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

Ilyas Bakbergenuly, Elena Kulinskaya, Stephan Morgenthaler

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7 Citations (Scopus)
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We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probability inline image, both for single-group studies and in combining results from several groups or studies in meta-analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta-analysis and result in abysmal coverage of the combined effect for large K. We also propose bias-correction for the arcsine transformation. Our simulations demonstrate that this bias-correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta-analyses of prevalence.
Original languageEnglish
Pages (from-to)896–914
Number of pages19
JournalBiometrical Journal
Issue number4
Early online date18 May 2016
Publication statusPublished - Jul 2016


  • inter-cluster correlation
  • meta-analysis
  • overdispersion
  • random effects
  • transformation bias

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