Signature
ENBS_ub = EVPI_pop - C_n
| Inputs | Definition | Unit |
|---|---|---|
EVPI_pop | Population expected value of perfect information for the same population, horizon, discount rate and threshold as the ENBS (HE-FM-VOI-002) | currency |
C_n | Expected total cost of the design, from HE-FM-ENBS-002 | currency |
ENBS_ub | Largest ENBS the design could have, population EVPI less the study cost | currency |
|---|
Function
Expected net benefit of sampling as population sample information less the cost of a study
Maps one proposed study design, through its population expected value of sample information and its expected total cost, to the expected net benefit of sampling, the net value of that study. Per-person EVPI and its population form are on the Value of Information page (HE-FM-VOI-001 and HE-FM-VOI-002), and the expected net benefit that fixes the current decision is on the Expected Net Benefit page (HE-FN-ENB-001). EVSI is defined on the EVSI page (HE-FN-EVSI-001), and population EVSI, per-person EVSI scaled by the discounted beneficiary population, is HE-FM-EVSI-004 there. This package adds ENBS for one design, the expected cost of a study with the opportunity loss to participants, the cost of waiting under only in research, the ceiling set by population EVPI and a search for the efficient sample size. Notation follows the Expected Net Benefit of Sampling article.
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Implementations
Excel
Population EVPI ceiling on ENBS in Excel
With population EVPI in PopulationEVPI and the expected study cost in StudyCost, the cell returns the ceiling. A value of zero or below rules the design out.
=PopulationEVPI-StudyCost
Assumptions
EVPI and EVSI on the same population and threshold
Population EVPI and population EVSI use the same beneficiary population, time horizon, discount rate and threshold. Otherwise EVSI can appear to exceed EVPI and the ceiling no longer holds.
Same study cost in the ceiling as in the ENBS
C_n is the full expected cost used for ENBS, including the participant loss of HE-FM-ENBS-002. Using the fixed cost alone gives a weaker screen that rules out fewer designs.
Worked examples
Population EVPI ceiling for the article's 600-patient trial
Per-person EVPI of GBP 400 across 8,000 discounted people gives population EVPI of GBP 3,200,000. Less the cost of GBP 1,460,000 the ceiling is GBP 1,740,000, above the trial's ENBS of GBP 940,000.
EVPI_pop = 3200000; C_n = 1460000; ENBS_ub = 1740000
Study costing more than population EVPI
An illustrative study costing GBP 3,500,000 against the article's population EVPI of GBP 3,200,000 has a ceiling of minus GBP 300,000, so it cannot be worthwhile whatever its EVSI.
EVPI_pop = 3200000; C_n = 3500000; ENBS_ub = -300000
Common errors
Population EVPI above the study cost read as proof that the study is worthwhile
With an illustrative discounted population of 4,000, population EVPI is GBP 1,600,000, above the GBP 1,460,000 cost of the article's 600-patient trial, yet its ENBS is minus GBP 260,000 (computed here for illustration). Population EVPI is a ceiling, and only ENBS for a feasible design shows that a study repays its cost.
Sources
Population EVPI as a necessary but not sufficient condition for research
Fenwick E, Steuten L, Knies S, et al. 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. Section on establishing whether more research is potentially worthwhile and good practice recommendation 5, where research is not worthwhile when its expected cost exceeds population EVPI, and population EVPI above the cost of research is a necessary, but not sufficient, condition because perfect information is not achievable with a finite sample.
Population EV(P)PI against the cost of any research study
Rothery C, Strong M, Koffijberg HE, et al. 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 key concepts, definitions and notation, after equation 7, where a population EV(P)PI below the estimated costs of any research study is a sufficient condition for research not being of value, and one above the cost is necessary but not sufficient.
HEMA report treating cost below EVPI as a first hurdle
Steuten L, Thavorn K, Cipriano LE, et al. Methods to Analyze and Present Uncertainty in Economic Evaluation to Support HTA Decisions (HEMA Report 2). Health Economics Methods Advisory; 2026. Table 5.2, page 41, where research costing less than EVPI is a first hurdle, with ENBS above zero still to be shown.
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