Signature
ENB_j = sum_(n=1)^N [lambda * E_jn - C_jn] / N
| Inputs | Definition | Unit |
|---|---|---|
lambda | Monetary value placed on one unit of health effect | currency per unit of health effect, for example £ per QALY |
E_jn | Health effect of option j in simulation n, listed across all simulations | health-outcome unit per person, for example QALYs |
C_jn | Total relevant cost of option j in simulation n, listed across all simulations | currency per person |
N | Number of probabilistic simulations averaged | count |
ENB_j | Mean across simulations of option j's health effect valued at lambda minus its cost | currency per person |
|---|
Function
Expected net benefit function
Maps the joint distribution of an option's uncertain costs and health effects, and a threshold, to the mean of its net benefit. The option with the highest expected net benefit is the one to adopt on current evidence, and the same quantity is the baseline for value of information analysis.
Try this function
Implementations
Excel
Expected NMB from a simulation table
With simulated effects of one option in the named range SimEffects and its simulated costs in SimCosts, one row per simulation, Excel averages the net monetary benefit at the threshold in the named cell Threshold.
=SUMPRODUCT(Threshold*SimEffects-SimCosts)/ROWS(SimEffects)
Assumptions
Same parameter draw for every option
In each simulation every option is evaluated with the same draw of the uncertain parameters. This keeps the correlation between the options' net benefits, on which the probability of cost-effectiveness and value of information depend, and reduces the Monte Carlo error in the difference between options.
Distributions that represent the evidence
Each uncertain parameter is sampled from a distribution chosen to represent the available evidence, not chosen arbitrarily, as the NICE manual requires. The mean is only as good as those distributions and the model structure.
Enough simulations for a stable mean
N is large enough for Monte Carlo error to be small relative to the differences between options. When two options have close expected net benefits, a small number of simulations can reverse their ranking by chance.
Adoption follows the highest mean
The option with the highest ENB_j at the stated threshold is adopted on current evidence, whether or not the difference is statistically significant. This is the maximum net monetary benefit rule on the net monetary benefit page applied to simulation means; the spread of net benefit informs the separate question of whether more evidence is worth acquiring.
Worked examples
Standard care over five simulations
Standard care A is evaluated at £25,000 per QALY in five illustrative, equally likely simulations with QALYs of 6.00, 5.80, 6.20, 5.60 and 5.90 and costs of £12,000, £11,000, £13,000, £12,000 and £12,000. Its net monetary benefits are £138,000, £134,000, £142,000, £128,000 and £135,500, with a mean of £135,500. The figures match the article's worked example.
lambda = 25000; N = 5; E_jn = [6.00,5.80,6.20,5.60,5.90]; C_jn = [12000,11000,13000,12000,12000]; ENB_j = 135500
New treatment over the same simulations
New treatment B, in the same five simulations, has QALYs of 6.20, 6.04, 6.48, 6.20 and 6.70 and costs of £21,000, £20,000, £22,000, £19,000 and £20,000. Its expected net monetary benefit is £137,700, £2,200 per patient more than A, so B is adopted. A has the higher net benefit in three of the five simulations, but B loses by small amounts and wins by large ones.
lambda = 25000; N = 5; E_jn = [6.20,6.04,6.48,6.20,6.70]; C_jn = [21000,20000,22000,19000,20000]; ENB_j = 137700
Common errors
Adopting the option that wins most simulations
The option with the highest probability of being cost-effective can have the lower expected net benefit. In the worked examples, A has the higher net benefit in 60% of simulations, but adopting it forgoes £2,200 per patient on average compared with B.
Reporting a deterministic result as expected net benefit
For a nonlinear model the output at the mean inputs differs from the mean of the outputs. Under a constant hazard equally likely to be 0.1 or 0.3 per year, mean survival at the mean hazard of 0.2 is 5 years, while the mean of the two survival times, 10 years and about 3.33 years, is about 6.67 years.
Running each option on different draws
Sampling parameters independently for each option breaks the pairing across options, removes the correlation between their net benefits and inflates the Monte Carlo error in the difference that drives the decision.
Sources
Mean net benefit as the adoption rule
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.
NICE manual on probabilistic expected values
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, sections 4.7.10 (distributions represent the available evidence), 4.7.11 (enough simulations to minimise Monte Carlo error) and 4.7.12 (the preferred cost-effectiveness estimate is derived from a probabilistic analysis when possible unless the model is linear).
Decision modelling textbook on expected net benefit
Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford: Oxford University Press; 2006.
Canonical Identity
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