A brief note on the random-effects meta-analysis model and its relationship to other models

Meta-analysis is a statistical method for combining quantitative results across studies. A fundamental decision in undertaking a meta-analysis is choosing an appropriate model for analysis. This is the second of two companion articles which have the joint aim of describing the different meta-analysis models. In the first article, we focused on the common-effect (also known as fixed-effect singular) model, and in this article, we focus on the random-effects model. We describe the key assumptions underlying the random-effects model, how it is related to the common-effect and fixed-effects plural models, and present some of the arguments for selecting one model over another. We outline some of the methods for fitting a random-effects model. Finally, we present an illustrative example to demonstrate how the results can differ depending on the chosen model and method. Understanding the assumptions of the different meta-analysis models, and the questions they address, is critical for meta-analysis model selection and interpretation.