Average Cost-Effectiveness Ratio

Average Cost-Effectiveness Ratio Compared with Incremental Ratios in Economic Evaluation

The average cost-effectiveness ratio (ACER) and the incremental cost-effectiveness ratio can rank the same treatments differently, and choosing the wrong one can approve a poor-value option or pass over a good one. Health technology assessment bodies base decisions between competing options on incremental ratios, because the choice turns on the extra cost of the extra health gained by moving from one option to the next, whereas an average ratio describes one option on its own. An average ratio can be written in two ways, and the NICE manual (PMG36) asks for incremental results. In an illustrative example below, average and incremental ratios point to different choices. An average ratio does carry information in some settings, including generalised cost-effectiveness analysis in the WHO-CHOICE programme, but ranking alternatives by average ratios is a long-standing error.

Two ways to write an average ratio

An average ratio divides what an option costs by what it achieves, without reference to any competing option. It can be written in two forms that are often confused. The simplest uses the totals for a single option, as follows.

$$ACER_i = \frac{C_i}{E_i}$$

where $ACER_i$ is the average cost-effectiveness ratio of option $i$, $C_i$ is its expected total cost and $E_i$ is its expected total health effect, for example in quality-adjusted life years (QALYs) or life-years. In this form the denominator counts all the health a patient group experiences while receiving the option, including health that would have occurred anyway, so the result is a cost per QALY lived rather than a cost per QALY gained.

The second form measures costs and effects against a do-nothing or null baseline, as follows.

$$ACER_{i,0} = \frac{C_i - C_0}{E_i - E_0}$$

where $ACER_{i,0}$ is the average ratio of option $i$ against the baseline, and $C_0$ and $E_0$ are the expected cost and health effect when none of the options is provided. When the baseline is defined as zero cost and zero effect the two forms coincide. In general they do not, and the second form is simply an incremental cost-effectiveness ratio (ICER) with doing nothing as the comparator. That observation explains most of what follows. An average ratio is informative when doing nothing is the real alternative, and misleading when it is not.

Why decisions between alternatives need incremental ratios

A decision maker choosing between mutually exclusive options, such as two drugs for the same patients, gives up one option to obtain the other. The question is whether the extra health from the more effective option is worth its extra cost, an opportunity cost question that only incremental differences answer. The standard textbook treatment of economic evaluation by Drummond and colleagues builds its decision rules on this incremental comparison, with options ordered by cost and those subject to dominance or extended dominance removed before ratios are compared with a threshold.

The ICER between two options is defined as follows.

$$ICER_{B,A} = \frac{C_B - C_A}{E_B - E_A}$$

where $ICER_{B,A}$ is the extra cost per extra unit of health effect of choosing option B instead of the less costly option A, and the other terms are as defined above. Two options can have very similar average ratios and a very high ICER between them, because a large part of each option's average is spread over health gains that both options deliver.

NICE writes the incremental approach into its reference case. Its manual for technology appraisal (PMG36) states that ICERs must be the ratio of expected additional total cost to expected additional QALYs compared with alternative technologies, and that results should be presented in a fully incremental analysis with dominated and extendedly dominated technologies removed. The manual also asks for expected net health benefits alongside ICERs, and allows net monetary benefits to be shown as well. The manual's decision rules are framed in incremental terms throughout.

Worked example with two treatments, two thresholds and two wrong answers

The figures below are illustrative. Two mutually exclusive treatments, A and B, are available for the same patient group, and the alternative is no treatment. Costs and QALYs are expected values per patient, discounted, and measured as differences from no treatment.

1. Calculate each average ratio against no treatment.

$$ACER_{A,0} = \frac{2000}{0.40} = 5000$$

where $ACER_{A,0}$ is the cost in pounds per QALY gained by A against no treatment.

$$ACER_{B,0} = \frac{9000}{0.60} = 15000$$

where $ACER_{B,0}$ is the cost in pounds per QALY gained by B against no treatment.

2. Calculate the incremental ratio of B against A. A is the less costly option, so B is compared with A, as follows.

$$ICER_{B,A} = \frac{9000 - 2000}{0.60 - 0.40} = \frac{7000}{0.20} = 35000$$

where $ICER_{B,A}$ is the cost in pounds of each extra QALY gained by choosing B instead of A.

3. Apply an illustrative threshold of £20,000 per QALY. Both average ratios are below £20,000, so an analyst who tests each option's average ratio against the threshold would call B cost-effective and might adopt it as the more effective option. The incremental ratio of £35,000 per QALY is above the threshold, so the extra 0.20 QALYs from B are not worth the extra £7,000 at this value of health, and A is the right choice. A check with net monetary benefit, the value of the health gained minus the cost, agrees. At £20,000 per QALY, A gives £6,000 (20,000 × 0.40 − 2,000) and B gives £3,000 (20,000 × 0.60 − 9,000).

4. Apply an illustrative threshold of £40,000 per QALY. Now the error runs the other way. An analyst who picks the option with the lowest average ratio still chooses A, at £5,000 per QALY. The incremental ratio of £35,000 per QALY is below the threshold, so B is the right choice. Net monetary benefit again agrees, as A gives £14,000 (40,000 × 0.40 − 2,000) and B gives £15,000 (40,000 × 0.60 − 9,000).

5. Add a shared baseline. Suppose untreated patients still live 5.00 QALYs and incur £1,000 of background care, so the totals are £3,000 and 5.40 QALYs for A and £10,000 and 5.60 QALYs for B. The total-based average ratios become about £556 per QALY for A (3,000 ÷ 5.40) and about £1,786 per QALY for B (10,000 ÷ 5.60), much lower than before, because they now spread costs over health that would have occurred without treatment. The ICER is unchanged at £35,000 per QALY ((10,000 − 3,000) ÷ (5.60 − 5.40)), since the shared baseline cancels out of every difference.

In this example, average ratios approve an option that should be rejected at one threshold, pass over the right option at another, and shrink with an arbitrary choice of baseline, while the incremental result and the net monetary benefit ranking agree throughout.

Where an average ratio carries information

An average ratio answers a narrower question than most appraisals ask. Its use is defensible in a few settings, each of which has doing nothing as a real alternative or uses the ratio for description rather than choice.

The first is a single programme whose only alternative is not to provide it. The average ratio against a do-nothing baseline is then the ICER of the programme, provided the baseline costs and effects are estimated properly rather than assumed to be zero. The second is a set of independent programmes, where funding one does not prevent funding another. In the textbook treatment of this case, each programme is compared with its own do-nothing alternative and, under a fixed budget and the usual assumptions of divisible programmes with constant returns, programmes are funded in ascending order of those ratios until the budget runs out.

Average ratios also have descriptive uses. Bang and Zhao, who developed confidence intervals for the ACER with censored data, note that it describes a treatment independently of its comparators, has an intuitive meaning such as cost per year of survival, and is less prone to the numerical instability an ICER shows when two options have very similar effects. None of those properties turns the ACER into a decision rule between alternatives, and the same authors acknowledge that the ICER could be more relevant to health economic and policy decisions.

Generalised cost-effectiveness analysis and WHO-CHOICE

A major use of average ratios is generalised cost-effectiveness analysis, the approach adopted by the World Health Organization's Choosing Interventions that are Cost-Effective (WHO-CHOICE) programme. Instead of measuring a new intervention against current practice, it measures interventions against a null scenario in which the interventions under study are not in place. Hutubessy, Chisholm and Tan-Torres Edejer describe the advantage of this counterfactual as the ability to identify current allocative inefficiencies as well as the efficiency of new opportunities, because the analysis no longer takes the existing mix of services as given.

Average and incremental ratios have separate jobs in this framework. In the 2021 update of WHO-CHOICE methods, Bertram and colleagues describe interventions being evaluated first individually against the null and then in combinations, starting with the most cost-effective intervention and adding others step by step to find the best package for each disease area. Their figure of the cost-effectiveness plane shows both average and incremental ratios, with the origin, the point of no costs and no effects, called the null position. Hutubessy and colleagues describe the output of adapting the analysis to a country as a set of average and incremental cost-effectiveness ratios, and state that generalised analysis does not replace context-specific evidence on adding new technologies to the existing mix.

WHO-CHOICE therefore keeps the incremental principle. The average ratio against the null evaluates single interventions and tests whether current practice is worth its cost, while incremental ratios along the sequence of combinations show what each addition buys. Hutubessy and colleagues also describe classifying interventions into bands, from very cost-effective to cost-ineffective, rather than relying on a traditional league table.

Assumptions behind any reading of an ACER

An average ratio is only interpretable when its baseline is stated. A ratio built on total QALYs and a ratio against a modelled null scenario are different quantities that share a name, and reports do not always say which they contain. The baseline also has to be estimated with the same model, population, perspective and time horizon as the option, or the differences that form the ratio mix unlike things.

Using average ratios for allocation assumes that the options are genuinely independent. Programmes that compete for the same patients or interact in their effects are not, and their average ratios against doing nothing can misstate what the second programme adds once the first is in place. Overlapping effects lead them to overstate it, and complementary effects to understate it. The budget rule also assumes that programmes can be scaled without changes in cost per unit of effect, which rarely holds exactly in health services.

Average, incremental and marginal ratios compared

Ratios with similar names answer different questions. Keeping them apart avoids most reporting errors, especially when results from different studies sit side by side.

Marginal cost-effectiveness concerns a change in the scale of one option, such as screening more often, rather than a choice between distinct options. An average ratio can hide a high marginal ratio in the same way it hides a high incremental one.

The classic error of ranking options by their average ratios

The error has a long history in the medical literature. Neuhauser and Lewicki analysed a protocol of six sequential stool guaiac tests for colon cancer screening and reported that, measured per cancer detected, the marginal cost of the sixth test might be 20,000 times the average cost. It became a standard teaching case, although Brown and Burrows later argued that the analysis contained two fundamental errors and that, once corrected, the marginal cost was modest, and a published comment by Gatsonis followed in the same issue. The original figure is disputed and should not be quoted without the correction. The lesson of the case does not depend on the figure, since an average taken over a whole programme can conceal what the last increment of that programme costs.

Hershey and colleagues tested whether presentation matters. They gave physicians hypothetical screening scenarios with either average ratios, calculated against no screening, or incremental ratios, calculated against the next best alternative. Incremental information significantly reduced preference for the most expensive strategies in two of three unfamiliar scenarios, while no such difference appeared in familiar ones. The authors suggest that, in unfamiliar settings, average ratios can hide the often high price of incremental health gains. Hoch and Dewa reach the same conclusion using results from a hypothetical trial, naming the ICER and the incremental net benefit as examples of correct summary measures.

Related errors follow the same pattern. A table of average ratios from separate studies is read as a funding ranking, although each ratio has its own baseline. A total-based average ratio is reported as a cost per QALY gained, as if every QALY lived were caused by the option. An average ratio below a cost-effectiveness threshold is taken to show that the option is cost-effective, which holds only if doing nothing is the sole alternative.

Sources

• Bang H, Zhao H. Average cost-effectiveness ratio with censored data. Journal of Biopharmaceutical Statistics. 2012;22(2):401-415. doi:10.1080/10543406.2010.544437
• Bertram MY, Lauer JA, Stenberg K, Tan Torres Edejer T. Methods for the economic evaluation of health care interventions for priority setting in the health system: an update from WHO CHOICE. International Journal of Health Policy and Management. 2021;10(Special Issue on WHO-CHOICE Update):673-677. doi:10.34172/ijhpm.2020.244
• Brown K, Burrows C. The sixth stool guaiac test: $47 million that never was. Journal of Health Economics. 1990;9(4):429-445. doi:10.1016/0167-6296(90)90004-m
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford: Oxford University Press; 2015.
• Gatsonis C. The long debate on the sixth guaiac test: time to move on to new grounds. Journal of Health Economics. 1990;9(4):495-497. doi:10.1016/0167-6296(90)90009-r
• Hershey JC, Asch DA, Jepson C, Baron J, Ubel PA. Incremental and average cost-effectiveness ratios: will physicians make a distinction? Risk Analysis. 2003;23(1):81-89. doi:10.1111/1539-6924.00291
• Hoch JS, Dewa CS. A clinician's guide to correct cost-effectiveness analysis: think incremental not average. Canadian Journal of Psychiatry. 2008;53(4):267-274. doi:10.1177/070674370805300408
• Hutubessy R, Chisholm D, Tan-Torres Edejer T. Generalized cost-effectiveness analysis for national-level priority-setting in the health sector. Cost Effectiveness and Resource Allocation. 2003;1:8. doi:10.1186/1478-7547-1-8
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated 13 October 2026. Sections 4.2.16 and 4.10.8.
• Neuhauser D, Lewicki AM. What do we gain from the sixth stool guaiac? New England Journal of Medicine. 1975;293(5):226-228. doi:10.1056/NEJM197507312930504