Random Effects Synthesis

An approach combining evidence that explicitly allows for and estimates genuine variation in the true effect between studies, rather than assuming one common effect.

Source: DerSimonian R, Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials. 1986;7(3):177-188. doi:10.1016/0197-2456(86)90046-2.

Random-effects synthesis assumes that the true effect is not identical across studies but varies around an average, so each study estimates its own slightly different effect drawn from a distribution. It allows this variation because studies differ in their patients, settings, and methods in ways that plausibly change how well a treatment works, making a single common effect unrealistic. By estimating both the average effect and how much it spreads, it gives a more honest, usually wider, interval than a fixed-effect analysis. Acknowledging real between-study variation is its purpose. Borenstein and colleagues (2009) describe this approach.

Source: Borenstein et al. 2009

Random-effects synthesis assumes that the true treatment effects vary across studies, following a distribution, so that the observed variation reflects both genuine between-study differences and sampling error. This contrasts with fixed-effect synthesis, which assumes a single common effect. The random-effects assumption is appropriate when the studies differ clinically or methodologically in ways that could change the effect. So random-effects synthesis rests on the assumption of genuine heterogeneity in the true effects, captured by the between-study variance, which distinguishes it from fixed-effect synthesis and makes it suitable when the studies are not expected to share an identical underlying effect.

Source: DerSimonian & Laird 1986

Random-effects synthesis is used when the studies differ in ways that could genuinely cause the true effect to vary, such as differences in populations, interventions, or settings, and when heterogeneity is present, so that assuming a single common effect would be unrealistic. It accounts for the variation and gives appropriately wider uncertainty. Where the studies are homogeneous, fixed-effect synthesis may suffice. So random-effects synthesis is used under genuine heterogeneity, and the clinical and methodological diversity of the studies, along with the assessed heterogeneity, guides its use over fixed-effect synthesis when combining the evidence.

Source: Higgins et al. 2003

Random-effects synthesis handles heterogeneity by incorporating the between-study variance into the model, so that the pooled estimate is of the mean of the varying true effects and its confidence interval is widened to reflect the additional uncertainty from the variation. As heterogeneity increases, the interval widens and the study weights become more similar. This explicitly accounts for the diversity among studies rather than ignoring it. So random-effects synthesis handles heterogeneity by modelling and estimating it, producing a pooled estimate and uncertainty that acknowledge the genuine variation in true effects, in contrast to fixed-effect synthesis, which assumes no such variation.

Source: DerSimonian & Laird 1986

Random-effects synthesis assumes the true effects vary across studies and estimates a between-study variance, giving relatively more weight to smaller studies and wider intervals under heterogeneity, while fixed-effect synthesis assumes a single common effect, attributes variation to chance, and weights purely by precision. Random-effects synthesis estimates the mean of varying effects and suits heterogeneous studies, whereas fixed-effect synthesis estimates the common effect and suits homogeneous ones. So the two differ in whether they allow the true effect to vary, affecting the weighting, uncertainty, and interpretation, with the choice depending on the heterogeneity among the studies being combined.

Source: DerSimonian & Laird 1986