Cost-Effectiveness Acceptability Frontier and Expected Opportunity Loss

Definition and scope

Decision summaries from joint uncertainty draws that distinguish the strategy with highest expected net benefit from the probability that a strategy is optimal and the expected loss from choosing it. The target population, use, and analysis remain protocol decisions; this card explains the choices and their consequences rather than approving a study.

Operational specification

Specify the candidate strategies, joint cost/effect draws, common uncertainty distribution, willingness-to-pay threshold, and net-benefit convention. The optimal decision under expected net benefit maximizes mean NMB, not the probability of being best. Preserve dependencies between strategies and between cost and effect within every draw.

Analysis and diagnostics

At each threshold compute NMB for every strategy and draw. Select the highest expected-NMB strategy; the CEAF reports the probability that this selected strategy is best. Expected opportunity loss for a chosen strategy is the mean of draw-specific maximum NMB minus that strategy's NMB. The minimum expected loss equals EVPI for the included decision and uncertainty distribution.

When NOT to use and common errors

Do not choose the strategy with the largest CEAC probability automatically, average patient-level ICERs, compare strategies generated under incompatible draws, or interpret probability of cost-effectiveness as the probability a technology benefits an individual.

Worked example and implementation boundary

At one illustrative threshold, synthetic NMB draws for strategy A are 100 and 500; strategy B has 250 and 250. A has expected NMB 300 and B has 250. Calculate expected loss for choosing A. Expected loss for A is 75. A has higher expected NMB even though it is best in only one of the two draws. The code performs that explicitly stated calculation with synthetic inputs. It is not a complete fitted analysis and does not demonstrate the identification assumptions, estimate sampling uncertainty, or certify application in another population.

Data-source and reporting requirements

Preserve the provenance, dates, units, and observation rule for each input. Claims capture services and transactions under observable benefits; absence of a record is not proof that an event or resource use did not occur. EHR and registry measurements depend on the collection process and may miss care outside the system. Linked sources add reconciliation and selection questions. Primary collection can improve a missing domain but still requires valid measurement and follow-up. Report which of these limitations affects the stated use, which evidence supports the chosen inputs, and what remains uncertain.

Worked example

Scenario

At one illustrative threshold, synthetic NMB draws for strategy A are 100 and 500; strategy B has 250 and 250. A has expected NMB 300 and B has 250. Calculate expected loss for choosing A.

Dataset

Synthetic inputs with units defined in the scenario; no patient data.

Steps

Result

Expected loss for A is 75. A has higher expected NMB even though it is best in only one of the two draws.

Trade-offs

Code example

loss_draw1 = 150
loss_draw2 = 0
draws = 2
result = (loss_draw1+loss_draw2)/draws
assert abs(result - 75.0) < 1e-9
print(result)

loss_draw1 <- 150
loss_draw2 <- 0
draws <- 2
result <- (loss_draw1+loss_draw2)/draws
stopifnot(abs(result - 75.0) < 1e-9)
print(result)

Citations

1. [1]Fenwick E, Claxton K, Sculpher M. Representing uncertainty: the role of cost-effectiveness acceptability curves. Health Economics. 2001;10(8):779-787.
2. [2]Caro JJ, et al. Modeling Good Research Practices—Overview: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-1. Value in Health. 2012.
3. [3]Alarid-Escudero F, et al. “Time Traveling Is Just Too Dangerous” but Some Methods Are Worth Revisiting: The Advantages of Expected Loss Curves Over Cost-Effectiveness Acceptability Curves and Frontier. Value in Health. 2019.