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Related Concept Videos

Sample Size Calculation01:19

Sample Size Calculation

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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Estimating Population Mean with Unknown Standard Deviation01:22

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Estimating Population Mean with Known Standard Deviation01:16

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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Updated: Apr 18, 2026

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Bayesian sample size determination using robust commensurate priors with interpretable discrepancy weights.

Lou E Whitehead1, James Ms Wason1, Oliver Sailer2

  • 1Biostatistics Research Group, Population Health Sciences Institute, Newcastle University, UK.

Statistical Methods in Medical Research
|April 16, 2026
PubMed
Summary
This summary is machine-generated.

Bayesian clinical trials can use historical data, but sample size calculations are often complex. This study introduces a linearization technique for more interpretable weights, simplifying expert elicitation in trial design.

Keywords:
Bayesian sample size determination, commensurate priorsHistorical borrowing, prior aggregation, uniform shrinkage

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Area of Science:

  • Clinical Research Methodology
  • Biostatistics
  • Evidence-Based Medicine

Background:

  • Randomized controlled trials (RCTs) are the gold standard for treatment efficacy.
  • Bayesian methods offer a framework for incorporating prior knowledge from historical studies into new trial designs.
  • Existing methods for borrowing strength from historical data often use discounting factors that lack interpretability.

Purpose of the Study:

  • To address the non-interpretability of discounting factors (weights) in Bayesian meta-analysis for clinical trials.
  • To develop a method for incorporating historical data from multiple sources that improves the elicitation of expert opinion.
  • To derive an analytical sample size formula that is sensitive to interpretable weights.

Main Methods:

  • Focusing on methods for incorporating historical data from multiple sources.
  • Highlighting issues of nonmonotonicity in sample size calculations related to discounting factors.
  • Proposing a linearization technique to ensure uniform changes in sample size with respect to weights.

Main Results:

  • The proposed linearization technique results in interpretable weights, expressed as a percentage of information to borrow or discount.
  • An analytical sample size formula was derived based on the proposed method.
  • The linearization facilitates a more straightforward elicitation of expert opinion on the degree of borrowing or discounting historical information.

Conclusions:

  • The developed method enhances the interpretability of weights in Bayesian clinical trial design.
  • This approach simplifies the process of incorporating expert knowledge into sample size determination.
  • Improved elicitation of expert opinion can lead to more efficient and robust clinical trial designs.