Concept Architecture
Concept
Theoretically, Sequential Sampling is a statistical sampling methodology in which data are evaluated continuously or at predefined intervals during collection, allowing recruitment to stop once sufficient evidence has been obtained. It is founded on sequential analysis and statistical decision theory, providing an alternative to fixed-sample designs by potentially reducing the number of observations required while maintaining predefined error rates. In health economics, sequential sampling is used within adaptive clinical trials and economic evaluations to improve study efficiency and reduce research costs.
Mathematically, sequential sampling is represented by sequential hypothesis testing procedures in which accumulated evidence is compared with predefined stopping boundaries after each observation or interim analysis. The mathematical framework controls Type I and Type II error probabilities while permitting early stopping for efficacy, futility or safety. The Sequential Probability Ratio Test (SPRT) is the classical canonical formulation.
In practice, sequential sampling is implemented by specifying stopping rules, interim analyses and statistical monitoring procedures before recruitment begins. Data are analysed as they accumulate, and recruitment continues until the stopping criteria are satisfied or the maximum sample size is reached. Health economists incorporate sequential sampling into trial-based economic evaluations to reduce unnecessary recruitment while preserving valid estimates of costs and health outcomes.
Purpose
Used to improve the efficiency of clinical studies by allowing recruitment to stop as soon as sufficient statistical evidence has accumulated while maintaining predefined levels of statistical validity.
Mathematical Formulae
Primary Formula
?? = L(H?) / L(H?)
Continue sampling while:
B < ?? < A
Stop and accept H? if:
?? � A
Stop and accept H? if:
?? � B
where:
A = (1 ? ?) / �
B = ? / (1 ? �)
Supporting Formulae
Power = 1 ? ?
Type I error = �
Type II error = ?
Related Mathematical Methods
- Sequential Probability Ratio Test (SPRT)
- Sequential analysis
- Group sequential methods
- Interim analysis
- Bayesian sequential analysis
- Adaptive trial design
Example
A clinical trial compares a new intervention with standard care using a sequential design with � = 0.05 and power = 80%. Interim analyses are performed after every 50 participants. After 250 participants, the accumulated likelihood ratio exceeds the upper stopping boundary, demonstrating treatment benefit. Recruitment is terminated early, reducing trial costs while maintaining the planned statistical error rates.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| LN | =LN(Likelihood_H1/Likelihood_H0) | Calculates the log likelihood ratio during sequential monitoring |
| IF | =IF(LR>=A,"Stop: Accept H1",IF(LR<=B,"Stop: Accept H0","Continue")) | Applies sequential stopping rules |
| NORM.S.INV | =NORM.S.INV(1-0.05) | Obtains critical values used when defining stopping boundaries |
VBA (Optional)
VBA can automate sequential monitoring by updating likelihood ratios after each interim analysis and notifying investigators when predefined stopping boundaries are reached.
Sources
- Wald A. Sequential Analysis. John Wiley & Sons.
- Jennison C, Turnbull BW. Group Sequential Methods with Applications to Clinical Trials.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Good Practices for Real-World Data Studies of Treatment and/or Comparative Effectiveness: Recommendations from the Joint ISPOR-ISPE Special Task Force on Real-World Evidence in Health Care Decision Making — Berger, Sox, Willke, Brixner, Eichler, Goettsch, Madigan, Makady, Schneeweiss, Tarricone, Wang, Watkins & Mullins, Vol. 20, No. 8 ed., 2017 (Value in Health)
The joint ISPOR-ISPE recommendations on good procedural practice for real-world data studies (observational studies and registries) used to inform healthcare decisions — study registration, replicability and stakeholder involvement — the reference for RWE credibility in HTA.
Journal ArticleView source →
Frequently Asked Questions (6)
What is sequential sampling?
A data collection approach in which the decision to continue or stop sampling is made based on accumulating data, rather than a fixed sample size.
Source: Wald 1947
How does sequential sampling differ from fixed-size sampling?
Fixed-size sampling decides the number of observations in advance and analyses only once they are all collected, whereas sequential sampling examines the data as they accumulate and lets that examination decide when to stop. Sampling continues until the evidence reaches a predefined level of certainty, so a clear answer can be reached with fewer observations, while an unclear one prompts further collection. This can save effort but requires statistical adjustment for the repeated looks. It stops when the data are conclusive, not at a set count. Whitehead (1997) describes this approach.
Source: Whitehead 1997
How does sequential sampling work?
Sequential sampling works by defining stopping criteria in advance and evaluating the accumulating data after each observation or group of observations against them: if the evidence crosses a boundary supporting a conclusion, sampling stops; otherwise it continues. Wald's sequential probability ratio test, for example, compares the likelihood of the data under competing hypotheses and stops when the ratio crosses preset limits. The boundaries are set to control error rates, so sequential sampling balances early stopping against the risk of a wrong conclusion, gathering only as much data as needed.
Source: Wald 1947
Why is sequential sampling used?
Sequential sampling is used because it can reach a conclusion with fewer observations than a fixed-sample approach when the evidence is strong, saving time, resources, and, in trials, participant exposure. By monitoring data as it accumulates and stopping once enough evidence is gathered, it avoids collecting more than necessary. This efficiency is valuable where observations are costly or where prompt decisions are wanted, so sequential sampling suits settings in which data arrive over time and early stopping, when justified, is beneficial, provided the stopping rules control error appropriately.
Source: Pocock 1977
What are the advantages of sequential sampling?
The advantages of sequential sampling are efficiency, since it often requires fewer observations than a fixed-sample approach when the effect is clear, reducing cost and, in research, exposure of participants; and flexibility, allowing decisions to be reached as soon as the evidence is sufficient. This can shorten studies and free resources. Because it adapts to the accumulating evidence, sequential sampling avoids over-collecting data when the answer emerges early. These advantages make it attractive for situations where data accrue over time and timely, efficient decisions are valued, given appropriate control of error.
Source: Wald 1947
What are the limitations of sequential sampling?
The limitations of sequential sampling include the need for predefined stopping rules that control error rates, since repeatedly evaluating accumulating data without adjustment inflates the chance of a false conclusion; the greater complexity of design and analysis than fixed-sample methods; and the possibility that estimates from early stopping are biased, tending to overstate effects. The eventual sample size is also uncertain at the outset. These limitations mean sequential sampling is applied with properly constructed stopping rules and careful interpretation of results from early stopping, weighing its efficiency against its added complexity and the risks of stopping early.
Source: Wald 1947
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 19 Nov 2025
Content version: 1.0.0
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- HE-ES-CTM-085
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