Signature
j* = argmax_(j in J) (lambda * E_j - C_j)
| Inputs | Definition | Unit |
|---|---|---|
lambda | Monetary value placed on one unit of health effect | currency per unit of health effect |
E_j | Expected health effect of option j | health-outcome unit per defined population or person |
C_j | Expected total relevant cost of option j | currency per defined population or person |
j* | Option with the highest net monetary benefit at threshold lambda | option index |
|---|
JSet of mutually exclusive options in the decision problem, indexed 1 to n (set of options)
Function
Net monetary benefit function
Values an option's expected health effect in money at a stated cost-effectiveness threshold and subtracts its expected cost, placing health and cost on one monetary scale.
Implementations
Excel
Return the highest-NMB option
Excel returns the option name with the highest NMB and flags a tie when more than one option shares the maximum.
=IF(COUNTIF(NMBValues,MAX(NMBValues))>1,"Equal highest NMB",INDEX(OptionNames,MATCH(MAX(NMBValues),NMBValues,0)))
Assumptions
Complete set of mutually exclusive options
J contains every relevant option, and each is evaluated on the same basis. Leaving out an option can change which option has the highest NMB.
Expected net benefit under uncertainty
Under probabilistic analysis the rule uses expected NMB, the mean across simulations, and not the probability that each option has the highest NMB.
Worked examples
Four options at £20,000 per QALY
Options A to D have expected costs of £10,000, £13,000, £18,000 and £22,000 and 4.0, 4.3, 4.5 and 4.8 expected QALYs. At £20,000 per QALY their NMBs are £70,000, £73,000, £72,000 and £74,000, so option D, the fourth, is selected. Option C, which is extendedly dominated, is not selected at this or any other threshold. The figures are illustrative.
J = [1,2,3,4]; lambda = 20000; E_j = [4.0,4.3,4.5,4.8]; C_j = [10000,13000,18000,22000]; j* = 4
Common errors
Choosing the option most likely to be cost-effective
The option with the highest probability of having the highest NMB across simulations can differ from the option with the highest expected NMB. The decision rule uses expected NMB.
Sources
Decisions based on mean net benefit
Claxton K. The irrelevance of inference: a decision-making approach to the stochastic evaluation of health care technologies. Journal of Health Economics. 1999;18(3):341-364.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0