Signature
V_1 = w_1 * Delta_E_1; V_2 = w_2 * Delta_E_2; Delta_E_w = V_1 + V_2
| Inputs | Definition | Unit |
|---|---|---|
w_1 | Multiplier applied to each QALY gained by the first group, 1 for no priority and above 1 for a priority group, for example 1.2 or 1.7 under the NICE severity modifier | multiplier, dimensionless |
Delta_E_1 | QALYs gained by the first group under the programme minus those under the comparator, summed over the people in the group | QALYs |
w_2 | Multiplier applied to each QALY gained by the second group, 1 when that group has no priority | multiplier, dimensionless |
Delta_E_2 | QALYs gained by the second group under the programme minus those under the comparator, summed over the people in the group | QALYs |
V_1 | Incremental QALY gain of the first group multiplied by the equity weight of that group | weighted QALYs |
|---|---|---|
V_2 | Incremental QALY gain of the second group multiplied by the equity weight of that group | weighted QALYs |
Delta_E_w | Sum over the groups of the weighted QALY gains, the gain the programme is credited with after weighting | weighted QALYs |
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 QALY total with SUMPRODUCT over group rows
With one row per group, the weights in a range named EquityWeight and the group QALY gains in GroupQALYGain, the formula returns the equity-weighted QALY gain for any number of groups, of which the two-group calculator form is the special case. The two ranges have the same length and order.
=SUMPRODUCT(EquityWeight,GroupQALYGain)
Assumptions
Equity weights act on incremental QALYs only
The weight multiplies the QALYs gained over the comparator, not total QALYs and not costs. PMG36 applies the severity weights to QALYs (section 6.2.16 and table 6.1), and Wailoo and colleagues describe them as applied to the incremental QALYs estimated in the cost-effectiveness assessment. Total QALYs that patients would have under current care attract no weight (HE-ER-ASF-005).
Equity weight reflects value outside the QALY
A decision-making modifier in PMG36 (section 6.2.11) is a factor that the estimated QALY cannot include. A weight is therefore set only for value that the QALY measure leaves out, and the same concern is not weighted twice under two names.
Weights multiplied in after the unweighted analysis
The formula applies fixed weights to QALY gains already estimated without weights, the approach of the NICE modifier. Wailoo, Tsuchiya and McCabe warn that such a simple calculation after estimating cost per unweighted QALY will in many situations not reflect the preferences on which the weights are based.
Source of the group weights
Each w_g is set before the calculation, for example from absolute and proportional shortfall through the band rule of HE-FM-ASF-003, or as the relative weight implied by an inequality aversion parameter (HE-FM-ATK-004). In NICE technology appraisal, social characteristics such as income do not earn a QALY weight (PMG36, section 4.12.7).
Worked examples
Two subgroups of one medicine weighted at 1.7 and 1
In the article's illustrative example, 300 patients in subgroup A each gain 0.6 QALYs and attract the weight of 1.7, and 700 patients in subgroup B each gain 0.8 QALYs at a weight of 1. The group gains are 300 × 0.6 = 180 and 700 × 0.8 = 560 QALYs, the weighted values 306 and 560, and the equity-weighted gain 866 QALYs against 740 unweighted.
w_1 = 1.7; Delta_E_1 = 180; w_2 = 1; Delta_E_2 = 560; V_1 = 306; V_2 = 560; Delta_E_w = 866
Same two subgroups with every equity weight set to 1
With both weights equal to 1 the weighted values equal the group gains and the equity-weighted total is the unweighted 740 QALYs, the limiting case in which equity weighting changes nothing.
w_1 = 1; Delta_E_1 = 180; w_2 = 1; Delta_E_2 = 560; V_1 = 180; V_2 = 560; Delta_E_w = 740
Common errors
Averaging per-patient weighted gains across groups of unequal size
Averaging the per-patient weighted gains of 1.02 and 0.8 QALYs and multiplying by 1,000 patients gives 910 weighted QALYs instead of 866. Subgroup A is only 30% of the patients, so each group's weighted gain has to be multiplied by its own number of patients before the groups are added.
Weighting severity and unmet need as two separate concerns
PMG36 states that the extent of unmet health need is reflected within the severity definition (section 6.2.12). A weight of 1.7 for severity combined with a further 1.2 for unmet need multiplies the gain by 2.04 and counts the same shortfall twice.
Sources
Cookson and colleagues on equity weights for health benefits
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 applies equity weights to the health benefits of people with different characteristics, or an equity parameter that implies such weights given the existing distribution of health, and notes that many proposed weighting systems rest on current severity of illness or lifetime health.
NICE severity modifier as 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 6.2.11 (modifiers are factors that go beyond QALYs, taken into account qualitatively or through QALY weighting), section 6.2.12 (unmet need reflected within the severity definition), sections 6.2.16 and 6.2.18 with table 6.1 (greater weight to QALYs for severe conditions, weights of 1, 1.2 and 1.7). Chapter 4, section 4.12.7 (results of a distributional analysis not weighted by social characteristics).
Wailoo and colleagues on severity weights applied to incremental QALYs
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, and that the definition giving the highest weight is used.
Wailoo, Tsuchiya and McCabe on weights added after the analysis
Wailoo A, Tsuchiya A, McCabe C. Weighting must wait: incorporating equity concerns into cost-effectiveness analysis may take longer than expected. PharmacoEconomics. 2009;27(12):983-989. Abstract, which states that equity weights have been assumed to enter as a separate simple calculation after estimating cost per unweighted QALY, and that in many situations such simple approaches will not reflect the preferences on which the weights are based.
Canonical Identity
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