When binary data exhibit the greater variation than expected, the statistical methods have to account for extra-binomial variation. Possible explanations for extra-binomial variation include intra-cluster dependence or the variability of binomial probabilities. Both of these reasons lead to overdispersion of binomial counts and the resulting heterogeneity in their meta-analysis. Variance stabilizing or normalizing transformations are often applied to binomial counts to enable the use of standard methods based on normality. In meta-analysis, this is routinely done for the inference on overall effect measure. However, these transformations might result in biases in the presence of overdispersion. We study biases arising in the result of transformations of binary variables in the random or mixed effects models. We demonstrate considerable biases arising from standard log-odds and arcsine transformations both for single studies and in meta-analysis. We also explore possibilities of bias correction. In meta-analysis, the heterogeneity of the log odds ratios across the studies is usually incorporated by standard (additive) random effects model (REM). An alternative, multiplicative random effects model is based on the concept of an overdispersion. The multiplicative factor in this overdispersed random effects model can be interpreted as an intra-class correlation parameter. This model arises when one or both binomial distributions in the 2 by 2 tables are changed to betabinomial distributions. The Mantel-Haenzsel and inverse-variance approaches are extended to this setting. The estimation of the random effect parameter is based on profiling the modified Breslow-Day test and improving the approximation for distribution of Q statistic in Mandel-Paule method. The biases and coverages from new methods are compared to standard methods through simulation studies. The misspecification of the REM in respect to the mechanism of its generation is an important issue which is also discussed in this thesis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:725811 |
| Date | January 2017 |
| Creators | Bakbergenuly, Ilyas |
| Publisher | University of East Anglia |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://ueaeprints.uea.ac.uk/65314/ |
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