Cost-Effectiveness Frontier

Cost-Effectiveness Frontier in Choices Between Several Strategies

When an economic evaluation compares more than two mutually exclusive strategies, the cost-effectiveness frontier marks the ones worth choosing between, and every strategy above it can be set aside whatever value is placed on health. Plotted with health effect across and cost up, it runs from the cheapest strategy to the most effective one, and the slope of each segment is the incremental cost-effectiveness ratio of moving one step along it. Suen and Goldhaber-Fiebert call the frontier the main result of all cost-effectiveness analyses, and the decision at any threshold is read from it. The NICE technology appraisal manual (PMG36) asks for results in a fully incremental analysis with dominated and extendedly dominated technologies removed, which amounts to reporting the frontier and the ratios along it.

Where the frontier sits on the cost-effectiveness plane

Each strategy is plotted at its expected total cost and expected total health effect, usually discounted QALYs per person, for the same population, perspective and time horizon. The HEMA report on uncertainty recommends probabilistic analysis as the general default for characterising uncertainty, partly because running a model at the mean of each input does not necessarily produce the expected costs and health effects, and it proposes reporting the deterministic result too, explaining any material difference. The frontier can be drawn on the cost-effectiveness plane relative to any one reference strategy without changing shape, since subtracting the same cost and effect from every point only moves the origin. The frontier is the lower right edge of the cloud of points, and Suen and Goldhaber-Fiebert note that finding it is equivalent to finding a section of the convex hull of the plotted strategies.

Their definition takes three strategies ordered by health effect, with $k$ lying between $i$ and $j$. Strategy $k$ is on the frontier only if it lies on or below the straight line joining the other two.

$$C_k \le (1 - a)\,C_i + a\,C_j, \qquad a = \frac{Q_k - Q_i}{Q_j - Q_i}$$

where $C_i$, $C_j$ and $C_k$ are the expected total costs of the three strategies, $Q_i$, $Q_j$ and $Q_k$ are their expected total QALYs with $Q_i \le Q_k \le Q_j$, and $a$ is how far along the way from $i$ to $j$ the health effect of $k$ lies. The right-hand side is the cost of reaching the health effect of $k$ by giving strategy $j$ to a share $a$ of the population and strategy $i$ to the rest. A strategy that fails this test for some pair without being strictly dominated is excluded by extended dominance, and one that costs more and gives less health than another is excluded by strict dominance; both are forms of dominance.

Along the frontier each segment joins one surviving strategy to the next more effective one, and its slope is the ICER of that step.

$$\text{ICER}_{j} = \frac{C_j - C_{j-1}}{Q_j - Q_{j-1}}$$

where $j$ is a frontier strategy, $j-1$ is the next less effective strategy on the frontier, and $C$ and $Q$ are expected total costs and QALYs as above. Each ratio is taken against the adjacent frontier strategy, which is the cheapest option only for the first step. Because the boundary bends upwards, the ratios rise from one segment to the next.

Building the frontier by elimination

The conventional method removes strategies in rounds. Suen and Goldhaber-Fiebert summarise it as ordering strategies by ascending cost, eliminating those that cost more but provide less benefit than an alternative, computing pairwise ICERs, and then discarding any strategy whose ICER is higher than that of the following strategy, repeating until nothing more can be removed. The repetition is needed because removing a strategy changes the comparator for the next one, and the recalculated ratio can reveal a further extendedly dominated strategy.

The NICE manual (PMG36, section 4.10.8) asks for economic evaluation results to be presented as a fully incremental analysis with dominated and extendedly dominated technologies removed. It allows pairwise comparisons when relevant and justified, for example when a technology is expected to displace one particular comparator. Section 4.2.16 adds that expected net health benefits should be presented as well as ICERs, which may be particularly informative when there are several technologies or comparators.

The net benefit route to the same frontier

A second route avoids the rounds of elimination. Net monetary benefit values the health produced by a strategy at a chosen value per QALY and subtracts its cost.

$$\text{NMB}_k(\lambda) = \lambda\,Q_k - C_k$$

where $\text{NMB}_k(\lambda)$ is the net monetary benefit of strategy $k$, $\lambda$ is the value placed on one QALY, and $Q_k$ and $C_k$ are as above. Suen and Goldhaber-Fiebert prove that every frontier strategy has the largest net monetary benefit for some positive value of $\lambda$, and that strictly or extendedly dominated strategies never do. A frontier strategy is the best choice for every $\lambda$ between the slope of the segment that enters it and the slope of the segment that leaves it, so the segment slopes are the switching values.

This gives a one-pass method. Net monetary benefit is calculated for every strategy over a grid of values of $\lambda$, and the strategies that come out on top somewhere in the grid form the frontier. The authors show that no frontier strategy relevant to the decision is missed if the grid includes zero, every positive pairwise ICER and the largest value relevant to the decision maker. At zero the cheapest strategy wins, and as $\lambda$ grows without limit the strategy with the most QALYs wins, so the most effective strategy is found once the grid reaches past the last ICER on the frontier. They suggest it for deterministic sensitivity analyses, where every run needs a new frontier.

Worked example with six rehabilitation options

The figures are illustrative. Six mutually exclusive options for rehabilitation after a hip fracture are compared per person over a lifetime, with costs in GBP and QALYs already discounted. R0 is usual care, and R1 to R5 are programmes listed in order of expected cost.

1. Remove strict dominance. R2 costs GBP 1,500 more than R1 and gives 0.02 fewer QALYs, so it is strictly dominated and leaves the analysis.

2. Compute ratios between neighbours. In cost order the remaining ratios are (4,000 − 2,000) / (5.10 − 5.00) = 20,000 for R1 against R0, (9,000 − 4,000) / (5.20 − 5.10) = 50,000 for R3 against R1, (10,000 − 9,000) / (5.30 − 5.20) = 10,000 for R4 against R3, and (19,000 − 10,000) / (5.45 − 5.30) = 60,000 for R5 against R4.

3. Remove extended dominance and recompute. The ratio falls from 50,000 to 10,000 after R3, so R3 is extendedly dominated. R4 is then compared with R1, giving (10,000 − 4,000) / (5.30 − 5.10) = 30,000. The sequence 20,000, 30,000 and 60,000 rises, so R0, R1, R4 and R5 form the frontier.

4. Check with the line test. R3 lies halfway between R1 and R4 in health, so $a = (5.20 - 5.10) / (5.30 - 5.10) = 0.5$. Giving R1 to half the patients and R4 to the other half yields 5.20 QALYs for 0.5 × 4,000 + 0.5 × 10,000 = GBP 7,000 per person, which is GBP 2,000 less than R3.

5. Confirm with net monetary benefit. PMG36 asks for net health benefits using values of GBP 25,000 and GBP 35,000 placed on a QALY gain, and the same two values are used here for net monetary benefit, in GBP per person.

For R1, for instance, 25,000 × 5.10 − 4,000 = 123,500 and 35,000 × 5.10 − 4,000 = 174,500. R1 has the highest value at GBP 25,000 and R4 at GBP 35,000, as the frontier predicts, since 25,000 lies between the slopes of 20,000 and 30,000 and 35,000 lies between 30,000 and 60,000. At the switching value of GBP 30,000, R1 and R4 tie at 149,000 while R3 reaches only 147,000.

6. Interpretation. At GBP 25,000 per QALY the decision is R1, and at GBP 35,000 it is R4. Compared only with usual care, R3 has a ratio of (9,000 − 2,000) / (5.20 − 5.00) = 35,000, which could look acceptable at the upper value, yet R3 is never the best choice at any value per QALY. R5 is on the frontier but would be chosen only at values above GBP 60,000 per QALY.

What being on the frontier does and does not mean

A place on the frontier means a strategy is the best choice at some value of health, not that it is cost effective. Suen and Goldhaber-Fiebert state the decision rule as choosing the strategy with the highest ICER at or below the willingness to pay for an extra unit of benefit, so a cost-effectiveness threshold is still needed to pick one point. A strategy off the frontier is not worth choosing on expected values for the population analysed, although the authors note it may still be of interest if a subgroup analysis puts it on the frontier for a particular subpopulation.

The frontier is also only as good as the set of strategies behind it. Adding a strategy can remove others by extended dominance, and leaving out a relevant comparator can make a strategy look efficient when it is not. Budget impact and equity lie outside the frontier and are judged separately.

Uncertainty and the probabilistic frontier

Frontier membership can change when parameter values change, and in a probabilistic sensitivity analysis it can differ from one simulation to the next. The HEMA report notes that the cost-effectiveness plane, being pairwise, becomes less useful when several comparators are relevant. It recommends presenting the cost-effectiveness acceptability frontier, a different object showing the probability that the option with the highest expected net benefit is cost effective, whenever more than two options are compared, because the option with the highest probability of being optimal is not necessarily the one with the highest expected net benefit, and the NICE manual (PMG36, section 4.7.15) asks for acceptability curves to include a representation and explanation of that frontier.

The IQWiG efficiency frontier and other frontiers

Germany's Institute for Quality and Efficiency in Health Care (IQWiG) developed a variant under the name efficiency frontier. In its General Methods version 6.1 of January 2022 the frontier was built from the interventions currently used and reimbursed in Germany in one therapeutic area, with benefit on the vertical axis and total net cost per patient on the horizontal axis, the reverse of the usual cost-effectiveness plane. It was meant to inform the negotiation of reimbursement prices without a willingness-to-pay threshold, on which the document says there was no agreement in Germany, and the last segment was extended to judge the cost-effectiveness ratio of a new intervention with more benefit and more cost than the comparators.

Version 6.1 also questioned the mixing assumption. It notes that a combination of two interventions is not always possible in practice, since it would mean redistributing patients between therapies, and that without extended dominance the result is a stepped absolute efficiency frontier whose segments no longer give a gradient that can be read as the reciprocal of a willingness to pay. In version 8.0, issued in December 2025, the efficiency frontier appears in the section on health economic evaluations outside the statutory procedure of §35b SGB V. Cost-effectiveness ratios for more than two treatments can be plotted as one or more efficiency frontiers formed under absolute and extended dominance, and the last segment no longer needs to be extended, as it was previously intended for deriving a price recommendation.

The names efficient frontier, used by Suen and Goldhaber-Fiebert, and efficiency frontier are also used for the same construct in cost-effectiveness analysis. The production possibility frontier and the frontiers estimated by data envelopment analysis are different, since they describe the most output obtainable from given inputs, not the choice between mutually exclusive strategies for one population.

Common errors in building or reading the frontier

The worked example shows what comparing the wrong pairs does. Three other mistakes can change the choice.

1. Reading the mix as a real option. A segment between two strategies stands for a theoretical split of patients between them. Where such a split is impossible or unacceptable, the extended dominance finding needs that caveat attached.
2. Treating the frontier as the decision. Every point on it is optimal for some value of health, but only the threshold picks one.
3. Inconsistent inputs. Strategies estimated for different populations, time horizons or price years cannot share one frontier.

Sources

• Institute for Quality and Efficiency in Health Care (IQWiG). General Methods, version 6.1 of 24 January 2022. Cologne: IQWiG; 2022. Section 4.6. https://www.iqwig.de/methoden/general-methods_version-6-1.pdf
• Institute for Quality and Efficiency in Health Care (IQWiG). General Methods, version 8.0 of 19 December 2025. Cologne: IQWiG; 2025. Section 4.15. https://doi.org/10.60584/General-Methods_V8.0
• 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, 4.7.15 and 4.10.8. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• Steuten L, Thavorn K, Cipriano LE, Guertin JR, McQueen B, Schmidler G, Sullivan S, Wailoo A, Sculpher M. Methods to Analyze and Present Uncertainty in Economic Evaluation to Support HTA Decisions. HEMA Report 2. Health Economics Methods Advisory; 2026. Sections 4.3, 6.4 and 6.6. https://hemamethods.org/wp-content/uploads/2026/10/HEMA-Report-2_For-Publication_100726.pdf
• Suen S, Goldhaber-Fiebert JD. An efficient, non-iterative method of identifying the cost-effectiveness frontier. Medical Decision Making. 2016;36(1):132-136. https://doi.org/10.1177/0272989X15583496