Cost-Effectiveness Acceptability Frontier

Cost-Effectiveness Acceptability Frontier and the Expected-Value Choice

The cost-effectiveness acceptability frontier (CEAF) is the line on an acceptability graph that tracks the option a decision maker should adopt at each threshold and reports how likely that choice is to be correct. It differs from the cost-effectiveness acceptability curves drawn on the same graph, because the option most often cost-effective across simulations need not be the option that maximises expected net benefit. It is built from the probabilistic results behind the cost-effectiveness plane. The NICE manual asks for it whenever acceptability curves are presented, and a 2026 methods advisory report recommends it whenever more than two options are compared.

Why acceptability curves alone can point to the wrong option

An acceptability curve answers one question for each option, the share of simulations in which that option is the best at a given threshold. The adoption decision answers a different question, which option has the highest mean net benefit, and under the net benefit approach that mean is what a decision maker maximising health gain from a fixed budget should use. When the distribution of net benefit is skewed, an option can win in most draws by small margins while another wins in fewer draws by large margins, and the two questions then give different answers.

Fenwick, Claxton and Sculpher set out the link between acceptability curves and decision making in 2001, proposed a cost-effectiveness frontier as a concept more relevant to decision making (later literature uses the name cost-effectiveness acceptability frontier), and clarified how the curves should be used when a decision involves several interventions. That original name should not be confused with the cost-effectiveness frontier page, which covers the efficient frontier of mean costs and effects used in incremental analysis. Barton, Briggs and Fenwick later showed, for comparisons of multiple options, that an option subject to extended dominance can have the highest probability of being cost-effective at some thresholds, and that the optimal option may never have the highest probability. They concluded that acceptability curves can represent decision uncertainty but should not be used to determine the optimal decision, and that the frontier shows the uncertainty surrounding the optimal choice. The 2026 Health Economics Methods Advisory (HEMA) report on uncertainty describes the frontier as showing the option with the greatest expected health benefit at each level of willingness to pay, which is not always the option most likely to be good value.

Computing the frontier from probabilistic draws

The frontier needs the output of a probabilistic sensitivity analysis or bootstrapped trial data, which supply a cost and an effect for every option in each simulation (Fenwick, Marshall, Levy and Nichol describe both routes). Net monetary benefit is calculated for each option in each draw, as follows.

$$\text{NMB}_{j,s}(\lambda) = \lambda E_{j,s} - C_{j,s}$$

where $\lambda$ is the cost-effectiveness threshold in currency per QALY, $E_{j,s}$ and $C_{j,s}$ are the effect and cost of option $j$ in simulation $s$, and $\text{NMB}_{j,s}$ is its net monetary benefit. The frontier at $\lambda$ is then defined as follows.

$$\text{CEAF}(\lambda) = \frac{1}{S} \sum_{s=1}^{S} \mathbf{1}\left[ \text{NMB}_{j^{*},s}(\lambda) = \max_{k} \text{NMB}_{k,s}(\lambda) \right]$$

where $S$ is the number of simulations, $j^{*}$ is the option with the highest mean net benefit across all $S$ draws at that threshold, $k$ runs over all options and $\mathbf{1}[\cdot]$ equals 1 when the condition holds and 0 otherwise. In words, the analyst finds the expected-value choice first and only then reads off its probability. The procedure has five steps.

1. Calculate net benefit. For each draw and option, compute NMB at the threshold.
2. Find the winner of each draw. Record which option has the highest NMB in that draw; the shares of wins give each option's acceptability curve.
3. Find the expected-value choice. Average NMB across draws for each option and take the largest.
4. Read the frontier. The frontier value is the winning share of the option chosen in step 3.
5. Repeat across thresholds. Plot the frontier over a grid of $\lambda$ values, marking which option it follows in each range.

Switch points and the shape of the frontier

Expected net benefit is linear in the threshold for every option, so the option chosen at step 3 changes only where two expected net benefit lines cross. Each crossing is a switch point, and there are at most one fewer switch points than options. For two options on the efficient frontier the crossing satisfies the following condition.

$$\lambda^{*} = \frac{\bar{C}_{2} - \bar{C}_{1}}{\bar{E}_{2} - \bar{E}_{1}}$$

where $\bar{C}$ and $\bar{E}$ are mean costs and effects across the draws, option 2 is the more costly and more effective option, and $\lambda^{*}$ is the switch point. This is the sequential ICER from a fully incremental analysis of mean values, so the frontier changes option at the same thresholds as the deterministic decision rule applied to expected costs and effects. Options that are dominated or extendedly dominated on mean values never carry the frontier, however high their acceptability curves rise.

Three features follow. The frontier is discontinuous, since it jumps from one option's curve to another's at each switch point, and it can fall as well as rise at a jump. It can sit below another option's curve over a range of thresholds, which is the visible sign that the most frequent winner is not the expected-value choice. In a two-option comparison the curves cross at 0.5, where the median incremental net benefit is zero, while the frontier switches where the mean is zero, so the two points separate when the distribution is skewed (see expected net benefit).

Worked example with three options and five draws

The figures are illustrative, and a real analysis would use thousands of draws. Current care A is the reference, and options B and C are compared with it, so A's net benefit is zero in every draw. Costs are in GBP and effects in QALYs.

Switch points (step 1). B against A gives an ICER of GBP 15,000 per QALY ($\Delta C / \Delta E = 3{,}000 / 0.20$). C against B gives an ICER of GBP 25,000 per QALY ($\Delta C / \Delta E = (5{,}500 - 3{,}000) / (0.30 - 0.20)$). Because 15,000 is below 25,000, B is not extendedly dominated, and the frontier should follow A below GBP 15,000, B between GBP 15,000 and GBP 25,000, and C above GBP 25,000. At GBP 15,000 the frontier drops from A's curve at 0.6 to B's at 0.4, a jump downwards.

Net benefit at GBP 20,000 per QALY (step 2). Each entry is 20,000 times the extra QALYs minus the extra cost.

B has the highest mean, 5,000 / 5 = 1,000, against 2,500 / 5 = 500 for C, so B is the expected-value choice. B wins in 2 of 5 draws and C in 3, so the acceptability curves give 0.4 for B and 0.6 for C, and the frontier is 0.4.

Three thresholds side by side (step 3). The same steps at GBP 10,000 and GBP 30,000 give the following.

The value of information (step 4). The expected value of perfect information is the mean of the best NMB in each draw minus the best mean NMB. At GBP 20,000 the best values are 8,000, 3,200, 700, 1,300 and 900, a mean of 2,820, so $\text{EVPI} = 2{,}820 - 1{,}000 = 1{,}820$. At GBP 30,000 the best values are 13,000, 6,200, 3,800, 4,700 and 4,100, a mean of 6,360, so $\text{EVPI} = 6{,}360 - 3{,}500 = 2{,}860$.

Interpretation. At GBP 20,000 the curve for C lies above the frontier, yet adopting C would give up GBP 500 of expected net benefit per person compared with B. The expected loss of each choice, its mean shortfall against the best option in each draw, makes the same point. It is GBP 1,820 for B, equal to EVPI because B is the expected-value choice, and GBP 2,320 for C, and the gap between them is that GBP 500. Moving from GBP 20,000 to GBP 30,000, the chance of a wrong decision falls from 0.6 to 0.4 while EVPI rises from 1,820 to 2,860, mainly because in draw 1 C falls GBP 13,000 short of B. Barton, Briggs and Fenwick showed that EVPI can increase when the probability of making the wrong decision decreases, and that the frontier can be augmented by EVPI to show the potential gains from further research.

Reading and reporting the frontier

A frontier is read at a vertical line drawn at the threshold of interest, noting which option it follows and at what height. Because the result depends on the cost-effectiveness threshold, the HEMA report recommends stating the threshold or threshold range explicitly.

Section 4.7.15 of the NICE manual (PMG36) says the presentation of acceptability curves should include a representation and explanation of the frontier, described as a region on a plot showing how likely the technology with the highest expected net benefit is to be cost effective. The same section asks for the probability of cost-effectiveness at maximum acceptable ICERs of GBP 25,000 to GBP 35,000 per QALY gained, together with the error probability, particularly when there are more than two alternatives. Section 4.7.12 says the committee's preferred estimate should come from a probabilistic analysis when possible unless the model is linear.

The HEMA report recommends that expected loss, the size of the potential loss from decision uncertainty, accompany the curves, and its proposed minimum reporting adds the number of simulations with evidence that the results are stable. It also cautions that no single output should determine how uncertainty is interpreted.

Thresholds at one and three times income per head, the GDP-based criteria once used by WHO-CHOICE, appear as two vertical lines on a frontier drawn per DALY averted (see the cost-effectiveness plane). A 2021 WHO-CHOICE update recommends against using a threshold as a decision rule.

What the frontier leaves out

The frontier is a probability, and probabilities say nothing about the size of what is at stake. A frontier of 0.4 can accompany a small or a large expected loss from a wrong choice, which is why EVPI, the starting point for value of information analysis, belongs beside it, and the HEMA report recommends reporting at least the population EVPI with the curves and frontier. The frontier also inherits every limitation of the probabilistic analysis behind it, so uncertainty that is not characterised in the input distributions, such as alternative model structures, is not reflected unless it is modelled. The HEMA report recommends reporting the probabilistic results for each scenario used to examine uncertainty outside the probabilistic analysis. Near a switch point the expected net benefits of two options are almost equal, so Monte Carlo error can move the switch, and section 4.7.11 of PMG36 asks for enough simulations to minimise that error.

Three misreadings recur.

• Treating a low frontier value as a reason to reject the expected-value choice; it measures decision uncertainty and points towards the value of further evidence, not towards another option.
• Reading the frontier as a confidence level for the ICER, or as a test of statistical significance.
• Relying on the scatter on the cost-effectiveness plane to show uncertainty across several options, which Barton, Briggs and Fenwick found of limited use because it cannot represent correlation between the options.

Sources

• Barton GR, Briggs AH, Fenwick EA. Optimal cost-effectiveness decisions: the role of the cost-effectiveness acceptability curve (CEAC), the cost-effectiveness acceptability frontier (CEAF), and the expected value of perfection information (EVPI). Value in Health. 2008;11(5):886-897. doi:10.1111/j.1524-4733.2008.00358.x
• 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(11):673-677. doi:10.34172/ijhpm.2020.244
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford: Oxford University Press; 2006.
• Fenwick E, Claxton K, Sculpher M. Representing uncertainty: the role of cost-effectiveness acceptability curves. Health Economics. 2001;10(8):779-787. doi:10.1002/hec.635
• Fenwick E, Marshall DA, Levy AR, Nichol G. Using and interpreting cost-effectiveness acceptability curves: an example using data from a trial of management strategies for atrial fibrillation. BMC Health Services Research. 2006;6:52. doi:10.1186/1472-6963-6-52
• Hutubessy R, Chisholm D, Edejer TT. 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; published 31 January 2022, last updated 13 October 2026. Sections 4.7.11, 4.7.12 and 4.7.15.
• 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. Pages ES9, 52 to 55, 65 and A2.