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Optimal group sizes for testing group mean differences using the Bayes factor.

Mirjam Moerbeek1

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Summary
This summary is machine-generated.

Determining optimal group sizes for studies is crucial. This research introduces a Bayesian approach to maximize the Bayes factor, offering a superior alternative to traditional methods for heterogeneous study designs.

Keywords:
Analysis of varianceBayes factorbudgetary constraintinformative hypothesisoptimal design methodology

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Area of Science:

  • Biostatistics
  • Statistical Study Design

Background:

  • Determining appropriate group sizes is essential for studies comparing mean outcomes.
  • Traditional optimal design methods, based on null hypothesis significance testing, have limitations, especially with heterogeneous costs or variances.
  • Bayesian hypothesis testing offers an alternative framework using the Bayes factor.

Purpose of the Study:

  • To determine optimal group sizes that maximize the Bayes factor for comparing mean outcomes across groups.
  • To investigate the influence of variances, costs, and group means on these optimal group sizes.
  • To compare the efficiency of Bayesian optimal design with conventional methods and equal group allocation.

Main Methods:

  • Utilizing the Bayes factor within a Bayesian hypothesis testing framework.
  • Calculating optimal group sizes by maximizing the Bayes factor.
  • Comparing derived optimal group sizes with those from conventional optimal design and equal group allocation.

Main Results:

  • Optimal group sizes are dependent on variances, costs, and group means.
  • Conventional optimal design and equal group sizes result in a smaller Bayes factor compared to the Bayesian optimal design.
  • The methodology was illustrated with examples in pain management and asthma research.

Conclusions:

  • The Bayesian approach provides a robust method for determining optimal group sizes, particularly in studies with heterogeneous parameters.
  • This method offers a more efficient design than traditional approaches, leading to stronger evidence for hypotheses.
  • A practical tool (Shiny app) is available to implement this optimal design methodology.