Signature
DOM_k = 1 if some j (j = 1 to J, j not equal to k) has C_j <= C_k and E_j >= E_k and (C_j < C_k or E_j > E_k); otherwise DOM_k = 0
| Inputs | Definition | Unit |
|---|---|---|
J | Number of mutually exclusive options in the comparison | count |
C_j | Expected total relevant cost of option j | currency per defined population or person |
C_k | Expected total relevant cost of option k | currency per defined population or person |
E_j | Expected health effect of option j | health-outcome unit per defined population or person |
E_k | Expected health effect of option k | health-outcome unit per defined population or person |
DOM_k | Equals 1 when at least one other option dominates option k and 0 otherwise | binary indicator |
|---|
Function
Dominance classification function
Maps the expected costs and expected health effects of mutually exclusive options to a classification of which options are dominated, a result that holds at every non-negative cost-effectiveness threshold.
Implementations
Excel
Flag dominated options in a table
With expected costs in B2:B10 and expected effects in C2:C10, the formula in row 2, filled down, counts options that cost no more and produce no less, then removes those identical to the option itself. A remaining count above zero means the option is dominated.
=IF(COUNTIFS($B$2:$B$10,"<="&B2,$C$2:$C$10,">="&C2)-COUNTIFS($B$2:$B$10,B2,$C$2:$C$10,C2)>0,"Dominated","Not dominated")
Assumptions
Exact duplicates handled separately
Options with identical expected cost and effect do not dominate each other under the rule, so duplicates are merged or one is retained before the screen.
Screen before sequential ratios
The screen runs on expected values before sequential ICERs are calculated and before extended dominance is checked, and it is repeated whenever an option is added.
Worked examples
Five options with one dominated
Five options cost £10,000, £13,000, £20,000, £18,000 and £22,000 and produce 4.0, 4.3, 4.4, 4.5 and 4.8 life years. The third option, at £20,000 and 4.4 life years, is dominated by the fourth, which costs £2,000 less and produces 0.1 more life years. The figures are illustrative and match the example on the cost-effectiveness analysis page.
J = 5; C_j = [10000,13000,20000,18000,22000]; E_j = [4.0,4.3,4.4,4.5,4.8]; C_k = 20000; E_k = 4.4; DOM_k = 1
Dominance through a tie in cost
Two options each cost £13,000, one producing 4.3 QALYs and the other 4.1 QALYs, alongside a £10,000 option producing 4.0 QALYs. The option producing 4.1 QALYs is dominated because another option costs no more and produces more health.
J = 3; C_j = [10000,13000,13000]; E_j = [4.0,4.3,4.1]; C_k = 13000; E_k = 4.1; DOM_k = 1
Common errors
Removing an option on cost alone
Excluding the more expensive of two options without checking effects removes options that buy additional health. An option is dominated only when another costs no more and produces no less, with at least one strict improvement.
Screening against the baseline only
Checking each option against current care alone misses options dominated by another new option, such as the third option by the fourth in the five-option example.
Sources
NICE manual on removing dominated options
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 (fully incremental analysis with dominated and extendedly dominated technologies removed).
Canonical Identity
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