Acceptability frontier and error probability

Selects the option with the highest expected net monetary benefit, the mean across simulations, and takes that option's CEAC value as the cost-effectiveness acceptability frontier at threshold lambda. The error probability is the complement, the share of simulations in which the chosen option does not have the highest net monetary benefit.

Signature

CEAF = CEAC_(j*), where j* = argmax_j ENB_j; P_err = 1 - CEAC_(j*)
Inputs
InputsDefinitionUnit
j*Index of the option with the highest ENB_j, the option chosen under current informationoption index
ENB_jMean net monetary benefit of option j across the same simulations, listed across optionscurrency per person
Output
CEAFCEAC value of the option with the highest expected net monetary benefit at threshold lambdaprobability from 0 to 1
P_errProbability that the option with the highest expected net monetary benefit is not the option with the highest net monetary benefitprobability from 0 to 1
  • CEAC_j Multi-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.

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  • 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).

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