reported at each value used in the decision.
Break-even weight read against the weights available
The value is compared with the weights the decision rule allows, for example the NICE severity weights of 1.2 and 1.7 (PMG36, table 6.1), or with the range of weights explored in a sensitivity analysis, as Cookson and colleagues recommend.
Worked examples
Severe subgroup break-even weight at GBP 35,000 per QALY
For the article's illustrative subgroup A, GBP 30,000 for 0.6 QALYs breaks even at a weight of about 1.43 at GBP 35,000 per QALY, below the 1.7 that the subgroup's severity earns.
Delta_C = 30000; lambda = 35000; Delta_E = 0.6; w_star = 1.4286
Severe subgroup break-even weight at GBP 25,000 per QALY
At GBP 25,000 per QALY the same subgroup needs a weight of 2.0, above every NICE severity weight.
Delta_C = 30000; lambda = 25000; Delta_E = 0.6; w_star = 2.0
Break-even weight below one for a subgroup already cost-effective
Subgroup B, at GBP 24,000 for 0.8 QALYs, has a break-even weight of about 0.857 at GBP 35,000 per QALY. A value below 1 shows that no priority weight is needed.
Delta_C = 24000; lambda = 35000; Delta_E = 0.8; w_star = 0.857
Common errors
Judging the break-even weight at one value of a QALY only
Subgroup A's weight of 1.7 clears the break-even weight of about 1.43 at GBP 35,000 per QALY but not the 2.0 needed at GBP 25,000. Reporting only the upper value suggests the severity weight is enough across the whole NICE range.
Break-even weight for a programme that loses health
With an illustrative extra cost of GBP 30,000 and a QALY loss of 0.1 at GBP 35,000 per QALY, the formula returns about minus 8.57, which has no meaning as a weight. A weight above 1 enlarges a loss, so the break-even weight is computed only for a QALY gain.
Sources
Cookson and colleagues on the concern for equity needed to choose a cost-ineffective option
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. Section on equity-weighting analysis, which uses equity weights to quantify how much concern for equity is required to choose cost-ineffective options that improve equity, and the Discussion, which recommends equity-weighting analysis as an aid to deliberation through sensitivity analysis of different equity parameters.
NICE severity weights and values of a QALY for the break-even comparison
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, table 6.1 (QALY weights of 1, 1.2 and 1.7) and section 6.3.2 (net health benefit at GBP 25,000 and GBP 35,000 per QALY with and without the QALY weighting).
Canonical Identity
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