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Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis

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Nonlinear transformations in mixed-effects models cause significant bias in group studies and meta-analyses. A proposed bias-correction for the arcsine transformation effectively reduces this issue, especially with small intracluster correlation.

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Area of Science:

  • Statistics
  • Biostatistics
  • Meta-analysis

Background:

  • Random and mixed-effects models are widely used in group-level studies and meta-analysis.
  • Nonlinear transformations of random variables can introduce bias in statistical inference.
  • Overdispersed binomial distributions are common in prevalence studies.

Purpose of the Study:

  • To investigate bias arising from nonlinear transformations in random or mixed-effects models.
  • To assess the impact of this bias on inference in group-level studies and meta-analysis.
  • To propose and evaluate a bias-correction method for the arcsine transformation.

Main Methods:

  • Simulations were used to study bias in overdispersed binomial distributions.
  • Standard log-odds and arcsine transformations were examined.
  • Bias-correction for the arcsine transformation was developed and tested.
  • The methods were applied to two meta-analysis examples of prevalence data.

Main Results:

  • Standard log-odds and arcsine transformations introduce considerable bias in estimated probabilities.
  • Bias is linear in the intracluster correlation coefficient (ρ) for small ρ.
  • Bias magnitude is independent of sample sizes and the number of studies (K).
  • Uncorrected biases lead to poor coverage of the combined effect, especially for large K.
  • The proposed bias-correction for the arcsine transformation performs well for small intraclass correlations.

Conclusions:

  • Nonlinear transformations in mixed-effects models can lead to substantial bias in meta-analysis.
  • Bias-correction methods are necessary for accurate inference, particularly with correlated data.
  • The bias-corrected arcsine transformation offers improved accuracy for prevalence meta-analyses.