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

Bakbergenuly, Ilyas, Kulinskaya, Elena and Morgenthaler, Stephan (2016) Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies. Biometrical Journal, 58 (4). 896–914. ISSN 1521-4036

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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 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.

Item Type:	Article
Uncontrolled Keywords:	inter-cluster correlation,meta-analysis,overdispersion,random effects,transformation bias
Faculty \ School:	Faculty of Science > School of Computing Sciences Faculty of Science
UEA Research Groups:	Faculty of Science > Research Groups > Data Science and Statistics Faculty of Medicine and Health Sciences > Research Centres > Business and Local Government Data Research Centre (former - to 2023) Faculty of Science > Research Groups > Norwich Epidemiology Centre Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre
Depositing User:	Pure Connector
Date Deposited:	13 Apr 2016 12:02
Last Modified:	12 May 2023 00:06
URI:	https://ueaeprints.uea.ac.uk/id/eprint/58207
DOI:	10.1002/bimj.201500115

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