Fixed Effect Synthesis

An approach to combining evidence assuming all studies estimate a single common true effect, weighting purely by statistical precision.

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.

Fixed-effect synthesis rests on the assumption that every study is estimating one and the same true effect, so the only reason results differ is chance within each study. On that assumption it combines them by weighting each purely by its statistical precision, letting larger studies dominate. This is appropriate when the studies are alike enough that a single common effect is plausible, but misleading when they genuinely differ. One shared true effect is what it presumes. Borenstein and colleagues (2009) describe this approach.

Source: Borenstein et al. 2009

Fixed-effect synthesis assumes that all the studies estimate the same single true effect, so that the differences among their observed results are due only to sampling error rather than to genuine variation in the effect. This assumption of homogeneity underlies the approach and determines when it is appropriate: it suits studies similar enough that a common effect is plausible. If the true effects vary across studies, the assumption fails and random-effects synthesis is preferred. So fixed-effect synthesis rests on the assumption of a common true effect across studies, which is the defining feature distinguishing it from random-effects synthesis.

Source: DerSimonian & Laird 1986

Fixed-effect synthesis is appropriate when the studies are sufficiently similar in populations, interventions, and methods that they can be assumed to estimate a common true effect, and when heterogeneity is minimal. In such cases, weighting purely by precision and treating variation as chance is reasonable. Where the studies are clinically or methodologically diverse and the true effects likely vary, random-effects synthesis is more suitable. So fixed-effect synthesis is used under homogeneity, and the degree of heterogeneity and the similarity of the studies guide whether it or random-effects synthesis is the appropriate approach to combining the evidence.

Source: Higgins et al. 2003

Fixed-effect synthesis weights studies by their statistical precision, typically the inverse of their variance, so that more precise studies, usually larger ones, receive more weight in the pooled estimate. Because it assumes a common effect, the weighting reflects precision alone, with no allowance for between-study variation. This gives the pooled estimate a strong influence from the larger studies. So fixed-effect synthesis combines studies through inverse-variance weighting based purely on precision, which is consistent with its assumption that all the studies estimate the same true effect and that differences among them are only random.

Source: DerSimonian & Laird 1986

Fixed-effect synthesis assumes a single common true effect and weights studies purely by precision, giving larger studies more influence and a narrower confidence interval, while random-effects synthesis assumes the true effects vary across studies, incorporates the between-study variance, weights smaller studies relatively more, and gives wider intervals when heterogeneity is present. Fixed-effect synthesis suits homogeneous studies, and random-effects synthesis suits heterogeneous ones. So the two differ in whether they assume a common effect or allow variation, which affects the weighting, the interval width, and the interpretation, with the choice depending on the heterogeneity among the studies.

Source: DerSimonian & Laird 1986