Concept Architecture
Concept
Theoretically, the Efficiency Frontier Method is an economic evaluation approach that identifies the set of interventions providing the greatest health benefit for a given level of cost or the lowest cost for a given level of health benefit. It is grounded in production theory and Pareto efficiency, where interventions lying on the efficiency frontier are considered economically efficient because no alternative provides greater effectiveness without increasing cost or lower cost without reducing effectiveness. In health economics, the method is used to compare multiple competing technologies and to identify those representing efficient resource allocation.
Mathematically, the efficiency frontier is constructed by plotting interventions on a cost-effectiveness plane according to their costs and health outcomes. Dominated interventions, which are more costly and less effective or exhibit extended dominance, are excluded. Straight-line segments joining the remaining non-dominated interventions form the efficiency frontier. Incremental Cost-Effectiveness Ratios (ICERs) are calculated only between adjacent interventions located on the frontier.
In practice, the Efficiency Frontier Method is applied using observed or modelled estimates of costs and health outcomes for competing interventions. The approach is widely used in health technology assessment to identify economically efficient treatment options and to determine whether new technologies extend or fall below the existing frontier. The method is particularly associated with reimbursement decision-making in several European health systems.
Purpose
Used to identify the economically efficient set of healthcare interventions by excluding dominated alternatives and constructing the cost-effectiveness frontier used to support reimbursement and resource allocation decisions.
Mathematical Formulae
Primary Formula
For adjacent interventions on the efficiency frontier:
ICER = (C? ? C?) / (E? ? E?)
where:
- C?, C? = costs of adjacent non-dominated interventions
- E?, E? = corresponding health effects
Supporting Formulae
Incremental Cost:
?C = C? ? C?
Incremental Effect:
?E = E? ? E?
Efficiency Frontier:
Frontier = set of non-dominated interventions connected by successive ICERs
Related Mathematical Methods
- Incremental Cost-Effectiveness Ratio
- Cost-Effectiveness Analysis
- Dominance Analysis
- Extended Dominance
- Cost-Effectiveness Plane
- Decision-Analytic Modelling
Example
Four treatment options are evaluated:
| Intervention | Cost | QALYs |
|---|---|---|
| A | �8,000 | 3.2 |
| B | �10,000 | 3.8 |
| C | �14,000 | 4.0 |
| D | �12,000 | 4.3 |
Intervention C is subject to extended dominance because it provides fewer additional QALYs per additional pound than intervention D. The efficiency frontier therefore consists of A, B and D.
The ICER between B and D is:
ICER = (�12,000 ? �10,000) � (4.3 ? 3.8)
ICER = �2,000 � 0.5 = �4,000 per QALY gained
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SORT | =SORT(A2:C10,2,1) | Orders interventions by increasing cost before frontier construction. |
| IF | =IF(AND(B3>B2,C3<=C2),"Dominated","Retain") | Identifies strictly dominated interventions. |
| IFERROR | =IFERROR((B3-B2)/(C3-C2),"Undefined") | Calculates ICERs between adjacent interventions. |
| LET | =LET(DC,B3-B2,DE,C3-C2,DC/DE) | Improves readability of ICER calculations. |
| FILTER | =FILTER(A2:C10,D2:D10="Retain") | Produces the final efficiency frontier dataset. |
VBA (Optional)
VBA can automate dominance testing, efficiency frontier construction and ICER calculation for multiple competing healthcare interventions.
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.
- Fenwick E, Claxton K, Sculpher M. Representing uncertainty: the role of cost-effectiveness acceptability curves. Health Economics.
- NICE. Health Technology Evaluation Manual.
- ISPOR Good Research Practices for Cost-Effectiveness Analysis.
Related Concepts (2)
Library
Publications
1
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 →
Frequently Asked Questions (6)
What is the efficiency frontier method?
An analytical approach that identifies the efficiency frontier among a set of interventions to determine which non-dominated options warrant incremental comparison.
Source: Black 1990
What does the efficiency frontier method involve?
Options are ordered by effect, dominated options are removed, incremental ratios are calculated between neighbours, and any option whose ratio falls below that of the option beneath it is removed as extendedly dominated. The ratios are then recalculated for the reduced set and the process repeats until they rise consistently across the survivors. The starting point is therefore a complete list of the mutually exclusive options under consideration, since an option omitted at the outset cannot be recovered later in the sequence.
Source: Drummond et al. 2015
Why is the efficiency frontier method iterative?
Because removing an extendedly dominated option changes the comparators for those around it, and the recalculated ratios can reveal a further option that has become extendedly dominated. A single pass therefore does not guarantee a clean set. The procedure ends when incremental ratios increase consistently, which is the condition indicating no further removals are possible. Working through the sequence by hand on more than a handful of options is error prone, which is why the calculation is normally scripted rather than done in a spreadsheet by inspection.
Source: Drummond et al. 2015
What does the efficiency frontier method produce?
A reduced set of options forming the frontier, each with an incremental ratio against its immediate predecessor, alongside a discarded set with the reason for each exclusion. The frontier is then compared against the threshold to select the most effective option whose ratio remains acceptable. Reporting the discarded options matters, since a reader cannot otherwise distinguish a considered exclusion from an oversight. The surviving ratios should rise across the set, and a sequence in which they do not is a reliable indication that the procedure was applied incompletely.
Source: Black 1990
What errors occur in the efficiency frontier method?
The commonest is calculating every option against a single common baseline rather than against the next less effective survivor, which produces ratios that cannot be compared with a threshold. The second is omitting the extended dominance step, which leaves options on the frontier that should not be there. The third is applying the method to options that are not mutually exclusive. The third error is the least visible, because the arithmetic proceeds normally and produces a plausible-looking frontier from options that should never have been compared this way.
Source: Drummond et al. 2015
How does uncertainty affect the efficiency frontier method?
Removals based on point estimates can reverse once distributions are considered, so an option discarded as dominated may be optimal in some simulations. Probabilistic analysis avoids the problem by comparing expected net benefit across all options rather than by sequential removal, which is preferred where uncertainty is being characterised. The deterministic method retains its value for structuring the comparison and setting out what was considered, provided its conclusions about which options remain viable are treated as provisional.
Source: Briggs, Claxton & Sculpher 2006
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Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 6 Aug 2025
Content version: 1.0.0
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