What to shrink? Random Effects in Discrete Data Meta-Analysis Keywords: meta-analysis, random effects, GLMM Traditional methods of random effects meta-analysis shrink study-specific estimates of relative effect size while ignoring the absolute prevalence in each group. Such an approach avoids issues of amalgamation such as Simpson's paradox. Due to limitations of this approach, some have turned to generalized linear mixed models (GLMMs) that estimate both relative effect size and absolute prevalence. Inclusion of a study-level random effect for the relative effect size in the GLMM parallels the traditional approach to meta-analysis. Treatment of the parameters for absolute prevalence has no similar analog in this literature. We examine the implications of including a random effect for prevalence, especially as related to the amalgamation paradox.
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