Concept Architecture
Concept
Theoretically, Efficiency Frontier Analysis is an analytical method used to identify the set of healthcare interventions that provide the greatest attainable health benefit for a given level of cost, or equivalently the lowest cost for a given level of health benefit. It is founded on production and welfare economics and defines an efficiency frontier consisting of non-dominated alternatives against which all other interventions are compared. In health economics, the frontier represents the benchmark for efficient resource allocation under budget constraints.
Mathematically, the efficiency frontier is constructed by plotting interventions in cost-effectiveness space and identifying the non-dominated set after eliminating strictly and extendedly dominated alternatives. Adjacent interventions on the frontier define incremental cost-effectiveness ratios (ICERs), and the frontier forms the piecewise linear boundary representing efficient choices. Interventions located above the frontier are inefficient because equivalent or greater health gains can be achieved at lower cost.
In practice, efficiency frontier analysis is performed during health technology assessment and economic evaluation by ranking interventions by effectiveness, removing dominated options, calculating ICERs sequentially and constructing the frontier. The method is used by reimbursement agencies and health economists to evaluate competing technologies and determine which interventions should be considered for funding.
Purpose
Used to identify economically efficient healthcare interventions, eliminate dominated alternatives, support reimbursement decisions, construct cost-effectiveness frontiers, evaluate competing technologies and optimise healthcare resource allocation.
Mathematical Formulae
Primary Formula
The efficiency frontier is defined by the sequence of non-dominated interventions joined by incremental cost-effectiveness ratios:
ICER = (C??? ? C?) / (E??? ? E?)
where:
- C? = cost of intervention i
- E? = effectiveness of intervention i
Supporting Formulae
Incremental Cost:
?C = C? ? C?
Incremental Effectiveness:
?E = E? ? E?
Incremental Cost-Effectiveness Ratio:
ICER = ?C / ?E
Related Mathematical Methods
- Dominance analysis
- Extended dominance analysis
- Incremental cost-effectiveness analysis
- Cost-effectiveness plane analysis
- Convex hull construction
- Frontier analysis
Example
Four interventions are evaluated.
| Intervention | Cost (�) | QALYs |
|---|---|---|
| A | 2,000 | 1.0 |
| B | 3,000 | 1.4 |
| C | 4,500 | 1.6 |
| D | 5,000 | 2.0 |
Intervention C is excluded through extended dominance. The efficiency frontier is formed by interventions A, B and D.
Incremental analysis:
- ICER (A?B):
(3000 ? 2000) / (1.4 ? 1.0) = �2,500 per QALY
- ICER (B?D):
(5000 ? 3000) / (2.0 ? 1.4) = �3,333 per QALY
Only interventions A, B and D remain on the efficiency frontier.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SORT | =SORT(A2:C10,3,1) | Orders interventions by effectiveness before frontier construction. |
| IF | =IF(ICER<=Threshold,""Efficient"",""Exclude"") | Applies the efficiency decision rule. |
| FILTER | =FILTER(A2:C10,D2:D10=""Efficient"") | Returns interventions remaining on the frontier. |
| INDEX | =INDEX(C:C,MATCH(MAX(QALYs),QALYs,0)) | Retrieves frontier interventions for reporting. |
| Scatter Chart | Cost vs QALYs | Produces the efficiency frontier graphically. |
VBA (Optional)
Automate dominance testing, ICER calculation and construction of the efficiency frontier for large health technology assessment datasets.
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.
- Gold MR, Siegel JE, Russell LB, Weinstein MC (eds.). Cost-Effectiveness in Health and Medicine.
Related Concepts (2)
Library
Publications
1
Productivity Growth in the English National Health Service from 1998/1999 to 2013/2014 — Bojke, Castelli, Grašič, Howdon & Street, Vol. 26, No. 5 ed., 2017 (Health Economics)
The York Centre for Health Economics measurement of NHS productivity growth as a chained index of outputs over inputs across 15 years, the standard methodological reference for English NHS productivity analysis.
Journal ArticleView source →
Frequently Asked Questions (6)
What is efficiency frontier analysis?
A method identifying the best-observed combinations of inputs and outputs among comparable units, forming a frontier against which all others are benchmarked.
Source: Farrell MJ. The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A. 1957;120(3):253-290. doi:10.2307/2343100.
What distinguishes data envelopment analysis from stochastic frontier analysis?
Both methods estimate a frontier of best-observed performance, but they treat deviations from it differently. Data envelopment analysis draws the frontier as a boundary enclosing the data using linear programming and attributes any shortfall entirely to inefficiency, making no allowance for chance. Stochastic frontier analysis fits a statistical function and splits the gap between random noise and genuine inefficiency. The choice matters because measurement error in one unit can distort a deterministic frontier. Jacobs, Smith and Street (2006) compare the two approaches for health services.
Source: Jacobs, Smith & Street 2006
How is an efficiency frontier constructed?
A frontier is constructed from the observed input and output data of a set of comparable units by identifying those that are not outperformed by any other, or by any combination of others, in converting inputs to outputs. These best performers form the boundary of what has been achieved. Data envelopment analysis builds such a frontier using linear programming, while stochastic frontier analysis estimates it statistically, each defining the frontier from which the efficiency of other units is measured.
Source: Farrell 1957
How does efficiency frontier analysis measure a unit's efficiency?
A unit's efficiency is measured by its distance from the frontier: a unit on the frontier is efficient, having the best observed input-output performance, while a unit inside it is inefficient, since the frontier shows that more output could be obtained from its inputs, or the same output from fewer. The size of the gap gives the extent of inefficiency and the improvement that would bring the unit to best-observed practice. The score is relative to the frontier the data define.
Source: Farrell 1957
What are the limitations of efficiency frontier analysis?
The frontier is defined by the units in the sample, so it reflects best observed rather than best possible practice, and all units could be inefficient together. Results are sensitive to how inputs and outputs are specified and to measurement error, which frontier methods may attribute to inefficiency. Case mix and quality are hard to incorporate, so a unit may appear on the frontier by producing cheaply while delivering poorer care. The analysis shows relative, not absolute, efficiency.
Source: Farrell 1957
How is efficiency frontier analysis used in health care?
It is used to benchmark providers such as hospitals against the best observed among them, identifying which are efficient and how far others could improve toward the frontier. It suits units with multiple inputs and outputs that a single ratio cannot summarise. Findings inform benchmarking, target-setting, and investigation of what distinguishes frontier units, and they are interpreted with care given their sensitivity to specification and their relative nature, prompting inquiry rather than settling performance judgements.
Source: Farrell 1957
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Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 21 Aug 2025
Content version: 1.0.0
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