title: Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies.
abstract: 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 p̂, 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.
authors.affiliation: School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK.
authors.forename: Ilyas
authors.initials: I
authors.lastname: Bakbergenuly
authors.affiliation: School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK.
authors.forename: Elena
authors.initials: E
authors.lastname: Kulinskaya
authors.affiliation: École polytechnique fédérale de Lausanne (EPFL), Station 8, 1015 Lausanne, Switzerland.
authors.forename: Stephan
authors.initials: S
authors.lastname: Morgenthaler
mesh_terms: D016010:Binomial Distribution; D003198:Computer Simulation; D008137:Longitudinal Studies; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D015995:Prevalence; D011336:Probability
keywords: Intracluster correlation; Meta-analysis; Overdispersion; Random effects; Transformation bias