Cost-Effectiveness Acceptability Curve (CEAC)

A cost-effectiveness acceptability curve shows how the probability that an intervention is cost-effective changes across a range of cost-effectiveness thresholds. The sections below explain how CEAC probabilities are calculated from probabilistic sensitivity analysis, how two-option and multi-option curves differ, and why probability alone should not determine the preferred alternative.

A CEAC describes decision uncertainty rather than the expected value of choosing an option. It should be interpreted alongside expected net benefit, the cost-effectiveness plane and information about the model’s assumptions and limitations.

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. Each point on the curve summarises results from probabilistic simulations at one threshold.

The probability depends on the intervention, comparator, model, outcome measure and threshold. It is not a universal characteristic of the intervention and should not be transferred to a different decision context.

• The horizontal axis shows the cost-effectiveness threshold in currency per health-outcome unit.
• The vertical axis shows a probability from zero to one or a percentage from 0% to 100%.
• Each curve represents one alternative under the stated model and evidence.
• Each point answers a threshold-specific uncertainty question.
• 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 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 is positive. The CEAC probability is the proportion of simulations satisfying that condition.

INMBᵢ(λ) = [λ × ΔEᵢ] − ΔCᵢ

Probability intervention is cost-effective at λ = Number of simulations with INMBᵢ(λ) > 0 ÷ Total simulations

In this notation:

• i identifies one probabilistic simulation.
• λ is the cost-effectiveness threshold.
• ΔEᵢ is the simulated incremental health effect.
• ΔCᵢ is the simulated incremental cost.
• INMBᵢ(λ) is the simulated incremental net monetary benefit at that threshold.

A worked two-option example

Suppose a probabilistic sensitivity analysis contains 10,000 simulations. At a threshold of £30,000 per QALY, the evaluated intervention has positive INMB in 7,800 simulations.

The estimated probability that the intervention is cost-effective at that threshold is therefore 78%. This does not mean that adopting the intervention has a 78% probability of producing a health gain or saving money.

Probability = 7,800 ÷ 10,000 = 0.78 = 78%

• The example uses synthetic simulation results.
• The 78% value applies only to the stated threshold, model and comparison.
• The remaining 22% of simulations favour the comparator on cost-effectiveness grounds.
• The result does not show how large the net benefit or loss is in either group of simulations.
• The result does not establish affordability or require reimbursement.

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.

• A CEAC point at one threshold should not be interpreted as applying at every threshold.
• Curve crossings show thresholds where the probability ranking of alternatives changes.
• A steep section shows that the probability changes quickly across a threshold interval.
• A flat section shows that probability is relatively insensitive to threshold changes over that interval.
• The plotted threshold range should be relevant to the decision context and clearly labelled.

How two-option and multi-option CEACs differ

With two alternatives, the intervention’s probability of being cost-effective is the proportion of simulations in which its INMB is positive. Except for exact ties, the comparator’s probability is the complement of that value.

With several mutually exclusive alternatives, NMB is calculated for every option within each simulation. An option’s CEAC probability is the proportion of simulations in which it has the greatest NMB among all included alternatives.

NMBᵢⱼ(λ) = [λ × Eᵢⱼ] − Cᵢⱼ

For each simulation i, the cost-effective option is the alternative j with the greatest simulated NMB at threshold λ.

• Multi-option CEAC probabilities depend on every alternative included in the analysis.
• Adding or removing an alternative can change all CEAC probabilities.
• Multi-option probabilities should sum to 100% at each threshold when alternatives are mutually exclusive and ties are handled consistently.
• A multi-option CEAC should not be created by comparing every option independently with one common baseline.
• Each alternative should use the same population, perspective, time horizon and evidence framework.

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 magnitude of its advantages and disadvantages.

Expected-value decision-making instead selects the option with the greatest average NMB across simulations. A less frequently optimal option may still have greater expected NMB if its favorable outcomes are substantially larger or its unfavorable outcomes are less severe.

• CEAC probability describes decision uncertainty.
• Expected NMB determines the preferred option under an expected-value decision rule.
• Probability and expected NMB answer different questions.
• A high probability does not indicate a large expected advantage.
• The preferred option should not be selected from CEAC height alone.

How the CEAF identifies the expected-value choice

A cost-effectiveness acceptability frontier shows the probability that the option with the greatest expected NMB is cost-effective at each threshold. It follows the expected-value choice rather than simply taking the highest probability curve.

The CEAF can lie below another option’s CEAC because the option with the greatest expected NMB need not have the highest probability of being optimal. This apparent difference is informative rather than contradictory.

• The CEAF identifies the probability associated with the expected-NMB-maximising option.
• A switch in the CEAF occurs when the option with greatest expected NMB changes.
• The CEAF should be labelled separately from ordinary option-level CEACs.
• The difference between CEAC and CEAF results can reveal why probability alone is an incomplete decision rule.

How the CEAC relates to the cost-effectiveness plane

The cost-effectiveness plane displays simulated incremental cost-and-effect pairs for a particular comparison. At a stated threshold, the proportion of two-option simulation points lying in the intervention-favouring region corresponds to the CEAC probability.

The plane retains information about the quadrants, scale and correlation of incremental costs and effects. The CEAC compresses those results into a probability at each threshold.

• The cost-effectiveness plane shows the joint distribution of incremental cost and effectiveness.
• The CEAC shows the proportion of simulations favoring an option across thresholds.
• The plane can reveal dominance patterns hidden by the CEAC.
• The CEAC is easier to read across many thresholds but provides less information about the underlying distribution.
• Both displays should use the same simulations and decision rule.

How the CEAC relates to expected value of perfect information

A CEAC shows how uncertain the identity of the cost-effective option is, but it does not measure the consequences of making the wrong decision. Value-of-information analysis incorporates the size of the potential net-benefit losses.

Expected value of perfect information compares the expected NMB available with perfect information with the greatest expected NMB available under current information. A high CEAC uncertainty does not necessarily imply high value of information, and a lower uncertainty does not necessarily imply that further research has little value.

• CEAC probability describes how often each option is optimal across simulations.
• Expected value of perfect information measures the expected loss from current uncertainty.
• Research value depends on the consequences of uncertainty as well as its probability.
• A CEAC should not be used alone to decide whether further research is worthwhile.

What curve endpoints can and cannot tell us

At a zero threshold, health outcomes receive no monetary value, so the least costly option tends to be preferred. At very high thresholds, health outcomes receive much greater weight, so the most effective option tends to become more attractive.

Uncertainty and correlations can prevent observed curves from reaching exactly zero or one within the plotted range. Endpoints should therefore be interpreted from the model and threshold range rather than treated as mandatory visual properties.

• A CEAC does not have to begin at zero or one.
• A CEAC does not have to end at zero or one.
• Curves may cross more than once when several alternatives or complex uncertainty patterns are present.
• A restricted threshold range can conceal crossings outside the displayed interval.
• Extrapolating a CEAC beyond the calculated 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 probability estimates, especially when alternatives have similar NMB.

The simulation count should be large enough for the reported probabilities and curve shape to be stable. Analysts should assess convergence rather than assume that one arbitrary number of simulations is always sufficient.

• Increasing the number of simulations reduces Monte Carlo error.
• Repeating an analysis with different random seeds can help assess numerical stability.
• Small probability differences may be simulation noise rather than meaningful evidence.
• The model’s convergence checks and final simulation count should be reported.
• More simulations do not correct biased inputs or structural model errors.

What uncertainty a CEAC does not capture automatically

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

A smooth CEAC can therefore give a false impression of completeness. Structural uncertainty, scenario analysis and evidence quality should be reported alongside the probabilistic result.

• Parameter uncertainty appears only when distributions have been assigned and sampled appropriately.
• Structural uncertainty requires alternative model structures or justified scenarios.
• Methodological uncertainty may require alternative perspectives, time horizons or assumptions.
• Threshold uncertainty is usually explored by presenting results across thresholds rather than sampling one universally correct threshold.
• Evidence omissions cannot be repaired by increasing the number of simulations.

How to calculate a CEAC in Excel

Excel can calculate a two-option CEAC when simulation-level costs and health outcomes have already been generated correctly. Each row should represent one internally consistent probabilistic simulation, and every threshold should be applied to the same simulation results.

The worksheet should keep sampled inputs, calculated outcomes, NMB values and probability summaries in clearly separated areas. The CEAC calculation should be auditable without relying on VBA.

1. Place one probabilistic simulation on each row.
2. Calculate simulated incremental cost and incremental effectiveness.
3. Enter the threshold values in a separate ordered range.
4. Calculate simulation-level INMB with =(Threshold*IncrementalEffect)-IncrementalCost.
5. Count positive INMB results with =COUNTIF(INMBRange,">0").
6. Divide the positive count by the number of valid simulations.
7. Repeat the calculation for every threshold.
8. Plot threshold values as X and probabilities as Y using an XY scatter chart with lines.
9. Set the vertical axis from 0 to 1 or from 0% to 100%.
10. Label every curve, threshold unit and probability scale clearly.

For several alternatives, calculate option-level NMB within each simulation. Identify the option with the maximum NMB in each row, then calculate the proportion of rows won by each alternative at every threshold.

Common mistakes and safeguards

CEAC errors often result from treating probability as value, comparing inconsistent simulations or omitting alternatives. These mistakes can produce a polished curve that answers the wrong decision question.

The safeguard is to preserve simulation-level consistency and report expected NMB alongside the CEAC. The model, alternatives, threshold range and included uncertainty should remain explicit.

• Selecting the highest CEAC curve instead of the greatest-expected-NMB option can produce the wrong decision.
• Treating 78% cost-effective as a 78% probability of clinical benefit misstates the result.
• Calculating the mean of simulation-specific ICERs produces an invalid basis for a CEAC.
• Sampling costs and effects independently when they are correlated distorts decision uncertainty.
• Adding or removing an alternative without recalculating all probabilities invalidates a multi-option CEAC.
• Allowing multi-option probabilities to sum to more or less than 100% indicates inconsistent classification or tie handling.
• Using too few simulations can create unstable curve crossings.
• Presenting only parameter uncertainty can conceal structural uncertainty.
• Treating a CEAC as an affordability analysis confuses cost-effectiveness with budget impact.

What should be reported

A transparent CEAC should allow readers to understand which uncertainty is represented and reproduce the probability calculation. A curve without its model context and expected-net-benefit result is insufficient.

The following information makes the CEAC auditable and prevents probability from being mistaken for the decision rule:

• Report every alternative included in the analysis.
• Report the population, perspective, time horizon and health-outcome measure.
• Report the probabilistic methods, distributions, correlations and simulation count.
• Report the threshold range, currency, price year and health unit.
• Report whether probabilities come from positive two-option INMB or maximum multi-option NMB.
• Report the expected NMB for every alternative at decision-relevant thresholds.
• Identify the option with the greatest expected NMB.
• Report the CEAF when it materially clarifies the expected-value decision.
• Report Monte Carlo stability checks.
• Report structural and methodological uncertainty separately.
• Report value-of-information results separately when further research is being considered.
• Report budget impact and wider HTA considerations separately from the CEAC.