Signature
C_n = C_F + c_V * n + s_inf * n * abs(INB)
| Inputs | Definition | Unit |
|---|---|---|
C_F | Cost that does not depend on the number of participants, such as set-up costs and salaries | currency |
c_V | Cost of recruiting, treating and following up each participant | currency per participant |
n | Number of participants in the study across both arms | participants |
s_inf | Proportion of the n participants allocated to the option with the lower expected net benefit on current information, 0.5 under equal allocation | proportion |
INB | Expected incremental net benefit per person of the new treatment over standard care on current information, negative when standard care is expected to be better | currency per person |
C_n | Expected total cost of the study, including the opportunity loss to participants | 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
Expected cost of a two-arm study in one Excel cell
With the fixed cost in FixedCost, the cost per participant in CostPerParticipant, the sample size in SampleSize, the share on the inferior option in InferiorShare and the expected incremental net benefit in ExpectedINB, the cell adds the three components. ABS keeps the participant loss positive when standard care is expected to be better.
=FixedCost+CostPerParticipant*SampleSize+InferiorShare*SampleSize*ABS(ExpectedINB)
Assumptions
Participants on the option expected to be better lose nothing
Participants allocated to the option with the higher expected net benefit receive what they would have received outside the study, and Fenwick and colleagues note that those in the optimal arm benefit while the study is conducted. The loss for the other arm is valued with the current expected incremental net benefit, on the same scale and threshold as EVSI.
Stated perspective for the cost of a study
Fenwick and colleagues state that the total cost is commonly determined from a societal perspective, although it may also be considered from the perspective of the sponsor of the study. The fixed and variable costs are those of the design as specified, so a change in follow-up or endpoints changes them.
Worked examples
Cost of the article's 600-patient trial with equal allocation
The article's illustrative study costs GBP 200,000 fixed plus GBP 2,000 per participant, and with equal allocation 300 participants receive standard care and forgo the expected incremental net monetary benefit of GBP 200 each, a loss of GBP 60,000. The total is GBP 1,460,000.
C_F = 200000; c_V = 2000; n = 600; s_inf = 0.5; INB = 200; C_n = 1460000
Cost of the article's 1,000-patient trial with equal allocation
For the article's largest design the variable cost is GBP 2,000,000 and the participant loss GBP 100,000, so the total is GBP 2,300,000.
C_F = 200000; c_V = 2000; n = 1000; s_inf = 0.5; INB = 200; C_n = 2300000
Cost of a 600-participant study with no participant on the inferior option
When no participant receives the option expected to be inferior, for example a follow-up study of patients on the option expected to be best (illustrative), the loss term is zero and the cost is the fixed and variable cost alone, GBP 1,400,000.
C_F = 200000; c_V = 2000; n = 600; s_inf = 0; INB = 200; C_n = 1400000
Common errors
Opportunity loss to participants left out of the study cost
Dropping the GBP 100,000 participant loss from the article's 1,000-patient trial raises its ENBS to GBP 600,000 instead of GBP 500,000, an overstatement of 20%. Rothery and colleagues include the opportunity cost to people while the research is under way in the cost of research.
Participant loss charged to every participant
Charging the GBP 200 loss to all 1,000 participants of the article's largest trial doubles the loss to GBP 200,000 and cuts its ENBS to GBP 400,000 instead of GBP 500,000 (computed here for illustration). Only those on the option expected to be inferior forgo benefit.
Sources
Three cost components of a research design
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 estimating the value of specific research, where the expected costs of a design include fixed costs such as set-up costs and salaries, a variable cost per study participant and the opportunity cost for participants who receive the technology expected to be inferior while the study is under way, with the total cost commonly determined from a societal perspective.
Reporting the costs of sample information for ENBS
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 the expected net benefit of sampling, where the costs of research include the opportunity costs to individuals while the research is under way, such as participants receiving a non-optimal intervention, and the reporting section, which lists the fixed cost, the variable costs of the design and the expected opportunity costs.
Canonical Identity
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