Signature
NHB_1 = dQ_1 - o_1 * H_d; NHB_2 = dQ_2 - o_2 * H_d; h1_1 = h0_1 + NHB_1 / N_1; h1_2 = h0_2 + NHB_2 / N_2; NHB_tot = NHB_1 + NHB_2
| Inputs | Definition | Unit |
|---|---|---|
dQ_1 | QALYs gained by the more deprived group under the programme against the comparator, summed over its members, before any health is displaced | QALYs |
o_1 | Proportion of H_d that falls on the more deprived group, at least 0 and at most 1, with o_1 plus o_2 equal to 1; equal sharing per head sets it to the group's share of the population | proportion |
H_d | Health displaced elsewhere by the programme's incremental cost, the cost divided by the value of a QALY as in HE-FM-CET-002 | QALYs |
dQ_2 | QALYs gained by the less deprived group under the programme against the comparator, summed over its members, before any health is displaced | QALYs |
o_2 | Proportion of H_d that falls on the less deprived group, at least 0 and at most 1, with o_1 plus o_2 equal to 1 | proportion |
h0_1 | Health per person of the more deprived group without the programme, for example quality-adjusted life expectancy (QALE) at birth | years of QALE per person |
N_1 | People in the more deprived group of the general population, above zero | persons |
h0_2 | Health per person of the less deprived group without the programme, in the same measure as h0_1 | years of QALE per person |
N_2 | People in the less deprived group of the general population, above zero | persons |
NHB_1 | QALYs gained by the more deprived group less its share of the health opportunity cost | QALYs |
|---|---|---|
NHB_2 | QALYs gained by the less deprived group less its share of the health opportunity cost | QALYs |
h1_1 | Baseline health per person of the more deprived group plus its net health benefit per person | years of QALE per person |
h1_2 | Baseline health per person of the less deprived group plus its net health benefit per person | years of QALE per person |
NHB_tot | Sum of the group net health benefits, the change in total population health against the comparator | QALYs |
Function
Distributional cost-effectiveness comparison of options by social group function
Maps each social group's baseline health, its QALY gain from a programme, its share of the health opportunity cost and its size, together with a chosen inequality aversion, to the group's health under the programme, the change in equally distributed equivalent (EDE) health and in the Atkinson index against the comparator, the programme's quadrant on the equity-efficiency impact plane, and the inequality aversion at which two options give equal EDE health. The health opportunity cost of the incremental cost is the live record HE-FM-CET-002, and the EDE and Atkinson index of each distribution are the live records HE-FM-ATK-002, HE-FM-ATK-003, HE-CF-ATK-001 and HE-FM-ATK-001, which are cited here and not redrafted. Other inequality indices for grouped data, such as the absolute gap and the concentration index, are in HE-FN-HINQ-001, and direct equity weights on QALY gains are in HE-FN-EQWA-001. The two-group closed approximation to the switching aversion belongs to the equity-efficiency trade-off package, while the computational function here solves the EDE comparison itself for any number of groups. Notation follows the Distributional Cost-Effectiveness article.
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Implementations
Excel
Group health after a programme from named cells for two groups
With cells named QALYGainWorse, QALYGainBetter, OCShareWorse, OCShareBetter, HealthOppCost, GroupSizeWorse, GroupSizeBetter, BaselineWorse and BaselineBetter, the first two formulas return health per person in the more and the less deprived group under the programme, held in cells named PostHealthWorse and PostHealthBetter, and the third returns the total net health benefit, held in NetHealthTotal. HealthOppCost is the result of HE-FM-CET-002.
=BaselineWorse+(QALYGainWorse-OCShareWorse*HealthOppCost)/GroupSizeWorse; =BaselineBetter+(QALYGainBetter-OCShareBetter*HealthOppCost)/GroupSizeBetter; =(QALYGainWorse-OCShareWorse*HealthOppCost)+(QALYGainBetter-OCShareBetter*HealthOppCost)
Assumptions
Groups cover the whole general population in a DCEA
Baseline health and group sizes refer to the full general population, people who receive the programme and people who do not. Asaria and colleagues give two reasons, that concern about health inequality usually relates to the general population and that in a budget-constrained system the resources used by recipients displace care that anyone could have received. A group's gain and its share of the displaced health are therefore spread over every member of the group.
Opportunity cost shares add to one in a DCEA
The shares o_1 and o_2 add to 1, so the groups together bear the whole of H_d. The tutorial apportions the opportunity cost equally to each individual, so each share equals the group's share of the population, and calls this convenient but not evidence based. The NICE support document on health inequalities keeps equal sharing in the base case, with slight and moderate gradients towards the more deprived groups as scenarios, and Love-Koh and colleagues estimate that 26% of the health effect of a change in English NHS spending falls on the most deprived fifth of the population and 14% on the least deprived fifth.
Health opportunity cost of a DCEA at a stated value of a QALY
H_d comes from HE-FM-CET-002 at a stated value of a QALY, and the group results change with it. PMG36 sections 6.3.4 to 6.3.8 describe a range of GBP 25,000 to GBP 35,000 per QALY gained, and the NICE support document asks a DCEA to present results at several values within the range in those sections.
Worked examples
Article's two groups with the opportunity cost shared equally per head
In the article's illustrative example two groups of 50,000 people have baseline QALE of 64 and 72 years and gain 400 and 1,400 QALYs, and the programme's GBP 30 million cost displaces 1,200 QALYs at GBP 25,000 per QALY. With each group bearing half, the more deprived group's net health benefit is minus 200 QALYs and the other group's 800, so health per person moves to 63.996 and 72.016 years, and total health rises by 600 QALYs.
dQ_1 = 400; dQ_2 = 1400; o_1 = 0.5; o_2 = 0.5; H_d = 1200; h0_1 = 64; h0_2 = 72; N_1 = 50000; N_2 = 50000; NHB_1 = -200; NHB_2 = 800; h1_1 = 63.996; h1_2 = 72.016; NHB_tot = 600
Article's two groups with 60% of the opportunity cost on the more deprived group
Under the article's illustrative gradient the more deprived group bears 720 of the 1,200 displaced QALYs and the other group 480, so the net health benefits are minus 320 and 920 QALYs and health per person moves to 63.9936 and 72.0184 years. Total health still rises by 600 QALYs, while the gap between the groups widens to 8.0248 years against 8.020 under equal sharing.
dQ_1 = 400; dQ_2 = 1400; o_1 = 0.6; o_2 = 0.4; H_d = 1200; h0_1 = 64; h0_2 = 72; N_1 = 50000; N_2 = 50000; NHB_1 = -320; NHB_2 = 920; h1_1 = 63.9936; h1_2 = 72.0184; NHB_tot = 600
Cost-neutral programme with no health opportunity cost in a DCEA
With H_d set to 0, each group's health moves by its own gain per person, to 64.008 and 72.028 years, and the total net health benefit equals the 1,800 QALYs gained. This is the limiting case in which the opportunity cost shares have no effect.
dQ_1 = 400; dQ_2 = 1400; o_1 = 0.5; o_2 = 0.5; H_d = 0; h0_1 = 64; h0_2 = 72; N_1 = 50000; N_2 = 50000; NHB_1 = 400; NHB_2 = 1400; h1_1 = 64.008; h1_2 = 72.028; NHB_tot = 1800
Common errors
Reading the equity impact of a DCEA from gross QALY gains
Before the opportunity cost is counted, the more deprived group in the article's example gains 400 QALYs, 0.008 years per person, yet after its equal share of the 1,200 displaced QALYs it loses 0.004 years per person. A programme whose benefits reach a disadvantaged group can still leave that group worse off once the displaced care is counted.
Splitting the opportunity cost equally per group when groups differ in size
With illustrative groups of 20,000 and 80,000 people, sharing 1,200 displaced QALYs equally per head puts 240 on the smaller group, whereas a half and half split puts 600 on it. With a gain of 400 QALYs the smaller group's net health benefit is 160 QALYs under per-head sharing and minus 200 under the half split, so the error turns a gain into a loss.
Sources
Asaria and colleagues on net health effects by subgroup after shared opportunity costs
Asaria M, Griffin S, Cookson R. Distributional cost-effectiveness analysis: a tutorial. Medical Decision Making. 2016;36(1):8-19. Section Estimating the distribution of health changes due to the interventions, which converts total costs into health opportunity costs at a threshold value, apportions them equally to each individual so that a subgroup with 10% of the population is allocated 360 of 3,600 QALYs, subtracts them from the subgroup's health gains to give its net health effect, and calls equal sharing convenient but not evidence based. Section Estimating the baseline health distribution, which requires the full general population.
NICE support document on the distribution of health opportunity costs in a DCEA
National Institute for Health and Care Excellence. Support document, health inequalities. Tools and resources of NICE technology appraisal and highly specialised technologies guidance, the manual (PMG36). London, NICE, 2022, last updated 13 October 2026; page last updated 13 May 2025. Section Distributional cost-effectiveness analysis methods, subsection Health opportunity cost and Table 2, which ask for health opportunity costs equally distributed between social groups in the base case, with slight (22%, 21%, 20%, 19% and 18%) and moderate (24%, 22%, 20%, 18% and 16%) gradients across five IMD groups starting with the most deprived, and for results at several values within the ranges in sections 6.3.4 to 6.3.8 of the manual; subsection Outputs, which asks for net health benefit for each IMD quintile. PMG36 sections 6.3.4 and 6.3.7 give the GBP 25,000 and GBP 35,000 points of that range.
Love-Koh and colleagues on the social distribution of displaced health
Love-Koh J, Cookson R, Claxton K, Griffin S. Estimating social variation in the health effects of changes in health care expenditure. Medical Decision Making. 2020;40(2):170-182. Abstract, which estimates that 26% of the total health effect of a change in English NHS expenditure would accrue to the fifth of the population living in the most deprived areas, against 14% to the fifth living in the least deprived areas.
Canonical Identity
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