Concept Architecture
Concept
Theoretically, Sample Size Optimisation is the process of determining the most appropriate sample size for a study by balancing statistical precision, study power, resource constraints and decision objectives. It extends conventional sample size determination by incorporating optimisation principles to achieve an efficient trade-off between the value of additional information and the costs of data collection. In health economics, sample size optimisation is widely applied in clinical trial design, economic evaluations and value of information analyses.
Mathematically, sample size optimisation is formulated as an optimisation problem in which sample size is selected to satisfy statistical criteria, such as target power and significance level, while minimising total expected costs or maximising expected net benefit. Conventional sample size formulae provide the statistical foundation, whereas optimisation methods incorporate cost functions, expected value of information or decision-theoretic objective functions to identify the optimal sample size.
In practice, sample size optimisation is undertaken during study design using assumptions regarding treatment effect, outcome variability, significance level, statistical power, recruitment costs and decision uncertainty. Health economists frequently combine standard power calculations with Expected Value of Sample Information (EVSI) or cost-effectiveness decision models to determine whether the additional information gained from recruiting more participants justifies the additional study costs.
Purpose
Used to determine the most efficient study sample size by balancing statistical validity, decision uncertainty, research costs and the expected value of additional information.
Mathematical Formulae
Primary Formula
n = ((Z??�?? + Z???)� ? 2��) / ?�
where:
- n = required sample size per group
- Z??�?? = critical value for the significance level
- Z??? = critical value for statistical power
- �� = outcome variance
- ? = minimum clinically important difference or expected treatment effect
Supporting Formulae
Power = 1 ? ?
EVSI(n) = Expected value of information obtained from a study of sample size n
Optimal n = argmax? [EVSI(n) ? Cost(n)]
Related Mathematical Methods
- Statistical power analysis
- Expected Value of Sample Information (EVSI)
- Expected Value of Perfect Information (EVPI)
- Bayesian decision analysis
- Optimisation
- Cost-effectiveness analysis
Example
A randomised controlled trial compares two treatments using quality-adjusted life-years (QALYs) as the primary outcome. The expected treatment difference is 0.08 QALYs, the standard deviation is 0.25 QALYs, � = 0.05 and power = 80%.
n = ((1.96 + 0.84)� ? 2 ? 0.25�) / 0.08�
n � 154 participants per treatment group.
An EVSI analysis subsequently demonstrates that increasing recruitment beyond 170 participants per group would generate information worth less than the additional recruitment costs, supporting an optimised sample size close to the calculated value.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| POWER | =POWER((1.96+0.84),2)*2*POWER(0.25,2)/POWER(0.08,2) | Calculates required sample size from standard assumptions |
| NORM.S.INV | =NORM.S.INV(0.975) | Obtains Z-value for the chosen significance level |
| NORM.S.INV | =NORM.S.INV(0.80) | Obtains Z-value corresponding to desired statistical power |
| Solver | Optimise EVSI ? Study Cost | Determines the economically optimal sample size |
VBA (Optional)
VBA can automate sample size optimisation by iteratively evaluating statistical power, study costs and EVSI across candidate sample sizes to identify the optimal design.
Sources
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Claxton K. The Irrelevance of Inference: A Decision-Making Approach to the Stochastic Evaluation of Health Care Technologies. Journal of Health Economics.
- ISPOR Good Practice Task Force Reports on Value of Information Analysis.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Economic Evaluation in Clinical Trials — Glick, Doshi, Sonnad & Polsky, 2nd Edition ed., 2015 (Oxford University Press)
Practical guidance on conducting cost-effectiveness analyses alongside controlled trials, covering trial design, measurement of costs and quality-adjusted life years, handling censored and missing data, and reporting stochastic uncertainty. Volume 4 in the Handbooks in Health Economic Evaluation series.
BookView source →
Frequently Asked Questions (6)
What is sample size optimisation?
The process of determining the number of trial participants needed to reliably detect a treatment effect of a specified, meaningful size.
Source: Friedman LM, Furberg CD, DeMets DL, Reboussin DM, Granger CB. Fundamentals of Clinical Trials. 5th ed. Springer; 2015. doi:10.1007/978-3-319-18539-2.
Why must a trial's sample size be neither too small nor too large?
A trial too small may fail to detect a real and important treatment effect, wasting the effort and exposing participants for an inconclusive answer, while one much larger than needed spends resources and enrols patients beyond what the question requires, and can flag trivial differences as significant. Sample size optimisation finds the number that gives a good chance of detecting an effect of a meaningful size, no more and no less. Getting it right balances reliability against cost and ethics. The right size answers the question efficiently. Friedman and colleagues (2015) describe this.
Source: Friedman et al. 2015
How is sample size determined?
Sample size is determined by a calculation based on the effect size the trial aims to detect, usually a meaningful difference on the primary endpoint; the desired statistical power, the probability of detecting that effect if it exists; the significance level, controlling the false-positive rate; and the variability of the outcome. These inputs, entered into an appropriate formula for the design and outcome, give the number of participants needed. Allowances are made for dropout. The calculation ensures the trial is adequately powered to detect the target effect, so the required sample size reflects these design choices.
Source: Friedman, Furberg & DeMets 2015
Why is sample size important?
Sample size is important because it determines whether a trial has adequate power to detect a meaningful treatment effect: too small a sample risks failing to detect a real effect, wasting resources and potentially missing a beneficial treatment, while an unnecessarily large sample wastes resources and exposes more participants than needed. An appropriate sample size ensures the trial can reliably answer its question while using participants and resources efficiently. Because both under- and over-sized trials have costs and ethical implications, determining the right sample size is a key part of designing a valid and efficient trial.
Source: Friedman, Furberg & DeMets 2015
What factors affect the required sample size?
The factors affecting the required sample size include the size of the treatment effect the trial aims to detect, with smaller effects needing larger samples; the desired power, with higher power requiring more participants; the significance level, with stricter thresholds needing larger samples; the variability of the outcome, with greater variability needing more; and the expected dropout, which requires enrolling extra participants. The design, such as the type of outcome and comparison, also matters. These factors together determine the sample size, so specifying them appropriately is necessary to calculate the number of participants a trial needs.
Source: Friedman, Furberg & DeMets 2015
What are the consequences of an inadequate sample size?
The consequences of an inadequate sample size include insufficient power, so the trial may fail to detect a real and meaningful treatment effect, producing a false-negative result that could wrongly suggest a treatment is ineffective and waste the resources and participants involved. Underpowered trials also give imprecise estimates and are more prone to unreliable findings. Ethically, exposing participants to a trial unlikely to yield a clear answer is problematic. These consequences mean adequate sample size is important, so trials are designed with enough participants to detect the target effect reliably and to justify their conduct.
Source: Friedman, Furberg & DeMets 2015
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 18 Nov 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-ES-CTM-081
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