Cost-Effectiveness Acceptability Curve (CEAC)

Cost-Effectiveness Acceptability Curve (CEAC) Calculation and Interpretation

A cost-effectiveness acceptability curve summarises a probabilistic sensitivity analysis by recording, at each threshold, the proportion of simulations in which each option has the highest net monetary benefit. The calculation differs between two-option and multi-option comparisons. The 2026 uncertainty report of the Health Economics Methods Advisory (the HEMA report) recommends CEACs, or where appropriate the cost-effectiveness acceptability frontier, for communicating probabilistic results, together with the population expected value of perfect information at a minimum.

A CEAC describes decision uncertainty rather than the expected value of choosing an option. Probability alone should not determine the preferred alternative, so the curve is read alongside expected net benefit, the expected loss from a wrong choice and the assumptions left outside the model.

What a CEAC shows

A CEAC plots the cost-effectiveness threshold on the horizontal axis and the probability that an alternative is cost-effective on the vertical axis. The probability depends on the intervention, comparator, model, outcome measure and threshold, so it is not a universal characteristic of the intervention. A CEAC does not show the magnitude of the expected net benefit or loss.

How CEAC probabilities are calculated

Probabilistic sensitivity analysis repeatedly samples uncertain model inputs and calculates costs and health outcomes for every alternative. Net monetary benefit (NMB) is then calculated within each simulation at each threshold.

For a two-option comparison, the intervention is cost-effective in a simulation when its incremental net monetary benefit (INMB) is positive. The CEAC probability is the proportion of simulations satisfying that condition.

$$\text{INMB}_i(\lambda) = \lambda \, \Delta E_i - \Delta C_i$$

Here $i$ identifies one probabilistic simulation, $\lambda$ is the cost-effectiveness threshold, $\Delta E_i$ is the simulated incremental health effect and $\Delta C_i$ is the simulated incremental cost. The CEAC averages, over all simulations, an indicator of whether this quantity is positive.

$$\text{CEAC}(\lambda) = \frac{1}{N} \sum_{i=1}^{N} \mathbf{1}\left[\text{INMB}_i(\lambda) > 0\right]$$

Here $N$ is the total number of simulations, and the indicator $\mathbf{1}[\cdot]$ equals one when the condition in brackets holds and zero otherwise.

Illustrative worked example with one threshold

The figures in this example are illustrative and are not taken from any real appraisal. A probabilistic sensitivity analysis contains 10,000 simulations, and at a threshold of GBP 30,000 per QALY the evaluated intervention has positive INMB in 7,800 of them.

$$\text{CEAC}(30{,}000) = \frac{7{,}800}{10{,}000} = 0.78$$

Here the estimated probability that the intervention is cost-effective at GBP 30,000 per QALY is 0.78, or 78%. This does not mean that adopting the intervention has a 78% probability of producing a health gain or saving money.

How the CEAC changes across thresholds

Changing the threshold changes the monetary value assigned to health outcomes in every simulation. Alternatives producing more health generally become more attractive as the threshold rises, while less costly alternatives may be preferred at lower thresholds.

The CEAC traces these changes across a selected threshold range. Its shape reflects the joint uncertainty in costs and health outcomes rather than uncertainty in the threshold itself. Because the result depends on the threshold, the HEMA report asks for the relevant threshold or threshold range to be stated explicitly.

• Curve crossings show thresholds where the probability ranking of alternatives changes.
• A restricted threshold range can conceal crossings outside the displayed interval.

How two-option and multi-option CEACs differ

With two alternatives, the comparator's probability is the complement of the intervention's, except for exact ties. With several mutually exclusive alternatives, NMB is calculated for every option within each simulation, and an option's CEAC probability is the proportion of simulations in which it has the greatest NMB among all included alternatives.

$$\text{CEAC}_j(\lambda) = \frac{1}{N} \sum_{i=1}^{N} \mathbf{1}\left[\text{NMB}_{ij}(\lambda) = \max_k \text{NMB}_{ik}(\lambda)\right]$$

Here $\text{NMB}_{ij}(\lambda) = \lambda E_{ij} - C_{ij}$ is the net monetary benefit of option $j$ in simulation $i$, $E_{ij}$ and $C_{ij}$ are its simulated health outcome and cost, and $k$ runs over every option included in the analysis.

• Multi-option probabilities depend on every alternative included, so adding or removing one can change them all.
• They should sum to 100% at each threshold when ties are handled consistently.
• A multi-option CEAC should not be built by comparing every option separately with one common baseline.

Why the highest CEAC probability is not always the decision

The option with the highest probability of being cost-effective is not necessarily the option with the greatest expected net benefit. Probability records how often an option ranks first but ignores the size of its advantages and disadvantages, and the HEMA report notes that a CEAC does not show the consequences of choosing an option that later proves not to be optimal.

Expected-value decision-making selects the option with the greatest average NMB across simulations. With several options the divergence can be marked. Barton, Briggs and Fenwick showed that an extendedly dominated option can have the highest probability of being cost-effective at some thresholds, and that the optimal option may never have the highest probability.

Expected loss as the companion to the CEAC

Expected loss measures the health or money expected to be forgone by deciding on current evidence, combining how likely a wrong choice is with how much would be lost if it were made. The HEMA report recommends that expected loss accompany the CEAC because it shows the size of the potential loss that the probability leaves out.

$$\text{EL}_j(\lambda) = \frac{1}{N} \sum_{i=1}^{N} \left[ \max_k \text{NMB}_{ik}(\lambda) - \text{NMB}_{ij}(\lambda) \right]$$

Here $\text{EL}_j(\lambda)$ is the expected loss from choosing option $j$ at threshold $\lambda$, measured in the same units as NMB. The option with the greatest expected NMB has the smallest expected loss, and that smallest value equals the per-person EVPI. A high probability of error does not on its own imply a high EVPI, and Barton, Briggs and Fenwick showed that EVPI can rise while the probability of a wrong decision falls.

The HEMA report gives an illustrative oncology case in which, at the threshold used, a new medicine has the highest net benefit in only 30% of simulations, so recommending it is wrong with a probability of about 70%. Its expected incremental net health benefit is still positive at 0.10 QALYs per patient, because the medicine is slightly worse than standard care in most simulations but gives a large survival gain in a minority. The expected loss from choosing the new medicine is 0.14 QALYs per patient against 0.24 QALYs from choosing standard care, and the difference of 0.10 QALYs is the expected incremental net health benefit, and the smaller loss of 0.14 QALYs is the per-patient EVPI.

The cost-effectiveness acceptability frontier follows the option with the greatest expected NMB and plots its probability of being cost-effective. The HEMA report recommends presenting the frontier when more than two options are compared, and the NICE manual (PMG36, section 4.7.15) asks for the presentation of CEACs to include a representation and explanation of the frontier. It also asks for the probability that the treatment is cost-effective at GBP 25,000 to GBP 35,000 per QALY gained and the error probability, particularly when there are more than two alternatives.

How the CEAC relates to the cost-effectiveness plane

The cost-effectiveness plane displays simulated incremental cost-and-effect pairs for one comparison. At a stated threshold, the proportion of two-option simulation points lying below the threshold line through the origin, whose slope is $\lambda$, corresponds to the CEAC probability. The plane is of limited use with several options because pairwise scatter plots cannot show the correlation between options.

What the ends and shape of the curve reveal

At a zero threshold, health outcomes receive no monetary value, so a two-option CEAC equals the proportion of simulations in which the intervention costs less. At very high thresholds the curve approaches the proportion of simulations in which the intervention produces more health.

Fenwick, O'Brien and Briggs showed that the smooth curve rising from zero towards one is only a special case. CEACs do not have to cut the vertical axis at zero, do not have to approach one, are not always monotonically increasing and are not cumulative distribution functions. Extrapolating a CEAC beyond the calculated threshold range is not justified.

How simulation count affects the curve

A CEAC is estimated from a finite number of probabilistic simulations. Too few simulations can produce visible Monte Carlo noise and unstable crossings, especially when alternatives have similar NMB.

The NICE manual (PMG36, section 4.7.11) asks for enough simulations to minimise the effect of Monte Carlo error, and notes that reviewing the variance of outputs as the number of simulations increases can show whether more runs are needed.

What uncertainty a CEAC does not capture

A CEAC reflects only the uncertainty represented in the probabilistic model. Parameters treated as fixed, excluded structural uncertainty and unmodelled evidence limitations do not appear in the curve.

The HEMA report warns that summarising uncertainty in a single CEAC can give a misleading impression of precision, and that presenting a CEAC prominently may draw attention away from uncertainties outside the probabilistic analysis. When scenario analysis is used outside the probabilistic analysis, it recommends reporting the probabilistic results for each scenario.

How to calculate a CEAC in Excel

Excel can calculate a two-option CEAC once simulation-level costs and health outcomes have been generated correctly. Every threshold should be applied to the same simulation results.

1. Place one probabilistic simulation on each row with its incremental cost and incremental effect.
2. Enter the threshold values in a separate ordered range.
3. Calculate simulation-level INMB with =(Threshold*IncrementalEffect)-IncrementalCost.
4. Count positive INMB results with =COUNTIF(INMBRange,">0") and divide by the number of valid simulations.
5. Repeat for every threshold and plot thresholds against probabilities as a labelled XY scatter chart with lines.

For several alternatives, option-level NMB is calculated within each simulation, the option with the maximum NMB in each row is identified, and the proportion of rows won by each alternative is calculated at every threshold. Expected loss follows from the same sheet as the row average of the maximum NMB minus each option's NMB.

Common mistakes and safeguards

CEAC errors often result from treating probability as value, comparing inconsistent simulations or omitting alternatives.

• Selecting the highest CEAC curve instead of the greatest-expected-NMB option can produce the wrong decision.
• Classifying simulations by whether their ICER falls below the threshold misclassifies the north-west and south-west quadrants; the sign of INMB avoids this.
• Treating a CEAC as an affordability analysis confuses cost-effectiveness with budget impact.
• Sampling costs and effects independently when they are correlated distorts decision uncertainty.
• Requiring a CEAC probability above 0.95 before adoption imposes an arbitrary rule of inference on a decision that should rest on expected net benefit.

What should be reported with a CEAC

The HEMA report proposes minimum reporting expectations that place the CEAC beside expected values and the consequences of error, and the list below draws on them.

1. Report every alternative and the expected incremental costs, health effects and net benefit from the probabilistic analysis, with the deterministic result and any material difference explained.
2. Report the probability that each option has the highest net benefit and the expected loss across the relevant threshold range and, where relevant, across a range of prices.
3. Report the frontier where more than two options are compared.
4. Report the number of simulations and evidence that the probabilistic results are stable.
5. State the important uncertainties omitted from the analysis and, where it can be judged credibly, their likely direction of effect.
6. Report value-of-information results, at a minimum the population EVPI.

Sources

• 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, O'Brien BJ, Briggs A. Cost-effectiveness acceptability curves: facts, fallacies and frequently asked questions. Health Economics. 2004;13(5):405-415. doi:10.1002/hec.903
• Claxton K. The irrelevance of inference: a decision-making approach to the stochastic evaluation of health care technologies. Journal of Health Economics. 1999;18(3):341-364. doi:10.1016/S0167-6296(98)00039-3
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford: Oxford University Press; 2006.
• Barton GR, Briggs AH, Fenwick EAL. 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
• 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 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. Executive summary, glossary and sections 6.1, 6.4 to 6.6, 6.8 and 7.4 and Appendix A.2. https://hemamethods.org/wp-content/uploads/2026/10/HEMA-Report-2_For-Publication_100726.pdf