Meta-Analysis: Random Effects Analysis

Assumption Underlying Random-Effects Meta-Analysis

The underlying assumption of random-effects meta-analysis lies on the allowance of the underlying true effect sizes to follow a normal distribution. The logic behind this allowance is that each study included in a meta-analysis may examine a different population and consequently might have genuine differences with the rest of the studies. For instance, consider a meta-analysis including 10 studies that examine the effectiveness of an educational intervention A, with another education intervention B. Each study includes equal [Page 1002]number of participants, coming from a classroom across Europe. Whether the 10 underlying true effects reduce to a common value or differ among studies is subject to the presence or absence of study-specific factors that might impact on the relative effectiveness of the educational interventions. The effect size (the measure that quantifies the difference in effectiveness between the two interventions) might differ according to the age of the children, the location of the school, the socioeconomic conditions of the country, and other factors. In such a case, a researcher may consider implausible that the relative effectiveness of “A versus B” in a class of 12-year-old children in Germany will be the same as a class of 10-year-old children in Italy. Then, the fixed-effect assumption is not appropriate and the variation among underlying effects can be modeled in a random-effects meta-analysis.

Heterogeneity

In a random-effects meta-analysis, two sources of variation exist. At first, each study is subject to random error, as in the fixed-effect analysis. The study random error expresses the uncertainty in the estimation of the intervention effect within each study and it reduces as the study sample size increases. The second source of variation is termed heterogeneity and refers to the dispersion among underlying true treatment effects. Heterogeneity implies that even if each study included in the meta-analysis were of infinite sample size, the observed effect sizes would not be identical (as they would in a fixed-effect analysis).

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