Signature
INHB_s = dQ_s - dC_s / lambda; EVPI_H = sum_(s=1)^S [max(INHB_s, 0)] / S - max(sum_(s=1)^S [INHB_s] / S, 0); EVPI_M = lambda * EVPI_H
| Inputs | Definition | Unit |
|---|---|---|
dQ_s | Expected QALYs of the new option less those of the comparator in draw s, listed across draws | QALYs per person |
dC_s | Expected cost of the new option less that of the comparator in draw s, listed across draws | currency per person |
lambda | Value placed on one QALY, used to convert cost into health forgone and EVPI into money, for example 25000 | currency per QALY |
S | Number of equally weighted probabilistic draws | count |
INHB_s | Incremental QALYs less incremental cost divided by the threshold for the new option against its comparator in draw s, listed across draws | QALYs per person |
|---|---|---|
EVPI_H | Expected value of perfect information for one person, measured in net health benefit | QALYs per person |
EVPI_M | Expected value of perfect information for one person, measured in net monetary benefit at the threshold lambda | 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.
Implementations
Excel
Two-option EVPI in QALYs from incremental QALY and cost columns
With the incremental QALYs of each draw in a range named IncQALY, the incremental costs in IncCost and the threshold in Threshold, SUMPRODUCT averages the positive INHB values and MAX takes the positive part of the mean INHB. Multiplying the result by Threshold gives EVPI in money.
=SUMPRODUCT((IncQALY-IncCost/Threshold>0)*(IncQALY-IncCost/Threshold))/ROWS(IncQALY)-MAX(0,AVERAGE(IncQALY)-AVERAGE(IncCost)/Threshold)
Assumptions
Exactly two options with the comparator as the zero reference
The decision is between one new option and one comparator, so the comparator's net benefit is zero in every draw. With three or more options the positive-part form no longer applies, and HE-FM-EVPI-001 or the computational function below is used instead.
Two-option EVPI reported at stated thresholds
EVPI depends on the threshold through INHB_s, so it is reported for explicit thresholds or plotted against the threshold, as the ISPOR methods report advises. For NICE the expected net health benefits are presented, when appropriate, at GBP 25,000 and GBP 35,000 per QALY (PMG36, section 4.10.8).
Same draws and threshold for the health and money forms of EVPI
EVPI_M equals lambda times EVPI_H only when both use the same draws and the same lambda. A money value of EVPI belongs to one threshold and is not rescaled to another.
Worked examples
Article's two-option EVPI at GBP 25,000 per QALY in QALYs and money
In the article's illustrative example the incremental cost is GBP 10,000 in every draw and the incremental QALYs are 0.50, 0.20, 0.70, 0.30 and 0.65. At GBP 25,000 per QALY the cost is worth 0.40 QALYs, the mean of the positive parts is 0.65 / 5 = 0.13 QALYs and the mean INHB is 0.07 QALYs, so EVPI is 0.06 QALYs per patient, or GBP 1,500 at the same threshold. This example is for reading, as its draw-by-draw lists may not run in the site calculator.
S = 5; dQ_s = [0.50,0.20,0.70,0.30,0.65]; dC_s = [10000,10000,10000,10000,10000]; lambda = 25000; INHB_s = [0.10,-0.20,0.30,-0.10,0.25]; EVPI_H = 0.06; EVPI_M = 1500
Article's two-option EVPI at GBP 35,000 per QALY in QALYs and money
At GBP 35,000 per QALY the same cost is worth about 0.2857 QALYs, only draw 2 has a negative INHB and EVPI falls to about 0.0171 QALYs per patient, or about GBP 600 at that threshold. A higher threshold moves the mean INHB further from zero and lowers EVPI. This example is for reading, as its draw-by-draw lists may not run in the site calculator.
S = 5; dQ_s = [0.50,0.20,0.70,0.30,0.65]; dC_s = [10000,10000,10000,10000,10000]; lambda = 35000; INHB_s = [0.2143,-0.0857,0.4143,0.0143,0.3643]; EVPI_H = 0.0171429; EVPI_M = 600
Two-option EVPI of zero at an illustrative GBP 60,000 per QALY
At an illustrative threshold of GBP 60,000 per QALY, above the values in PMG36, the cost is worth about 0.1667 QALYs and the drug's INHB is positive in all five draws. The drug is best in every draw, so EVPI is zero, a limiting case of the formula. This example is for reading, as its draw-by-draw lists may not run in the site calculator.
S = 5; dQ_s = [0.50,0.20,0.70,0.30,0.65]; dC_s = [10000,10000,10000,10000,10000]; lambda = 60000; INHB_s = [0.3333,0.0333,0.5333,0.1333,0.4833]; EVPI_H = 0; EVPI_M = 0
Common errors
Converting a two-option EVPI to money at a different threshold
Multiplying the EVPI of 0.06 QALYs found at GBP 25,000 by GBP 35,000 gives GBP 2,100 per patient. The EVPI at GBP 35,000 is about 0.0171 QALYs, or GBP 600, because the threshold also changes which draws favour the drug.
Reporting a single two-option EVPI as if it did not depend on the threshold
In the article's example EVPI is 0.06 QALYs per patient at GBP 25,000 per QALY and about 0.017 at GBP 35,000, more than two thirds lower. A single figure without its threshold cannot be compared with the cost of research.
Sources
ISPOR methods report on reporting EVPI in net benefit at stated thresholds
Rothery C, Strong M, Koffijberg HE, Basu A, Ghabri S, Knies S, Murray JF, Sanders Schmidler GD, Steuten L, Fenwick E. Value of information analytical methods. Report 2 of the ISPOR Value of Information Analysis Emerging Good Practices Task Force. Value in Health. 2020;23(3):277-286. Section on reporting, which states that VOI is expressed in net health benefit or net monetary benefit when a cost-effectiveness model is used, and that because both depend on the threshold, VOI is reported for explicit thresholds or as a function of the threshold.
ISPOR introduction worked example of EVPI in net health benefit
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 states its EVPI in units of net health benefit (NHB) and takes the current decision as the option with the highest expected NHB, the choice of a risk-neutral decision maker.
NICE PMG36 section 4.10.8 on net health benefit at two QALY values
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance, the manual (PMG36). London, NICE, 2022, last updated 13 October 2026. Section 4.10.8, which asks for expected net health benefits to be presented when appropriate, using values placed on a QALY gain of GBP 25,000 and GBP 35,000.
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