Signature
EVPI = sum_(s=1)^S [NBmax_s] / S - ENB_cur
| Inputs | Definition | Unit |
|---|---|---|
NBmax_s | Largest net benefit among all options in draw s, the value of the option that would be chosen if that draw were known to be true, listed across draws | currency per person |
S | Number of probabilistic draws, or equally likely states, from which net benefit is calculated | count |
ENB_cur | Highest expected net benefit among the options, that of the option chosen on current information, calculated from the same draws | currency per person |
EVPI | Expected value of perfect information about all modelled parameters for one person facing the decision | currency per person |
|---|
Function
Value of information function
Maps the joint distribution of net benefit across the options in a decision to the expected gain from resolving some or all of the uncertainty before choosing, compared with choosing the option with the highest expected net benefit on current information.
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Implementations
Excel
EVPI from a table of draws
With each option's net benefit in adjacent columns B to D, one row per draw, a helper column RowMax holds =MAX(B2:D2) filled down and a helper row ColMeans holds the mean of each option's column. Excel subtracts the largest column mean from the mean of the row maxima.
=AVERAGE(RowMax)-MAX(ColMeans)
Assumptions
Order of expectation and maximisation
With perfect information the choice can differ in each draw, so the maximum is taken inside the average. On current information one option is chosen for all draws, so the average is taken first and the maximum second. EVPI is therefore zero or positive, and zero only when the same option is best in every draw.
Net benefit on a stated basis
Every draw's net benefit uses the same threshold, population, perspective and time horizon as the adoption decision, and NBmax_s and ENB_cur come from the same set of draws.
Only represented uncertainty is valued
EVPI values resolution of the uncertainty in the probabilistic model. Parameters held fixed and structural alternatives that are not parameterised contribute nothing, so an incomplete uncertainty model understates the value of information.
Worked examples
Two equally likely states
Strategy A has a net monetary benefit of £1,000 in state 1 and £200 in state 2, and strategy B £600 and £800, each state having probability 0.5. The best values are £1,000 and £800, with a mean of £900. On current information B is chosen, with expected net monetary benefit £700, so EVPI is £200 per patient. The figures match the article's worked example.
S = 2; NBmax_s = [1000,800]; ENB_cur = 700; EVPI = 200
Five draws of a two-option model
In the five illustrative draws on the expected net benefit page, the highest net benefits are £138,000, £134,000, £142,000, £136,000 and £147,500, with a mean of £139,500. Treatment B is chosen on current information with expected net benefit £137,700, so EVPI is £1,800 per patient, the same as the mean loss from choosing B in the three draws where A is better.
S = 5; NBmax_s = [138000,134000,142000,136000,147500]; ENB_cur = 137700; EVPI = 1800
Common errors
Maximising within each draw for the current decision
Taking the best option in each draw for the second term gives current information the benefit of perfect information and reduces EVPI to zero.
Reading a high error probability as high EVPI
EVPI combines the probability of a wrong decision with the size of the loss. In the worked example on the CEAC page, the chosen option is wrong in 80% of draws but EVPI is only £200 per person, because the losses are small.
Sources
Value of information in a decision-making framework
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.
Decision modelling textbook on EVPI
Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford: Oxford University Press; 2006.
Canonical Identity
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