Fixed Effects and Random Effects in Meta-Analysis

This chapter introduces fixed-effects and random-effects models used in meta-analysis where fixed-effects is the weighted mean method and random effects is the DerSimonian-Laird random-effects model implemented in R libraries rmeta, meta, and metafor. When meta-analyzing effect sizes from different studies (such as separate clinical trials), the fundamental assumption in the fixed-effects model that the true effect size is the same for all studies may be impractical. Therefore, the random-effects meta-analysis model can incorporate both within-study and between-study variability which may be an important source of heterogeneity for meta-analysis. In practice, many analysts perform both a fixed-effects and a random-effects meta-analysis of the same set of studies – even if there is an “a priori” basis for believing the fixed-effects model is appropriate. The chapter discusses meta-analysis methods for synthesizing studies using publicly available data sets with both fixed-effects and random-effects models.