Signature
CEAC_j = (1/N) * sum_(i=1)^N [1(NMB_ij >= NMBmax_i)]
| Inputs | Definition | Unit |
|---|---|---|
N | Number of probabilistic simulations in which every option is evaluated | count |
NMB_ij | Simulated health effect of option j valued at lambda minus its simulated cost in simulation i, listed across all simulations | currency per person |
NMBmax_i | Largest net monetary benefit among all included options in simulation i, listed across all simulations | currency per person |
CEAC_j | Proportion of simulations in which option j has the highest net monetary benefit at threshold lambda | 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.
Try this function
Implementations
Excel
Share of draws won by one option
With each option's net monetary benefit in adjacent columns B to D, one row per simulation, a helper column RowMax holds =MAX(B2:D2) filled down. The formula then returns the share of rows in which the option in the named range OptionNMB equals the row maximum.
=SUMPRODUCT(--(OptionNMB=RowMax))/ROWS(OptionNMB)
Assumptions
Every option evaluated in the same simulations
All options are run with the same parameter draw in each simulation, so NMBmax_i compares options under the same state of the world and the correlation between their net benefits is preserved.
Complete set of options
The probabilities depend on every option included. Adding or removing an option can change every CEAC value, so all probabilities are recalculated whenever the set of options changes.
Worked examples
Two options with the most frequent winner not preferred
At one stated threshold, option A has net monetary benefits of £10,000, £12,000, £9,000, £11,000 and £8,000 in five illustrative simulations, and option B has £10,200, £12,300, £9,100, £11,400 and £3,000. A has the highest value only in the fifth draw, so its CEAC is 0.2 and B's is 0.8. The figures match the article's worked example.
N = 5; NMB_ij = [10000,12000,9000,11000,8000]; NMBmax_i = [10200,12300,9100,11400,8000]; CEAC_j = 0.2
Common errors
Building a multi-option curve from pairwise comparisons
Comparing each option separately with one common baseline and plotting the pairwise probabilities gives values that can sum to more than 1 and do not answer which option is best. Each draw is credited to the single option with the highest net monetary benefit.
Sources
CEACs for several interventions
Fenwick E, Claxton K, Sculpher M. Representing uncertainty: the role of cost-effectiveness acceptability curves. Health Economics. 2001;10(8):779-787.
CEACs, the frontier and EVPI with multiple options
Barton GR, Briggs AH, Fenwick EA. 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.
Canonical Identity
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