Signature
EVPI = P_err * L_wrong
| Inputs | Definition | Unit |
|---|---|---|
P_err | Share of draws in which another option has a strictly higher net benefit than the option chosen on current evidence, entered as a proportion | proportion |
L_wrong | Mean of the opportunity loss over only those draws in which the option chosen on current evidence is not the best, zero if there are none | QALYs or currency per person |
EVPI | Expected value of perfect information for one person, the mean opportunity loss over all draws | QALYs or currency per person |
|---|
Function
Expected value of perfect information function for a single adoption decision
Maps the net benefit of every option in every probabilistic draw, at a stated cost-effectiveness threshold, to the expected net benefit forgone per person by choosing on current evidence rather than with all uncertainty removed. Its inputs are the draw by option table of net benefit NB_ds and the threshold lambda, and its output is EVPI, in QALYs when net health benefit is used and in currency when net monetary benefit is used. The mean of the maxima less the maximum of the means is live in the Value of Information package as HE-FM-VOI-001, with population scaling in HE-FM-VOI-002, the partial form in HE-FM-VOI-003 and the error probability in HE-FM-CEAC-003. This package adds the opportunity-loss form, the two-option form in health units, the split of EVPI into error probability and loss when wrong, and the closed form for a normally distributed incremental net benefit. Notation follows the Expected Value of Perfect Information article.
Try this function
Implementations
Excel
Error probability and loss when wrong from an opportunity-loss column
With the opportunity loss of each draw in a range named Loss, COUNTIF gives the share of draws with a positive loss and AVERAGEIF the mean loss over those draws. IFERROR returns zero for the loss when no draw has one.
=COUNTIF(Loss,">0")/COUNT(Loss)*IFERROR(AVERAGEIF(Loss,">0"),0)
Assumptions
Ties counted as correct decisions in the EVPI error split
A draw in which the chosen option ties with the best has no loss and is not counted as an error, in line with the acceptability curve's treatment of ties in HE-FM-CEAC-002. Counting ties as errors raises P_err and lowers L_wrong but leaves their product unchanged.
Error probability and loss from the same draws and threshold as EVPI
P_err and L_wrong come from the same draws, the same threshold and the same current choice as EVPI. An error probability read from an acceptability curve at another threshold cannot be combined with a loss computed at this one.
Worked examples
Article's error probability and loss when wrong at GBP 25,000 per QALY
The drug is the wrong choice in two of the five illustrative draws, so P_err is 0.4, and the losses there are 0.20 and 0.10 QALYs, a mean of 0.15. The product is 0.06 QALYs per patient, the article's EVPI.
P_err = 0.4; L_wrong = 0.15; EVPI = 0.06
Article's error probability and loss when wrong at GBP 35,000 per QALY
At GBP 35,000 per QALY only draw 2 favours standard care, so P_err is 0.2 and the loss when wrong is about 0.0857 QALYs. The product is about 0.0171 QALYs per patient. The error probability halves but EVPI falls by more than two thirds, because the loss when wrong also shrinks.
P_err = 0.2; L_wrong = 0.0857143; EVPI = 0.0171
Rare but costly error giving a larger EVPI than a frequent small one
An illustrative current choice that is wrong in only 5% of draws but loses 2 QALYs per patient when wrong has an EVPI of 0.1 QALYs. That is more than an illustrative choice wrong in 45% of draws with a mean loss of 0.1 QALYs, whose EVPI is 0.045 QALYs.
P_err = 0.05; L_wrong = 2; EVPI = 0.1
Common errors
Reporting the mean loss when wrong as EVPI
Dividing the total loss of 0.30 QALYs in the article's example by the 2 draws with a loss gives 0.15 QALYs, the loss when wrong, not the EVPI of 0.06. The loss is averaged over all draws, or the loss when wrong is multiplied by P_err.
Reading the error probability alone as the cost of uncertainty
Between GBP 25,000 and GBP 35,000 per QALY the error probability in the article's example halves, 40% at the lower value and 20% at the higher, while EVPI falls by more than two thirds, 0.06 QALYs at the lower value and about 0.017 at the higher. The probability of a wrong decision says nothing about the size of the loss.
Sources
HEMA Report 2 on the cost of uncertainty as likelihood and size of a wrong choice
Steuten L, Thavorn K, Cipriano LE, Guertin JR, McQueen B, Schmidler G, Sullivan S, Wailoo A, Sculpher M. Methods to analyze and present uncertainty in economic evaluation to support HTA decisions. HEMA Report 2. Health Economics Methods Advisory, 2026. Glossary entry on the cost of uncertainty, the health expected to be lost by deciding on current evidence, combining how likely a wrong choice is with how much would be lost if it were made, and section 6.4, which asks reports to combine outputs on the probability of an incorrect decision with its consequences.
ISPOR introduction on loss only in iterations with an incorrect decision
Fenwick E, Steuten L, Knies S, Ghabri S, Basu A, Murray JF, Koffijberg HE, Strong M, Sanders Schmidler GD, Rothery C. Value of information analysis for research decisions, an introduction. Report 1 of the ISPOR Value of Information Analysis Emerging Good Practices Task Force. Value in Health. 2020;23(2):139-150. Box 4, which notes that iterations where uncertainty has not led to an incorrect decision carry no opportunity loss, that the incorrect iterations carry some loss, and that EVPI is the average of the loss over all iterations.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0