Key Difference Between Fixed-Effect and Random-Effects Meta-Analysis

The main difference between a fixed-effect and a random-effects meta-analysis lies in their underlying assumptions about the nature of the effect size being investigated and the generalizability of the findings.

• Fixed-effect meta-analysis: assumes a single, common effect size (or "true effect") that all studies in the meta-analysis are trying to estimate. Any variation in the observed effect sizes across studies is attributed solely to random sampling error within each study. Consequently, the fixed-effect model calculates the weighted average of the study estimates using the inverse of the estimates' variance as the study weight. This approach prioritizes larger studies with smaller variances.
• Random-effects meta-analysis: acknowledges that the true effect size may vary across studies due to methodological or substantive differences. Each study is considered to be estimating a different, but related, population effect size, and these effect sizes are assumed to follow a distribution. The random-effects model takes into account both within-study and between-study variability and considers studies as random samples from a larger population of studies with diverse true effect sizes.

Implications of Model Choice

This fundamental difference in assumptions leads to several practical implications:

• Weighting of studies: Fixed-effect models typically give more weight to larger studies with smaller variances, potentially leading to a situation where a single large study can dominate the analysis. In contrast, random-effects models assign more balanced weights, acknowledging the unique contribution of each study, even smaller ones.
• Width of confidence intervals: Confidence intervals for the pooled effect size are typically narrower in fixed-effect models than in random-effects models. This is because fixed-effect models only account for within-study variability, while random-effects models also incorporate between-study variability, leading to greater uncertainty in the overall estimate.
• Generalizability of findings: Fixed-effect models limit inferences to the specific set of studies included in the meta-analysis. In other words, they focus on the "typical intervention effect" observed in the analyzed studies. On the other hand, random-effects models allow for broader generalizations to the larger population of studies from which the included studies were drawn.
• Sensitivity to bias: Random-effects models can be more sensitive to publication bias, particularly when small studies with potentially biased results receive more weight.
• Applicability in specific contexts: Fixed-effect models might be more appropriate when studies are highly similar and can be considered replicates, or in situations like legal applications where generalizability beyond the specific studies is not desired. However, in most meta-analysis scenarios involving studies pulled from the literature, where heterogeneity is expected, random-effects models are generally preferred.

The choice between fixed-effect and random-effects models is a crucial decision in meta-analysis, impacting the interpretation and generalizability of the findings. Researchers should carefully consider the nature of the research question, the characteristics of the included studies, and the potential for biases when selecting the appropriate statistical model.