Signature
CEAF = CEAC_(j*), where j* = argmax_j ENB_j; P_err = 1 - CEAC_(j*)
| Inputs | Definition | Unit |
|---|---|---|
j* | Index of the option with the highest ENB_j, the option chosen under current information | option index |
ENB_j | Mean net monetary benefit of option j across the same simulations, listed across options | currency per person |
CEAF | CEAC value of the option with the highest expected net monetary benefit at threshold lambda | probability from 0 to 1 |
|---|---|---|
P_err | Probability that the option with the highest expected net monetary benefit is not the option with the highest net monetary benefit | probability from 0 to 1 |
CEAC_jMulti-option CEAC value of option j at threshold lambda, listed across options (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.
Implementations
Excel
Frontier value at one threshold
With CEAC values in the named range CEACValues and expected net monetary benefits in ENBValues, both listed in the same option order, Excel returns the CEAC of the option with the highest expected net monetary benefit. The error probability is 1 minus this cell.
=INDEX(CEACValues,MATCH(MAX(ENBValues),ENBValues,0))
Assumptions
Frontier and CEACs from the same simulations
ENB_j and CEAC_j are calculated from the same draws at the same threshold, so the frontier switches between options at the threshold where the expected net monetary benefits cross, which need not be where the curves cross.
Worked examples
Frontier below the other option's curve
In the two-option example, option A has an expected net monetary benefit of £10,000 and option B £9,200, so A, the first option, is chosen. The frontier takes A's CEAC of 0.2, below B's 0.8, and the error probability is 0.8. B wins four draws by between £100 and £400 but loses one by £5,000, so its frequent small gains do not outweigh the single large loss.
CEAC_j = [0.2,0.8]; ENB_j = [10000,9200]; j* = 1; CEAF = 0.2; P_err = 0.8
Common errors
Choosing the option with the highest CEAC
The option most often optimal need not have the highest expected net monetary benefit. In the worked example, choosing B because its CEAC is 0.8 forgoes £800 per person on average compared with A. With several options, an extendedly dominated option can have the highest CEAC at some thresholds.
Sources
Proposal of the acceptability frontier
Fenwick E, Claxton K, Sculpher M. Representing uncertainty: the role of cost-effectiveness acceptability curves. Health Economics. 2001;10(8):779-787.
NICE manual on the acceptability frontier
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 (the presentation of CEACs includes a representation and explanation of the cost-effectiveness acceptability frontier, the probability that the technology with the highest expected net benefit is cost effective, and the error probability).
Canonical Identity
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