Concept Architecture
Concept
Theoretically, Optimal Sample Size is the sample size that maximises the expected net benefit of conducting research by balancing the value of reducing decision uncertainty against the cost of collecting additional data. It is founded on Bayesian decision theory and value of information analysis and provides an economically efficient approach to research design. In health economics, optimal sample size is determined by identifying the number of study participants that yields the greatest Expected Net Benefit of Sampling.
Mathematically, the optimal sample size is obtained by maximising the Expected Net Benefit of Sampling across alternative sample sizes. As sample size increases, the Expected Value of Sample Information generally increases because uncertainty is reduced, while research costs also increase. The economically optimal sample size occurs where the difference between these quantities is greatest.
In practice, optimal sample size is estimated by calculating Expected Value of Sample Information and Expected Net Benefit of Sampling for multiple candidate sample sizes using probabilistic sensitivity analysis and Bayesian updating. Health economists use this approach to design clinical trials and observational studies that provide sufficient information to improve decision-making while avoiding unnecessary research expenditure.
Purpose
Used to determine the economically efficient study sample size that maximises the expected value of additional information after accounting for research costs.
Mathematical Formulae
Primary Formula
n* = arg max? ENBS(n)
where:
n* = optimal sample size
ENBS(n) = Expected Net Benefit of Sampling for sample size n
Supporting Formulae
Expected Net Benefit of Sampling:
ENBS(n) = EVSI(n) ? C(n)
where:
EVSI(n) = Expected Value of Sample Information for sample size n
C(n) = research cost associated with sample size n
Decision rule:
Optimal sample size = value of n that produces the maximum ENBS
Related Mathematical Methods
- Expected Net Benefit of Sampling
- Expected Value of Sample Information
- Expected Value of Perfect Information
- Bayesian Decision Theory
- Value of Information Analysis
- Clinical Trial Design
- Research Prioritisation
Example
A health technology assessment evaluates candidate clinical trial sample sizes of 150, 300, 450 and 600 participants. The Expected Net Benefit of Sampling is estimated for each design. The 450-participant study produces the highest ENBS because the additional value of reducing uncertainty beyond this point is smaller than the additional research cost. Consequently, 450 participants represent the economically optimal sample size.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| MAX | =MAX(B2:B10) | Identify the largest ENBS across candidate sample sizes. |
| MATCH | =MATCH(MAX(B2:B10),B2:B10,0) | Locate the optimal sample size. |
| INDEX | =INDEX(A2:A10,MATCH(MAX(B2:B10),B2:B10,0)) | Return the optimal sample size corresponding to the maximum ENBS. |
| IF | =IF(B2=MAX($B$2:$B$10),"Optimal","") | Flag the economically optimal study design. |
VBA (Optional)
VBA can automate ENBS calculations across candidate sample sizes and identify the sample size that maximises the expected economic value of additional research.
Sources
- Claxton K. The irrelevance of inference: a decision-making approach to the stochastic evaluation of health care technologies. Journal of Health Economics. 1999;18(3):341?364.
- Ades AE, Lu G, Claxton K. Expected value of sample information calculations in medical decision modelling. Medical Decision Making. 2004;24(2):207?227.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- ISPOR Value of Information Good Practice Reports.
- NICE. NICE Health Technology Evaluations: The Manual.
Related Concepts (2)
Library
Publications
1
Value of Information Analysis for Research Decisions — An Introduction: Report 1 of the ISPOR Value of Information Analysis Emerging Good Practices Task Force — Fenwick, Steuten, Knies, Ghabri, Basu, Murray, Koffijberg, Strong, Sanders Schmidler & Rothery, Vol. 23, No. 2 ed., 2020 (Value in Health)
The introductory ISPOR good-practice report on value-of-information (VOI) analysis, explaining how VOI quantifies the value of reducing decision uncertainty through further research and where it fits in resource-allocation decisions.
Journal ArticleView source →
Frequently Asked Questions (6)
What is the optimal sample size?
The sample size for a proposed study that maximises the expected net benefit of sampling, balancing information value against rising cost.
Source: Ades, Lu & Claxton 2004
What does the optimal sample size balance?
The optimal sample size for a study is the one that maximises the expected net benefit of sampling, balancing two opposing forces. A larger study yields more information and so more value from better decisions, but it also costs more and delays the decision, and the extra value gained per patient eventually falls. The optimum sits where the added value of one more patient just matches the added cost. It weighs information against expense rather than fixing an arbitrary power. Willan and Pinto (2005) describe this.
Source: Willan & Pinto 2005
How is the optimal sample size determined?
The optimal sample size is determined by computing the expected net benefit of sampling, the expected value of sample information minus the study cost, for a range of sample sizes and finding the size that maximises it. The expected value of sample information rises with sample size, as larger studies resolve more uncertainty, while the cost rises too, so the net benefit peaks at an intermediate size. Identifying that peak gives the optimal sample size, balancing the diminishing gains in information against the growing cost.
Source: Ades, Lu & Claxton 2004
Why is the optimal sample size useful?
The optimal sample size is useful because it grounds the choice of study size in the value the information provides rather than only in conventional power calculations, ensuring the study is neither too small to be worthwhile nor larger than its added value justifies. By maximising the expected net benefit of sampling, it directs research resources efficiently, matching the study's size to where its net value is greatest. This makes the optimal sample size a value-based complement to traditional sample-size determination for planning research.
Source: Claxton & Posnett 1996
How does the optimal sample size differ from conventional sample size calculation?
The optimal sample size is chosen to maximise the expected net benefit of sampling, weighing the value of information against cost, whereas conventional sample-size calculation chooses a size to achieve a target statistical power for detecting a specified effect at a given significance level. The value-of-information approach considers the consequences of the decision and the cost of research, while the conventional approach focuses on statistical detection. So they rest on different criteria, and the optimal sample size reflects economic value rather than only statistical power.
Source: Ades, Lu & Claxton 2004
What are the limitations of determining the optimal sample size?
Determining the optimal sample size depends on the value-of-information estimates, which rest on the model, the assumed parameter distributions, and the population and decision relevance period, and on the assumed study cost, so uncertainty in these affects the result. Computing the expected value of sample information across sample sizes can be demanding. Forecasting the future decision context adds uncertainty. These limitations mean the optimal sample size is treated as an informative guide, computed with appropriate methods and its sensitivity to the key assumptions examined, rather than an exact prescription.
Source: Claxton & Posnett 1996
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 31 Oct 2025
Content version: 1.0.0
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- Persistent URI
- https://healtheconomics.wiki/concept/optimal-sample-size
- Term code
- HE-EM-VI-007
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