Cost-Effectiveness Acceptability Frontier

Concept

Theoretically, the Cost-Effectiveness Acceptability Frontier (CEAF) is a graphical representation of decision uncertainty that identifies the intervention with the highest expected net benefit at each willingness-to-pay threshold and shows the probability that this optimal intervention is cost-effective. It is based on decision theory, probabilistic sensitivity analysis and the expected net benefit framework. Unlike the Cost-Effectiveness Acceptability Curve, which evaluates a single intervention, the CEAF identifies the optimal strategy among all competing alternatives.

Mathematically, the Cost-Effectiveness Acceptability Frontier is constructed by first identifying the intervention with the greatest expected net monetary benefit at each willingness-to-pay threshold and then calculating the probability that this intervention is cost-effective across probabilistic simulations. The frontier therefore combines expected value maximisation with the probability of making the correct reimbursement decision.

In practice, the Cost-Effectiveness Acceptability Frontier is generated following probabilistic sensitivity analysis using Monte Carlo simulation. In health economics, it is used when evaluating multiple competing interventions to communicate decision uncertainty while explicitly accounting for the optimal strategy at each willingness-to-pay threshold.

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Purpose

Used to identify the optimal intervention across alternative willingness-to-pay thresholds, quantify decision uncertainty, support probabilistic sensitivity analysis, and inform health technology assessment and reimbursement decisions involving multiple competing interventions.

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Mathematical Formulae

Primary Formula

CEAF(?) = P(NMB? = max(NMB?, ?, NMB?))

where:

• ? = willingness-to-pay threshold
• NMB? = net monetary benefit of the intervention with the highest expected net benefit
• k = number of competing interventions

Supporting Formulae

NMB = ??E ? ?C

Expected NMB = E(NMB)

Related Mathematical Methods

• Probabilistic sensitivity analysis
• Monte Carlo simulation
• Net monetary benefit analysis
• Expected value analysis
• Cost-Effectiveness Acceptability Curve
• Cost-effectiveness plane

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Example

Three interventions are compared using 10,000 probabilistic simulations.

At a willingness-to-pay threshold of �30,000 per QALY, Intervention B has the highest expected net monetary benefit.

Intervention B is optimal in 8,200 simulations.

CEAF Probability = 8,200 � 10,000

CEAF Probability = 0.82 (82%)

The Cost-Effectiveness Acceptability Frontier therefore indicates an 82% probability that Intervention B is the optimal decision at �30,000 per QALY.

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Excel Implementation

Function	Example Formula	Health Economics Application
MAX	=MAX(B2:D2)	Identifies the intervention with the highest net monetary benefit for each simulation.
COUNTIF	=COUNTIF(E2:E10001,"B")/COUNT(E2:E10001)	Calculates the probability that the optimal intervention is selected across simulations.
Scatter Chart	Probability vs Threshold	Generates the Cost-Effectiveness Acceptability Frontier across willingness-to-pay thresholds.

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VBA (Optional)

Automate probabilistic sensitivity analyses, identify the intervention with the highest expected net monetary benefit at each willingness-to-pay threshold and generate the Cost-Effectiveness Acceptability Frontier.

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Sources

• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
• Fenwick E, Claxton K, Sculpher M. Representing Uncertainty: The Role of Cost-Effectiveness Acceptability Curves. Health Economics.
• Fenwick E, Claxton K, Briggs A. Cost-Effectiveness Acceptability Curves and Frontiers. Pharmacoeconomics.
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
• NICE. Health Technology Evaluation Manual.