Concept Architecture
Efficiency Frontier: Concept Architecture
Find the options that remain worth comparing
In a cost-effectiveness comparison, the efficiency frontier connects strategies that are not ruled out by simple or extended dominance for the stated set of options and outcome measure. This page shows how to construct that frontier, read its slopes, and distinguish being on the frontier from being the preferred choice.
Plot comparable costs and effects
Put each mutually exclusive strategy's expected effectiveness on the horizontal axis and expected cost on the vertical axis. Use the same population, perspective, price year, time horizon, and outcome scale for every option. A frontier drawn from incompatible estimates does not support a valid incremental comparison.
Sort alternatives by effect or cost and first remove any option that costs more while providing no more effect than another available option. The remaining candidates are assessed for extended dominance: a middle option can be less efficient than a feasible combination or sequence of more and less effective options. NICE's economic evaluation manual calls for fully incremental analysis after removing dominated and extendedly dominated technologies.
Work through three illustrative strategies
Suppose A costs £1,000 and yields 1.0 quality-adjusted life years, B costs £1,800 and yields 1.2, and C costs £2,000 and yields 1.5. B is neither simply dominated by A nor by C: it costs and produces more than A, but costs and produces less than C. Its incremental cost per quality-adjusted life year relative to A is £800/0.2 = £4,000.
Moving directly from A to C costs £1,000 for 0.5 additional quality-adjusted life years, or £2,000 per quality-adjusted life year. Because B's incremental ratio exceeds that of moving from A to C, B is extendedly dominated under the usual convex-combination interpretation. A and C form the frontier for these three options. The ISPOR-linked analysis of cost-effectiveness frontiers describes exclusion by strict and extended dominance.
Read slopes as incremental choices
For adjacent frontier options and ordered by increasing effect, the segment's slope is the incremental cost-effectiveness ratio:
After removing extendedly dominated options, the slopes between successive frontier strategies should increase as more effectiveness is obtained at greater cost, apart from ties and special cases requiring careful handling. The next more effective frontier option is the relevant incremental comparator, rather than automatically comparing every strategy only with usual care. NICE's quality appraisal checklist emphasizes these incremental rules.
Use the decision context, not the line alone
A strategy on the frontier is efficient relative to the options included, but is not automatically cost-effective at a particular willingness-to-pay threshold. At a specified threshold, compare expected net benefit across the available options; changing the threshold can change the preferred frontier point. Missing relevant comparators can also change the frontier.
The plotted frontier normally uses expected costs and effects from a stated analysis. Parameter uncertainty can change the positions and even the dominance status of options; examine probabilistic results and credible scenarios rather than treating the drawn line as certain. Do not confuse this cost-effectiveness frontier with a production frontier relating resource inputs to maximum feasible output or with a cost-effectiveness acceptability frontier, which summarizes probabilities for the option with highest expected net benefit.
Report the full comparison
Show all candidate strategies' costs and effects, identify every dominance exclusion, and give incremental ratios for adjacent remaining alternatives. State why strategies are feasible and mutually comparable, and explain whether mixing or sequencing them is meaningful for the extended-dominance interpretation.
The frontier makes the opportunity cost of greater effectiveness visible within the compared set. It cannot determine a decision without the relevant threshold, evidence, equity considerations, and omitted consequences being considered.
Related Concepts (1)
Institutional Perspectives (1)
- IQWiG
Indication-Specific Efficiency Frontier Sets the Maximum Reimbursable Price
When a formal cost-benefit assessment is undertaken, IQWiG uses an efficiency-frontier method rather than a fixed cross-indication threshold: existing interventions in the same indication are plotted with net cost on one axis and value of benefit on the other, the non-dominated options are linked to form the efficiency frontier, and the maximum reimbursable price for a new drug is inferred from its position relative to that frontier (its willingness-to-pay is indication-specific, derived from the slope of the frontier / the "proportional rule").
IQWiG, General Methods; Caro et al., efficiency frontier approach (Health Economics, 2010)View source →
Library
Publications
1
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 an efficiency frontier?
The boundary formed by non-dominated interventions plotted by cost and effect, showing the best attainable outcome at each level of spending.
Source: Black 1990
How is an efficiency frontier constructed?
Options are plotted with effect on one axis and cost on the other. Any option costing more and producing less than another is removed as dominated. Any option lying above the line joining two others is removed as extendedly dominated, since a combination of those two would deliver more health for the same outlay. The remaining options are joined in order of increasing effect, and the resulting boundary shows the best attainable outcome at each level of spending. Options lying on the frontier are described as efficient in the narrow sense that no other available option or combination delivers more health for the same outlay, which says nothing about whether any of them is worth funding.
Source: Black 1990
What does the slope of an efficiency frontier mean?
Each segment's slope is the incremental cost-effectiveness ratio between the two options it connects, so the frontier displays the whole sequence of ratios geometrically. Because dominated and extendedly dominated options have been removed, the slope rises at every step, meaning each further 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 to choose. This is why the frontier is read from the bottom upward, moving to the next option only while the additional cost per unit of health remains acceptable.
Source: Drummond et al. 2015
Why must options on an efficiency frontier be mutually exclusive?
Because the construction assumes only one will be chosen, so that selecting a point means forgoing the others. Where options are independent and could all be funded, dominance in this sense does not apply, and the correct procedure ranks them by their individual ratios and funds downward until the budget is exhausted. Applying frontier logic to independent options discards alternatives that should have been assessed on their own merits. Independent options are also assessed differently in another respect, since adopting several of them together is possible and the frontier construction has no way to represent that.
Source: Drummond et al. 2015
How is an efficiency frontier used in appraisal?
It identifies which options remain candidates and what each successive improvement costs, which turns a set of pairwise comparisons into a single ordered picture. Some appraisal frameworks use it to establish the price at which a new treatment would sit on the frontier for its indication, working backwards from the ratios of existing options rather than applying an external threshold. That approach makes the comparison internal to the therapeutic area rather than across the whole system. Using the frontier this way makes the standard internal to the therapeutic area, which avoids relying on a threshold and imports whatever inefficiency the existing options embody.
Source: Black 1990
What are the limitations of an efficiency 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 distributions are considered. Extended dominance assumes options can be mixed in any proportion, which real treatments rarely permit. And it collapses all health into a single measure, so options differing in the kind of benefit they produce appear directly comparable when they may not be. Presenting the scatter from probabilistic analysis alongside the frontier is the usual response, since it shows how firmly each option's position is established.
Source: Briggs, Claxton & Sculpher 2006
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British health economist
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