Cost of the blend that matches the middle option

Finds the share p of the population given the more effective neighbour H, with the remainder given L, so that the blend matches the expected effect of M, then the saving of that blend against M. A positive saving means M lies above the frontier and is extendedly dominated.

Signature

p = (E_M - E_L) / (E_H - E_L); C_mix = C_L + p * (C_H - C_L); S_mix = C_M - C_mix
Inputs
InputsDefinitionUnit
E_MExpected health effect of the middle optionhealth-outcome unit per defined population or person
E_LExpected health effect of the less effective neighbourhealth-outcome unit per defined population or person
E_HExpected health effect of the more effective neighbourhealth-outcome unit per defined population or person
C_LExpected cost of the less effective neighbourcurrency per defined population or person
C_HExpected cost of the more effective neighbourcurrency per defined population or person
C_MExpected cost of the middle optioncurrency per defined population or person
Output
pProportion of the population given H in the blend, the remainder being given Lproportion
C_mixExpected cost of the blend of L and H that produces the expected effect of Mcurrency per defined population or person
S_mixExpected cost of M minus the expected cost of the blendcurrency per defined population or person

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.

Implementations

  • Excel

    Saving from the matching blend

    Excel calculates the blend share, the blend cost and the saving against the middle option in one formula using named cells.

    =MiddleCost-(LowerCost+(MiddleEffect-LowerEffect)/(HigherEffect-LowerEffect)*(HigherCost-LowerCost))

Assumptions

  • Proportional blending

    Expected costs and effects of the blend are the population-share weighted averages of those of L and H, with E_L below E_M and E_M below E_H so that p lies between 0 and 1. The blend is a geometric device; the recommendation is L or H, whichever has the higher net monetary benefit at the threshold.

Worked examples

  • Blend of the neighbours matching the middle option

    For options costing £13,000, £18,000 and £22,000 with 4.3, 4.5 and 4.8 QALYs, giving 40% of the population the most effective option and 60% the least effective one produces 4.5 QALYs at £16,600. The blend saves £1,400 against the middle option for the same health, so the middle option lies above the line joining its neighbours.

    C_L = 13000; E_L = 4.3; C_M = 18000; E_M = 4.5; C_H = 22000; E_H = 4.8; p = 0.40; C_mix = 16600; S_mix = 1400

Common errors

  • Treating indivisible options as blendable without comment

    Where options cannot be split across a population and decisions face a fixed budget, the middle option can still give the most health among affordable options, and a blend would give some people a less effective option. This equity concern is reported alongside the frontier result.

Sources

  • Mixed strategies that dominate an option

    Cantor SB. Cost-effectiveness analysis, extended dominance, and ethics: a quantitative assessment. Medical Decision Making. 1994;14(3):259-265.

    View source →

Canonical Identity

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