Concept Architecture
Concept
Theoretically, Weak Dominance is a decision rule used in decision analysis and health economics to compare competing interventions. An intervention is weakly dominated if another intervention performs at least as well on one outcome and no worse on another, with at least one comparison showing a strict improvement. The concept originates from decision theory and welfare economics and exists to eliminate inefficient alternatives from consideration before conducting incremental economic evaluation.
Mathematically, weak dominance is represented by inequalities comparing costs and health outcomes between alternatives. An intervention is weakly dominated when another intervention has costs that are less than or equal to those of the comparator and effects that are greater than or equal to those of the comparator, with at least one inequality being strict. This establishes a partial ordering of alternatives based on efficiency.
In practice, weak dominance is identified during incremental cost-effectiveness analysis by ranking interventions according to cost and comparing costs and outcomes sequentially. Weakly dominated interventions are excluded from the efficient set before calculating incremental cost-effectiveness ratios for the remaining non-dominated alternatives.
Purpose
Used to identify inefficient healthcare interventions, eliminate inferior alternatives from incremental analysis, construct the efficiency frontier and improve the validity of cost-effectiveness evaluations.
Mathematical Formulae
Primary Formula
For interventions A and B, intervention A weakly dominates intervention B if:
C? � C?,?E? � E?
with at least one strict inequality:
C? < C??or?E? > E?
where:
- C = cost
- E = effectiveness
Supporting Formulae
None.
Related Mathematical Methods
- Incremental cost-effectiveness analysis
- Dominance analysis
- Extended dominance analysis
- Efficiency frontier analysis
Example
Three interventions are evaluated.
| Intervention | Cost (�) | QALYs |
|---|---|---|
| A | 10,000 | 2.0 |
| B | 12,000 | 2.0 |
| C | 14,000 | 2.4 |
Intervention A weakly dominates Intervention B because it provides the same health outcome (2.0 QALYs) at a lower cost (�10,000 versus �12,000). Intervention B is therefore removed from the incremental analysis before calculating ICERs.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(AND(B2<=B3,C2>=C3,OR(B2<B3,C2>C3)),""Weakly Dominates"","""") | Identify weak dominance between two interventions |
| AND | =AND(B2<=B3,C2>=C3) | Test dominance conditions |
| OR | =OR(B2<B3,C2>C3) | Confirm at least one strict inequality |
| SORT | =SORT(A2:C10,2,1) | Rank interventions by increasing cost before dominance analysis |
VBA (Optional)
Automate identification and removal of weakly dominated interventions before incremental cost-effectiveness analysis.
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.
- ISPOR Good Practice Reports.
Related Concepts (2)
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 a weak dominance?
A situation where an intervention is inferior not to any single alternative but to a combination of two other available options.
Source: Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
What does weak dominance mean in cost-effectiveness analysis?
Weak dominance, also termed extended dominance, arises when an option is not beaten by any single alternative on both cost and effect, yet is beaten by a mixture of two others. A combination of a cheaper and a more effective option can deliver the same expected effect as the option in question at lower cost, or more effect at the same cost. Such an option is ruled out on efficiency grounds even though no single competitor dominates it outright.
Source: Drummond et al. 2015
How is weak dominance identified?
Options are ranked by cost and the incremental cost-effectiveness ratios between successive options are calculated. Weak dominance shows as an incremental ratio that rises and then falls, meaning a later option has a lower ratio than the one before it. When this occurs, the intermediate option is inefficient, because a combination of its neighbours achieves the same effect for less. Removing it and recomputing the ratios restores a sequence in which cost-effectiveness ratios increase steadily along the frontier.
Source: Drummond et al. 2015
How does weak dominance differ from strict dominance?
Strict dominance occurs when a single option costs more and produces less than another, so it is beaten outright by that one alternative. Weak dominance involves no such single beating; the option is excluded only because a combination of two others offers better value. Strict dominance is visible from a direct pairwise comparison, whereas weak dominance emerges only when options are ordered and their incremental ratios examined together. Both remove an option from the efficient set, for different reasons.
Source: Drummond et al. 2015
Why are weakly dominated options excluded?
They are excluded because a decision maker who could adopt them could obtain at least as much health for less, or more health for the same cost, by using a combination of other available options. Retaining a weakly dominated option on the frontier would produce incremental ratios that fall as effect rises, which cannot guide a consistent decision rule. Excluding it leaves a set of options whose ratios increase along the frontier, so each successive step buys effect at a rising price.
Source: Drummond et al. 2015
What role does weak dominance play in identifying cost-effective options?
Removing strictly and weakly dominated options leaves the efficient frontier, the set from which a cost-effective choice is made. Along this frontier the incremental cost-effectiveness ratios increase in order, so a decision maker can move up it until the ratio exceeds what they are willing to pay for additional health. Weak dominance matters because an option that looks reasonable in isolation may be inefficient once combinations are allowed, and overlooking it would admit a choice that wastes resources.
Source: Drummond et al. 2015
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 8 Aug 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-EE-CEA-068
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