Signature
CEAC = (1/N) * sum_(i=1)^N [1(lambda * Delta_E_i - Delta_C_i > 0)]
| Inputs | Definition | Unit |
|---|---|---|
N | Number of probabilistic simulations, each with its own draw of every uncertain parameter | count |
lambda | Monetary value placed on one unit of health effect at this point of the curve | currency per unit of health effect, for example £ per QALY |
Delta_E_i | Health effect of the intervention minus that of the comparator in simulation i, listed across all simulations | health-outcome unit per person, for example QALYs |
Delta_C_i | Cost of the intervention minus that of the comparator in simulation i, listed across all simulations | currency per person |
CEAC | Proportion of simulations in which the intervention has positive incremental net monetary benefit at threshold lambda, read as the probability that it is cost-effective given the model and current evidence | probability from 0 to 1 |
|---|
Function
Cost-effectiveness acceptability function
Maps the simulated costs and health effects of mutually exclusive options from a probabilistic sensitivity analysis, together with a threshold, to the probability that each option has the highest net monetary benefit at that threshold. Evaluated across a range of thresholds, it traces the cost-effectiveness acceptability curve.
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Implementations
Excel
Two-option CEAC in one cell
With simulated incremental effects in the named range IncEffect and incremental costs in IncCost, one row per simulation, SUMPRODUCT counts the draws with positive incremental net monetary benefit at the threshold in the named cell Threshold and divides by the number of simulations.
=SUMPRODUCT(--(Threshold*IncEffect-IncCost>0))/ROWS(IncEffect)
Excel
CEAC values across a threshold range
With threshold values in column H from row 2, the formula in I2, filled down, returns the CEAC at each threshold from the same simulations. Column H against column I is then plotted as an XY scatter chart with lines, with the vertical axis fixed from 0 to 1.
=SUMPRODUCT(--($H2*IncEffect-IncCost>0))/ROWS(IncEffect)
Assumptions
Paired incremental results from one probabilistic analysis
Delta_E_i and Delta_C_i come from the same simulation, in which every uncertain parameter is sampled from a distribution representing current evidence. Sampling costs and effects separately would discard their correlation and distort the curve.
Sign of incremental net monetary benefit classifies each draw
A draw favours the intervention when lambda times Delta_E_i minus Delta_C_i is greater than zero. This rule is correct in all four quadrants of the cost-effectiveness plane, including south-west draws, where the intervention is favoured only when the saving per unit of effect forgone exceeds lambda.
Probability conditional on the represented uncertainty
Reading the proportion as the probability of cost-effectiveness treats the model parameters as uncertain quantities with distributions, as probabilistic sensitivity analysis does. The value reflects only the uncertainty in the model: parameters held fixed and structural alternatives not modelled do not appear in it.
Worked examples
Five simulations at £30,000 per QALY
Five illustrative simulations give incremental effects of 0.40, 0.25, 0.10, 0.30 and minus 0.05 QALYs and incremental costs of £6,000, £9,000, £5,000, £4,000 and minus £3,000. At £30,000 per QALY the incremental net monetary benefits are £6,000, minus £1,500, minus £2,000, £5,000 and £1,500, so three of the five are positive and the CEAC is 0.6. The fifth draw lies in the south-west quadrant with a ratio of £60,000 per QALY forgone and counts in favour of the intervention, because the saving per QALY forgone exceeds the threshold. A real analysis would use thousands of simulations.
lambda = 30000; N = 5; Delta_E_i = [0.40,0.25,0.10,0.30,-0.05]; Delta_C_i = [6000,9000,5000,4000,-3000]; CEAC = 0.6
Same simulations at a zero threshold
At a threshold of zero, health effects receive no monetary value, so a draw favours the intervention only when it saves money. Only the fifth draw does, so the curve starts at 0.2 rather than at zero. As the threshold grows very large, the curve approaches the share of draws with a health gain, here 0.8, so it need not reach 1.
lambda = 0; N = 5; Delta_E_i = [0.40,0.25,0.10,0.30,-0.05]; Delta_C_i = [6000,9000,5000,4000,-3000]; CEAC = 0.2
Common errors
Classifying draws by ICER below the threshold
Counting a draw as cost-effective when its ratio lies below lambda misclassifies north-west draws, where a negative ratio means the intervention is dominated, and south-west draws, where the intervention is favoured only when the ratio exceeds lambda. In the first worked example the fifth draw, at £60,000 per QALY forgone, would be counted against the intervention and the CEAC would fall from 0.6 to 0.4.
Reading the CEAC as a probability of clinical benefit
A CEAC of 0.6 is the share of simulations with positive incremental net monetary benefit at one threshold. It is not the probability that the intervention improves health or saves money, and it says nothing about the size of the gain or loss in either group of simulations.
Treating the CEAC as a significance test
Requiring the curve to exceed 0.95 before adoption imposes a statistical convention on a decision problem. The adoption decision rests on expected net benefit, and the spread of net benefit bears on whether further evidence is worth acquiring.
Sources
Origin of the acceptability curve
van Hout BA, Al MJ, Gordon GS, Rutten FFH. Costs, effects and C/E-ratios alongside a clinical trial. Health Economics. 1994;3(5):309-319.
Shapes and misreadings of the CEAC
Fenwick E, O'Brien BJ, Briggs A. Cost-effectiveness acceptability curves: facts, fallacies and frequently asked questions. Health Economics. 2004;13(5):405-415.
NICE manual on presenting CEACs
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 31 March 2026. Chapter 4 Economic evaluation, section 4.7.15 (cost-effectiveness acceptability curves plot a range of maximum acceptable ICERs against the probability that the intervention is cost effective; the probability at £25,000 to £35,000 per QALY gained and the error probability are presented).
Canonical Identity
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