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.
Original language | English |
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Pages (from-to) | 896–914 |
Number of pages | 19 |
Journal | Biometrical Journal |
Volume | 58 |
Issue number | 4 |
Early online date | 18 May 2016 |
DOIs | |
Publication status | Published - Jul 2016 |
Keywords
- inter-cluster correlation
- meta-analysis
- overdispersion
- random effects
- transformation bias
Profiles
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Elena Kulinskaya
- School of Computing Sciences - Emeritus Professor
- Norwich Epidemiology Centre - Member
Person: Honorary, Research Group Member