Concept Architecture
Concept
Theoretically, the Cost-Effectiveness Frontier is a graphical representation of the set of non-dominated healthcare interventions that provide the greatest health benefit for a given level of cost. It is founded on the principles of economic efficiency, dominance and opportunity cost, and exists to identify interventions that are potentially efficient compared with available alternatives while excluding those that are strictly or extendedly dominated.
Mathematically, the Cost-Effectiveness Frontier is represented by the piecewise linear boundary connecting non-dominated interventions on the cost-effectiveness plane after dominated alternatives have been removed. The slope of each frontier segment corresponds to the Incremental Cost-Effectiveness Ratio (ICER) between adjacent interventions and represents the additional cost required to obtain an additional unit of health outcome.
In practice, the Cost-Effectiveness Frontier is constructed by ordering interventions by effectiveness, eliminating dominated and extendedly dominated alternatives, and calculating ICERs between successive non-dominated interventions. It is widely used in health technology assessment to compare competing interventions and to determine which options remain economically efficient at alternative willingness-to-pay thresholds.
Purpose
Used to identify economically efficient healthcare interventions, eliminate dominated alternatives, support incremental cost-effectiveness analysis, inform health technology assessment, and guide reimbursement and resource allocation decisions.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
ICER = (C? ? C???) � (E? ? E???)
Related Mathematical Methods
- Incremental Cost-Effectiveness Ratio (ICER)
- Dominance analysis
- Extended dominance analysis
- Incremental analysis
- Cost-effectiveness plane
Example
Five treatment options are evaluated.
| Intervention | Cost (�) | QALYs |
|---|---|---|
| A | 5,000 | 2.0 |
| B | 8,000 | 2.8 |
| C | 9,000 | 2.6 |
| D | 12,000 | 3.4 |
| E | 18,000 | 3.8 |
Intervention C is strictly dominated because it costs more than A while providing fewer QALYs than B. The Cost-Effectiveness Frontier consists of A, B, D and E. ICERs are calculated only between adjacent interventions on the frontier.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SORT | =SORT(A2:C6,3,1) | Orders interventions by effectiveness. |
| IF | =IF(AND(B3>B2,C3<=C2),"Dominated","Retain") | Identifies strictly dominated interventions. |
| FILTER | =FILTER(A2:C6,D2:D6="Retain") | Returns the non-dominated interventions. |
| INDEX | =INDEX(B:B,ROW())-INDEX(B:B,ROW()-1) | Calculates incremental costs. |
| INDEX | =INDEX(C:C,ROW())-INDEX(C:C,ROW()-1) | Calculates incremental QALYs. |
VBA (Optional)
Automate the identification of dominated interventions, construction of the Cost-Effectiveness Frontier and calculation of sequential ICERs.
Sources
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- NICE. Health Technology Evaluation Manual.
- Husereau D, Drummond M, Augustovski F, et al. CHEERS 2022 Statement. BMJ. 2022.
Related Concepts (2)
Library
Publications
2
Methods for the Economic Evaluation of Health Care Programmes — Drummond, Sculpher, Claxton, Stoddart & Torrance, 4th Edition ed., 2015 (Oxford University Press)
The standard international reference text for economic evaluation methods in health care, covering cost-effectiveness, cost-utility and cost-benefit analysis, measurement of costs and outcomes, evidence synthesis, and the characterisation of uncertainty.
BookView source →Applied Methods of Cost-Effectiveness Analysis in Healthcare — Gray, Clarke, Wolstenholme & Wordsworth, 1st Edition ed., 2011 (Oxford University Press)
A practical, worked-example guide to conducting cost-effectiveness analysis, structured around outcomes, costs, modelling with decision trees and Markov models, and presenting results. Volume 3 in the Handbooks in Health Economic Evaluation series, developed from the University of Oxford course.
BookView source →
Frequently Asked Questions (6)
What is a cost-effectiveness frontier?
The set of non-dominated interventions on a cost-effectiveness plane, connecting options offering the best available combination of cost and effect.
Source: Black 1990
How is a cost-effectiveness frontier constructed?
Every option is plotted on a plane with effect on one axis and cost on the other. Options costing more and producing less than another are removed as dominated. Options lying above the line joining two others are removed as extendedly dominated, since a combination of those two would deliver more health for the same money. The remaining options are joined in order of increasing effect, and the resulting line is the frontier, along which each step upward buys additional health at a rising price.
Source: Black 1990
What does the slope of a cost-effectiveness frontier mean?
Each segment's slope is the incremental cost-effectiveness ratio between the two options it joins, so the frontier displays the whole sequence of ratios geometrically. Because dominated and extendedly dominated options have been removed, the slope increases at every step, meaning each additional increment of health costs more than the last. Where the slope exceeds the threshold, moving further along the frontier is no longer worthwhile, which identifies the option that should be chosen.
Source: Drummond et al. 2015
Why does a cost-effectiveness frontier require options to be mutually exclusive?
Because the construction assumes only one option will be chosen, so that adopting a point on the frontier means forgoing the others. Where options are independent and could all be funded, dominance in this sense does not apply and the correct procedure is to rank them by their individual ratios and fund downward until the budget is exhausted. Applying frontier logic to independent options discards alternatives that should have been considered on their own merits.
Source: Drummond et al. 2015
What is extended dominance on a cost-effectiveness frontier?
An option is extendedly dominated when it lies above the line connecting two other options, so a mixture of those two would produce the same or more health at lower cost. It is not dominated in the simple sense, since no single option beats it on both dimensions, which is why it survives the first pass and must be removed separately. Failing to remove extendedly dominated options produces incremental ratios calculated against the wrong comparator, and the resulting ranking can recommend the wrong choice.
Source: Drummond et al. 2015
What are the limitations of a cost-effectiveness frontier?
It is drawn from point estimates and shows nothing of the uncertainty around them, so an option removed as dominated may not be dominated once uncertainty is taken into account. It assumes the options are genuinely mutually exclusive and perfectly divisible in the case of extended dominance, which mixtures of real treatments rarely are. And it collapses all health into one measure, so options differing in the kind of benefit they produce appear comparable when they may not be.
Source: healtheconomics.wiki
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Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 5 Aug 2025
Content version: 1.0.0
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