Expected Net Benefit of Sampling

Expected Net Benefit of Sampling in Research Design

Expected net benefit of sampling, or ENBS, tells a health system whether a particular study is worth paying for and which version of it is best. It sets the expected improvement in later treatment decisions, summed over everyone they affect, against everything the study costs, including the health forgone by people allocated to the worse option or kept waiting while it runs. A positive value means the design is expected to repay its cost. ENBS is the final step of a value of information analysis, after the screens based on the expected value of perfect information and the expected value of partial perfect information, and the 2026 HEMA report on uncertainty in HTA treats a positive ENBS as the test for asking for more evidence.

From sample information to a net value for one study

The calculation starts from the per-person expected value of sample information (EVSI), the expected gain from deciding after a proposed study reports rather than now. The ISPOR value of information task force (Rothery and colleagues, 2020) defines ENBS as the difference between population EVSI and the cost of the data collection, a measure of the net value of any particular study.

$$\text{ENBS}(n) = \text{EVSI}(n) \times \sum_{t=0}^{T} \frac{I_t}{(1+d)^t} - C(n)$$

where $n$ indexes the study design (sample size, allocation, follow-up), $\text{EVSI}(n)$ is per-person EVSI, $I_t$ is the number of people facing the decision in period $t$, $T$ is the time horizon over which the evidence stays useful, $d$ is the discount rate per period and $C(n)$ is the expected total cost of the study. The same discounted population turns per-person EVPI into population EVPI.

Fenwick and colleagues (2020) list 3 cost components, fixed costs such as set-up and salaries, a variable cost per participant, and an opportunity cost for participants who receive the option expected to be inferior while the study runs.

$$C(n) = C_F + c_V \, n + L(n)$$

where $C_F$ is the fixed cost, $c_V$ is the variable cost per participant and $L(n)$ is the expected net benefit forgone during the study. Value of information is expressed as net monetary benefit or net health benefit, both of which depend on the cost-effectiveness threshold, so Rothery and colleagues ask for results at explicit thresholds or across a range of them.

The last screen in a value of information sequence

Claxton and Posnett (1996) proposed a decision-analytic approach to trial design that accounts for the costs of sampling and the benefits of sample information, with a set of screens or hurdles for research proposals. The task force recommendations set out these screens in sequence. Research stops when its expected cost exceeds population EVPI, population EVPPI is compared with the cost of research on particular parameters, population EVSI is compared with the cost of a proposed study, and the most efficient design is the one with the greatest ENBS.

The earlier screens can only rule research out. Rothery and colleagues state that population EVPI or EVPPI above the cost of a study is necessary but not sufficient for research to be of value, since no finite study delivers perfect information. Fenwick and colleagues treat a positive ENBS as sufficient for the worth of a specific study, and when no design has a positive ENBS the current evidence should be considered sufficient for decision making. Rothery and colleagues add that ENBS of zero or more is necessary only if the study informs this decision alone and has no wider value, so a study that would also inform other decisions or jurisdictions can be worth more than its ENBS suggests.

Choosing sample size, follow-up and allocation

Conventional sample size calculation fixes the number of participants from type I and type II error rates and a clinically important difference. Willan and Pinto (2005) note that the usual 0.05 and 0.2 error rates take no account of the cost of either error, and show how to find the sample size that maximises the difference between the value of the information and the cost of the trial. Claxton and Posnett had argued that the traditional approach can give unbounded or arbitrary sample sizes.

$$n^* = \arg\max_{n \in \mathcal{N}} \text{ENBS}(n)$$

where $n^*$ is the efficient design and $\mathcal{N}$ is the set of feasible designs. Per-person EVSI rises with sample size but never exceeds per-person EVPI, while variable and opportunity costs keep growing with each participant, so ENBS typically rises to a peak and then falls.

The design space is wider than sample size. Conti and Claxton (2009) show that sample sizes and their allocation between arms should be chosen to maximise ENBS, and that when several types of study could inform different parameters ENBS must be estimated across all of them together to find the best portfolio.

Time, delay and who bears the cost of research

People treated before a study reports cannot benefit from it. Fenwick and colleagues recommend adjusting the beneficiary population for the time a study takes and, when funding is delayed while evidence is gathered, for the patients enrolled. Participants in the better arm benefit during the study, an effect most pronounced in rare diseases. Eckermann and Willan (2008) show that time for accrual, follow-up and analysis shrinks the population that can benefit, lowering EVSI and the expected net gain of a trial, their name for ENBS and pointing to smaller trials where trials are worthwhile.

The access arrangement during the study changes the cost side. McKenna and Claxton (2011) separate the effect of a research decision on patients enrolled in the trial, on those not enrolled and on everyone treated after it reports, and examine whether approval should be withheld until the research reports. Fenwick and colleagues explain that restricting a technology to people in research avoids committing irrecoverable costs, while patients outside the study miss what may be the best treatment. The same trial can therefore have a different ENBS under approval with research and under only in research.

How HTA uses ENBS when deciding on more evidence

The HEMA report (Steuten and colleagues, 2026) states that EVSI and ENBS value the information from a specific study against its cost. It holds that further research, only in research or managed access where routine adoption is compatible with it, is warranted only when the expected value of resolving the uncertainty exceeds the cost of the research and of the health forgone by waiting, which is the condition of a positive ENBS. It recommends reporting EVPI with every probabilistic analysis and using EVPPI and EVSI where a research decision is actually in prospect, and its stylised examples treat research costing less than EVPI as a first hurdle only.

The report also uses ENBS to set a price. Where uncertainty would be worth resolving but a manufacturer declines to undertake or fund feasible research, it suggests a reduced price at the research-indifference price, the price at which the ENBS of the best available study falls to zero. For managed access with evidence development, a form of managed entry agreement, its conditions include resolvable uncertainty, extra information worth more than it costs, recoverable adoption costs and a credible expectation that the research will be done and reported.

Its recommendations ask whether further research is feasible and whether its expected value justifies the cost, delay and burden involved.

Worked example with four trial sizes

All numbers are illustrative. A new treatment is compared with standard care and the uncertainty is summarised as 2 states. With probability 0.6 the treatment works well and its incremental net monetary benefit (INMB) is GBP 1,000 per patient, and with probability 0.4 it works poorly and its INMB is −GBP 1,000.

1. Current decision and EVPI. Expected INMB is 0.6 × 1,000 − 0.4 × 1,000 = 200, so the treatment is adopted. Perfect information would switch to standard care in the poor state, so per-person EVPI is 0.4 × 1,000 = 400.

2. Per-person EVSI. A trial points to the true state with probability $a$, assumed to be 0.7, 0.8, 0.9 and 0.95 for 100, 300, 600 and 1,000 patients (a real analysis derives these from the likelihood). For any $a$ above 0.6 an unfavourable result leads to standard care and a favourable one to adoption, so the expected value with the trial is 0.6a × 1,000 − 0.4(1 − a) × 1,000 = 1,000a − 400.

$$\text{EVSI} = (1{,}000a - 400) - 200 = 1{,}000a - 600$$

where $a$ is the accuracy of the trial result and 200 is the expected INMB of the current decision. EVSI is GBP 100, 200, 300 and 350 per patient, always below the EVPI of GBP 400.

3. Population value and costs. The discounted number of future patients whose treatment follows the result is 8,000 for every design, a simplification since larger trials take longer. The study costs GBP 200,000 fixed plus GBP 2,000 per participant, and with equal allocation half the participants receive standard care and forgo the expected INMB of GBP 200 each.

4. The efficient design. For 600 patients, 300 × 8,000 = 2,400,000 and the cost is 200,000 + 1,200,000 + 60,000 = 1,460,000, so ENBS is 2,400,000 − 1,460,000 = 940,000. All four designs are worthwhile and 600 patients is the efficient size, with population EVPI of 400 × 8,000 = 3,200,000 capping every row.

5. Delay under only in research. Suppose the treatment is available only in research, so 2,000 people treated outside the 600-patient trial while it runs miss GBP 200 each. That adds 2,000 × 200 = 400,000 to the cost, and ENBS falls to 940,000 − 400,000 = 540,000. If the 300-patient trial reports sooner with 1,000 people waiting, its ENBS becomes 770,000 − 200,000 = 570,000 and the smaller trial is now efficient.

6. Interpretation. Research is worth commissioning, but the best size depends on who carries the cost while it runs, which a sample size chosen for statistical power alone ignores.

Choices that move the answer

ENBS depends on the model, the data the study would generate and the people it would reach. The following choices can change its sign and the efficient design, and Rothery and colleagues ask for all assumptions to be stated.

• Threshold. INMB, and so EVSI, changes with the threshold, and a design efficient at one threshold may not be at another.
• Population and horizon. Cohort size, time to report and the useful life of the evidence scale the gain directly.
• The simulated data. Rothery and colleagues recommend a data-generating distribution that mirrors how the study would be analysed, including expected censoring, missing data and measurement bias.
• Implementation. Heath (2022) notes that standard EVSI ignores the slow and often incomplete uptake of findings and so misstates a study's value.

Misreadings of ENBS

ENBS answers a narrow question about one design for one decision. Treating it as a broader verdict leads to recurring errors.

• Reading a high population EVPI as proof that research is worthwhile. EVPI is a ceiling, and only ENBS for a feasible design shows that a study repays its cost.
• Subtracting study cost from per-person EVSI. The cost belongs against the population value, after scaling and discounting.
• Treating a negative ENBS as a verdict on all research. It applies to the design evaluated, and a smaller or shorter study may still be worthwhile.
• Leaving out the cost of waiting. Health forgone by participants and by patients denied access during an only in research period is part of the cost.
• Treating a positive ENBS as a guarantee. The HEMA report notes that the research still has to be done and reported, and the decision reassessed.

Sources

• Claxton K, Posnett J. An economic approach to clinical trial design and research priority-setting. Health Economics. 1996;5(6):513-524. https://doi.org/10.1002/(SICI)1099-1050(199611)5:6%3C513::AID-HEC237%3E3.0.CO;2-9
• Conti S, Claxton K. Dimensions of design space: a decision-theoretic approach to optimal research design. Medical Decision Making. 2009;29(6):643-660. https://doi.org/10.1177/0272989X09336142
• Eckermann S, Willan AR. Time and expected value of sample information wait for no patient. Value in Health. 2008;11(3):522-526. https://doi.org/10.1111/j.1524-4733.2007.00296.x
• 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. https://doi.org/10.1016/j.jval.2020.01.001
• Heath A. Calculating expected value of sample information adjusting for imperfect implementation. Medical Decision Making. 2022;42(5):626-636. https://doi.org/10.1177/0272989X211073098
• McKenna C, Claxton K. Addressing adoption and research design decisions simultaneously: the role of value of sample information analysis. Medical Decision Making. 2011;31(6):853-865. https://doi.org/10.1177/0272989X11399921
• 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. https://doi.org/10.1016/j.jval.2020.01.004
• Steuten L, Thavorn K, Cipriano LE, et al. Methods to Analyze and Present Uncertainty in Economic Evaluation to Support HTA Decisions. Steuten et al. 2026 (HEMA Report 2). Health Economics Methods Advisory; 2026. https://hemamethods.org/wp-content/uploads/2026/10/HEMA-Report-2_For-Publication_100726.pdf
• Willan AR, Pinto EM. The value of information and optimal clinical trial design. Statistics in Medicine. 2005;24(12):1791-1806. https://doi.org/10.1002/sim.2069