Signature
D_M = (C_M - C_L) / (E_M - E_L) - (C_H - C_M) / (E_H - E_M)
| Inputs | Definition | Unit |
|---|---|---|
C_M | Expected cost of the intermediate option being tested | currency per defined population or person |
C_L | Expected cost of the next less effective option still in the comparison | currency per defined population or person |
E_M | Expected health effect of the intermediate option being tested | health-outcome unit per defined population or person |
E_L | Expected health effect of the next less effective option | health-outcome unit per defined population or person |
C_H | Expected cost of the next more effective option still in the comparison | currency per defined population or person |
E_H | Expected health effect of the next more effective option | health-outcome unit per defined population or person |
D_M | Sequential ICER of M against L minus the sequential ICER of H against M; M is extendedly dominated when D_M is greater than 0 | currency per unit of health effect |
|---|
Function
Extended dominance function
Maps the expected costs and effects of options that survive the dominance screen, ordered by effect, to a flag for each intermediate option that a blend of its neighbours would beat.
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Implementations
Excel
Flag an extendedly dominated middle option
Excel calculates D_M, the sequential ICER into the middle option minus the sequential ICER out of it, using named cells for the three adjacent options, and flags the middle option when D_M is greater than 0.
=IF((MiddleCost-LowerCost)/(MiddleEffect-LowerEffect)-(HigherCost-MiddleCost)/(HigherEffect-MiddleEffect)>0,"Extendedly dominated","Retain")
Assumptions
Dominated options removed first
The three options remain after dominated options, including ties, have been removed, so expected cost and expected effect both rise from L to M to H and both denominators are positive.
Adjacent options, recalculated after each removal
L, M and H are consecutive in the current ordering by expected effect. After any removal, adjacency changes, the sequential ICERs are recalculated and the check is repeated until the ICERs rise with effect.
Equal sequential ratios
When D_M equals 0, the two sequential ICERs are equal and M lies on the straight line joining L and H, so it is not treated as extendedly dominated.
Worked examples
Middle option extendedly dominated
Three options cost £13,000, £18,000 and £22,000 and produce 4.3, 4.5 and 4.8 QALYs. The sequential ICER into the middle option is £25,000 per QALY and the next is about £13,333 per QALY, so D_M is about £11,667 per QALY. Because D_M is greater than 0, the middle option is extendedly dominated. The figures are illustrative and match options B, C and D in the article's four-option example.
C_L = 13000; E_L = 4.3; C_M = 18000; E_M = 4.5; C_H = 22000; E_H = 4.8; D_M = 11666.67
Frontier after recalculation
With option C removed, A, B and D are consecutive. A costs £10,000 for 4.0 QALYs, B £13,000 for 4.3 and D £22,000 for 4.8. The ICER from A to B is £10,000 per QALY and from B to D is £18,000, so D_M is minus £8,000 per QALY. Because D_M is not greater than 0, B is retained and A, B and D form the frontier.
C_L = 10000; E_L = 4.0; C_M = 13000; E_M = 4.3; C_H = 22000; E_H = 4.8; D_M = -8000
Common errors
Not recalculating after a removal
Keeping ICERs computed before a removal leaves comparisons with an option that is no longer adjacent. In the example, the ICER for D is recalculated against B, £18,000 per QALY, rather than kept at about £13,333 against C.
Testing before dominated options are removed
Sequential ICERs calculated while a dominated option remains can be negative or misleading, so the extended dominance check gives unreliable results.
Relying on a common baseline
An option can have an acceptable ICER against a common baseline and still be extendedly dominated, because the baseline comparison ignores the next option on the frontier.
Sources
Extended dominance and mixed strategies
Cantor SB. Cost-effectiveness analysis, extended dominance, and ethics: a quantitative assessment. Medical Decision Making. 1994;14(3):259-265.
NICE manual on extended dominance
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 31 March 2026. Chapter 4 Economic evaluation, section 4.10.8 (extendedly dominated technologies, where a combination of 2 or more other technologies would be more cost effective, removed from the fully incremental analysis).
Extended dominance in practice
Postma MJ, de Vries R, Welte R, Edmunds WJ. Health economic methodology illustrated with recent work on Chlamydia screening: the concept of extended dominance. Sexually Transmitted Infections. 2008;84(2):152-154.
Canonical Identity
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