Fixed-Effect and Random-Effects Models in Meta-Analysis

Fixed-effect and random-effects models are two fundamental approaches in meta-analysis for combining effect estimates from multiple studies into a pooled estimate. The fixed-effect model, also known as the common-effect model, assumes all included studies estimate a single underlying effect, with observed differences due to sampling error. In contrast, the random-effects model assumes that the true effects may vary across studies because of differences in populations, interventions, settings, or other study characteristics. Students will learn how these assumptions influence the interpretation of pooled estimates: a fixed-effect estimate represents the common effect under its model assumptions, whereas a random-effects estimate typically represents the mean of a distribution of true study effects. Understanding these distinctions is essential for selecting a model that aligns with the research question and the characteristics of the available evidence.

The second component focuses on the mathematical principles underlying pooled effect estimation, particularly inverse-variance weighting. In this approach, each study receives a weight based on the precision of its effect estimate, with its sampling variance determining its contribution to the pooled result. For random-effects models, the weighting also incorporates the between-study variance (tau^2), which represents variation in true effects across studies. Students will be introduced to methods for estimating (tau^2), including DerSimonian–Laird and restricted maximum likelihood (REML), and will examine how heterogeneity influences study weights and the pooled estimate. The session also covers confidence intervals for pooled effects and introduces the Hartung–Knapp–Sidik–Jonkman approach, which can provide adjusted uncertainty estimates in random-effects meta-analysis, particularly when the number of studies is limited.

The final component examines the advantages, limitations, and assumptions of both models, emphasizing that model selection should not rely solely on a statistical test for heterogeneity. Students will consider the research objective, the expected diversity of true effects, the design and characteristics of the included studies, and the intended interpretation of the pooled estimate. Although the random-effects model accounts for between-study variation, it does not eliminate heterogeneity or automatically make the results more reliable; its appropriateness depends on the underlying assumptions and the quality of the evidence. By the end of this session, students should be able to explain the differences between fixed-effect and random-effects models, describe inverse-variance weighting and the estimation of between-study variance, interpret pooled estimates and their confidence intervals, and justify a model choice based on the research question and study characteristics.