Equity-Efficiency Trade-off

Equity-Efficiency Trade-off: When Maximising Health and Reducing Inequality Pull Apart

Health economists judge spending on two grounds: how much health a budget buys in total, and how that health is shared between social groups. Often the two agree, but sometimes the option that buys the most health widens the gap between better-off and worse-off groups, and a decision maker has to say how much total health a fairer distribution is worth. This page explains when equity and efficiency conflict and the tools that put a number on the trade-off: the health equity impact plane, inequality aversion, equity weights and the fair innings argument. It reports public estimates of inequality aversion in England, works through an illustrative choice between two programmes of equal cost, and sets out how NICE and the World Health Organization handle the trade-off.

Two objectives for one budget

In economic evaluation, efficiency usually means getting the most health from a fixed budget. The NICE manual for technology appraisal (PMG36) justifies cost-effectiveness analysis by NICE's focus on maximising health gains from a fixed NHS and personal social services budget. Cookson and colleagues link this to opportunity cost: with a fixed budget, a cost-effective programme has a positive net health impact, because its gains outweigh the health lost when spending is shifted from other programmes.

Equity concerns how health, or access to care, is distributed. Standard analysis adds up QALYs without asking who receives them, on what Cookson and colleagues call the standard value judgement that "a QALY is a QALY". That rule is itself a distributional choice. Concern for equity adds a second objective, such as reducing unfair health inequality or giving priority to the severely ill, and a trade-off arises only when the two objectives rank the options differently.

When equity and efficiency conflict and when they do not

Cookson and colleagues, among them Griffin, Norheim and Culyer, set out the health equity impact plane to show whether a trade-off exists. The vertical axis shows net health impact, the health gained minus the health displaced elsewhere. The horizontal axis shows net health equity impact, the effect on the chosen equity objective after allowing for the same opportunity costs.

The authors note that many policies fall into the first two cells. Vaccination and infectious disease control may be win-win, delivering large gains per unit of cost and disproportionate benefit to disadvantaged groups, while high-cost hospital treatments in low- and middle-income countries may be lose-lose. Conflict arises when disadvantaged groups gain less from a funded technology, for example because access costs are higher in remote rural areas, or because preventive programmes that rely on changes in behaviour may have more success in advantaged communities.

Measuring the trade-off with inequality aversion

Distributional cost-effectiveness analysis (DCEA) models the distribution of health under each option and then evaluates the distributions against the twin aims of more total health and less unfair inequality. In the tutorial by Asaria, Griffin and Cookson, the evaluation measures the change in total health and in inequality, then applies dominance rules that need minimal assumptions about values. Under Atkinson's theorem, one distribution dominates another when their Lorenz curves do not cross and the more equal one has at least as much mean health; under Shorrocks' theorem, it dominates when its generalised Lorenz curve, the Lorenz curve multiplied by mean health, lies wholly above the other. Only when these rules cannot rank the options, as when generalised Lorenz curves cross, is an explicit social welfare function needed.

The usual form is based on the Atkinson index, which summarises a distribution as equally distributed equivalent (EDE) health. For a population divided into groups:

$$ h_{EDE} = \left[ \sum_{g} s_g , h_g^{,1-\varepsilon} \right]^{\frac{1}{1-\varepsilon}}, \quad \varepsilon \neq 1 $$

where $h_{EDE}$ is EDE health, $s_g$ is the population share of group $g$, $h_g$ is the health of group $g$, such as quality-adjusted life expectancy, and $\varepsilon$ is the inequality aversion parameter. At $\varepsilon = 0$ it reduces to mean health, so the standard rule is the special case of zero aversion, and at $\varepsilon = 1$ it becomes the weighted geometric mean. For a small gain, the parameter implies that a QALY for a group with health $h_{low}$ is worth $(h_{high}/h_{low})^{\varepsilon}$ times a QALY for a group with health $h_{high}$.

Equity weights and the rule that a QALY is a QALY

Equity weights depart from equal weighting by multiplying the health gains of chosen groups. Wagstaff argued in 1991 that a common theme in criticisms of the QALY approach was a concern about inequality, and proposed a method for incorporating both inequality and other distributional concerns into resource allocation decisions. Cookson and colleagues describe equity-weighting analysis as a way to show how much concern for equity is needed to choose a fairer but less cost-effective option, using weights for groups or an equity parameter such as $\varepsilon$.

Their simpler equity constraint analysis counts the cost of choosing fairer options. Williams and Cookson made the same point about real decisions: every departure from a strict cost-effectiveness approach has an opportunity cost, and its size tests how much weight an equity concern is deemed to merit. Equity-weighted analysis is best reported beside the unweighted result, so the health given up stays visible.

The fair innings argument

Williams argued in 1997 that many equity principles may need to be traded off against efficiency, and examined one of them. The fair innings argument, which he explored, holds that everyone is entitled to some normal span of health; anyone who falls short has been cheated, while anyone who exceeds it is living on borrowed time. The principle is based on outcomes, concerns a whole lifetime rather than a point in time, reflects aversion to inequality, and can be quantified.

Williams added that age at death should be no more than a first approximation, because quality of life matters as well as length. His analysis suggested that this view of intergenerational equity requires greater discrimination against the elderly than efficiency alone would dictate. The World Health Organization's report on fair choices takes a similar lifetime view, arguing that there are good reasons to start with those worse off over their lifetime.

How much inequality aversion the public expresses

The value of $\varepsilon$ is a social value judgement, and surveys of the public are one way to inform it. Robson and colleagues analysed responses from 244 members of the public in England and found a median Atkinson parameter of 10.95, which at their baseline quality-adjusted life expectancy of 62 years for the poorest fifth and 74 for the richest implies weighting gains to the poorest fifth almost seven times (6.95) as highly; they also report that an earlier English study by Dolan and Tsuchiya implies 28.9. The implied weight depends on the baseline gap as well as on $\varepsilon$, so the same parameter gives a smaller weight in the worked example below; the Atkinson index page covers the elicitation.

Worked example: two programmes with the same cost

The figures in this example are illustrative. A health system can fund programme E or programme F at the same cost. A more deprived group makes up 40% of the population, with a baseline quality-adjusted life expectancy of 66 years, and a less deprived group makes up 60%, with 74 years. Mean health is 0.4 × 66 + 0.6 × 74 = 70.8 years and the gap is 8 years.

1. Net out the opportunity cost. Each programme displaces 0.10 years per person elsewhere in the system, spread evenly. E gives gross gains per person of 0.20 years to the more deprived group and 0.70 to the less deprived, so net gains of 0.10 and 0.60. F gives gross gains per person of 0.60 and 0.35, so net gains of 0.50 and 0.25.

2. Place each programme on the plane. The mean net gain is 0.4 × 0.10 + 0.6 × 0.60 = 0.40 years under E and 0.4 × 0.50 + 0.6 × 0.25 = 0.35 years under F. With the absolute gap as the equity measure, E widens it to 74.6 − 66.1 = 8.5 years and F narrows it to 74.25 − 66.5 = 7.75 years. Against doing nothing, E is win-lose and F is win-win, but between them there is a trade-off: E gives 0.05 years more per person, one-eighth of its net gain, and F a gap 0.75 years narrower.

3. Find the switching weight. If a gain to the more deprived group carries weight $w$, the weighted mean gains are $w \times 0.04 + 0.36$ under E and $w \times 0.20 + 0.15$ under F. Setting them equal gives:

$$ w^{*} = \frac{0.36 - 0.15}{0.20 - 0.04} = \frac{0.21}{0.16} = 1.3125 $$

where $w^{*}$ is the weight on the more deprived group's QALYs above which F is preferred.

4. Translate the weight into inequality aversion. At baseline health the implied weight is $(74/66)^{\varepsilon}$, so:

$$ \varepsilon^{*} \approx \frac{\ln 1.3125}{\ln (74/66)} = \frac{0.2719}{0.1144} \approx 2.38 $$

where $\varepsilon^{*}$ is the approximate switching value of the inequality aversion parameter and $\ln$ is the natural logarithm. This uses the weights at baseline health; solving the EDE formula directly for the value at which the two programmes tie gives about 2.35.

5. Compare EDE health. The table applies the EDE formula to the health levels after each programme, with differences calculated before rounding.

6. Interpret the result. A health-maximising rule picks E, as does any Atkinson function with $\varepsilon$ below about 2.35. At the English median of 10.95 the implied weight at baseline is $(74/66)^{10.95} \approx 3.50$, and F leads by 0.18 years of EDE health per person. The decision therefore rests on whether the decision maker's aversion lies above or below about 2.35, a judgement the analysis can locate but not make.

How NICE and the World Health Organization handle the trade-off

NICE states the trade-off in its principles: its committees strive to balance the most overall benefit for the greatest number of people with fairness and respect for individual choice. Overall population needs are paramount, but in some circumstances the needs of particular groups may override them, and under Principle 9 guidance should support strategies that improve population health as a whole while offering particular benefit to the most disadvantaged.

In technology appraisal, the PMG36 reference case gives an additional QALY the same weight whoever receives it, except in specific circumstances (Table 4.1 and section 6.2.10). Severity is the main exception: the committee may weight QALYs by 1.2 when the proportional QALY shortfall is 0.85 to 0.95 or the absolute shortfall is 12 to 18, and by 1.7 when they are at least 0.95 or at least 18, whichever implies the greater severity (sections 6.2.12 to 6.2.18; see proportional shortfall and absolute shortfall). Section 6.3.2 keeps the cost visible: net health benefit should be presented at £25,000 and £35,000 per QALY with and without the weighting, and a technology with negative unweighted net health benefit may still be recommended on an ethical and moral rationale.

Health inequalities are handled by deliberation rather than by weights. The PMG36 support document on health inequalities states that functions using inequality aversion parameters should not be applied to QALYs. It asks for results by quintile of the Index of Multiple Deprivation, with displaced health shared equally in the base case and scenarios with slight and moderate gradients towards more deprived groups.

The World Health Organization's Consultative Group on Equity and Universal Health Coverage reported in 2014 on fair progress towards universal health coverage. It named three groups of criteria for sorting services into priority classes: cost-effectiveness, priority to the worse off and financial risk protection. It stated that an exclusive focus on cost-effectiveness is generally found indefensible, and called it generally unacceptable to expand coverage for well-off groups before worse-off groups when costs and benefits are not vastly different.

Common misreadings of the equity-efficiency trade-off

Two errors are common in reading equity-efficiency analyses. Many programmes are win-win or lose-lose, so not every equity concern costs health. An equity weight does not remove opportunity cost: choosing F in the worked example still gives up 0.05 years per person.

The answer also turns on choices made before any calculation: relative or absolute inequality, which groups define unfair inequality, who bears the displaced health, and lifetime or prospective health. Finally, severity weighting differs from concern for socioeconomic health equity: NICE's severity modifier looks at future health lost by people living with a condition under current care, while the fair innings argument looks at lifetime health and DCEA at differences between social groups.

Sources

• Asaria M, Griffin S, Cookson R. Distributional cost-effectiveness analysis: a tutorial. Medical Decision Making. 2016;36(1):8-19. https://pmc.ncbi.nlm.nih.gov/articles/PMC4853814/
• 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. https://pmc.ncbi.nlm.nih.gov/articles/PMC5340318/
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 31 March 2026. Table 4.1 and sections 4.2.15, 6.2.10 to 6.2.18 and 6.3.2. https://www.nice.org.uk/process/pmg36
• National Institute for Health and Care Excellence. Support document: health inequalities. Technology evaluation methods support document for PMG36, last updated 13 May 2025. https://www.nice.org.uk/process/pmg36/resources/support-document-health-inequalities-15313210669/chapter/distributional-cost-effectiveness-analysis-methods
• National Institute for Health and Care Excellence. Our principles. Web page, accessed 2 October 2026. https://www.nice.org.uk/about-us/our-principles
• Robson M, Asaria M, Cookson R, Tsuchiya A, Ali S. Eliciting the level of health inequality aversion in England. Health Economics. 2017;26(10):1328-1334. https://pmc.ncbi.nlm.nih.gov/articles/PMC6120144/
• Wagstaff A. QALYs and the equity-efficiency trade-off. Journal of Health Economics. 1991;10(1):21-41.
• Williams A. Intergenerational equity: an exploration of the 'fair innings' argument. Health Economics. 1997;6(2):117-132.
• Williams AH, Cookson RA. Equity-efficiency trade-offs in health technology assessment. International Journal of Technology Assessment in Health Care. 2006;22(1):1-9.
• World Health Organization. Making fair choices on the path to universal health coverage: final report of the WHO Consultative Group on Equity and Universal Health Coverage. Geneva: WHO; 2014. https://www.who.int/publications/i/item/9789241507158