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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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The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
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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.
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Bayesian sample size determination for diagnostic accuracy studies.

Kevin J Wilson1, S Faye Williamson2, A Joy Allen3,4

  • 1School of Mathematics, Statistics & Physics, Newcastle University, Tyne and Wear, UK.

Statistics in Medicine
|April 11, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new Bayesian method for determining sample size in diagnostic accuracy studies, leveraging prior data from analytical validity. This approach can reduce sample size requirements when prior information is available.

Keywords:
Bayesian assurancebinomial intervalscontingency tablespower calculationssensitivityspecificity

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Area of Science:

  • Biostatistics
  • Medical Diagnostics
  • Health Technology Assessment

Background:

  • Diagnostic test development involves sequential stages: analytical validity, diagnostic accuracy, and clinical utility.
  • Accurate sample size determination is crucial for reliable diagnostic test evaluation.
  • Existing methods may not fully leverage available prior information.

Purpose of the Study:

  • To propose a novel Bayesian approach for sample size determination in diagnostic accuracy studies.
  • To integrate data from the analytical validity stage into sample size calculations.
  • To offer a flexible method that can utilize or ignore prior data during accuracy inference.

Main Methods:

  • A Bayesian approach using assurance for sample size calculation based on posterior probability interval width.
  • Utilization of prior information from analytical validity studies.
  • Sensitivity analyses to assess prior choice robustness and evaluation of prior-data conflict.

Main Results:

  • The proposed assurance-based Bayesian approach can reduce the required sample size compared to traditional methods when prior information is suitable.
  • Sensitivity analyses demonstrate the robustness of the sample size to prior selection.
  • Prior-data conflict evaluation provides insights into model assumptions.

Conclusions:

  • The novel Bayesian sample size determination method offers an efficient alternative, particularly when prior data is available.
  • This approach enhances the evaluation of diagnostic test accuracy by optimizing sample size.
  • The method is illustrated with a practical application in diagnosing ventilator-associated pneumonia.