Examples
Worked examples
- Is an instance
A meta-analysis of 15 randomized trials testing a drug's effect on blood pressure plots each trial's effect size against its standard error. Several small trials cluster at the bottom of the funnel showing unusually large benefits, while the larger, more precise trials cluster near a smaller pooled effect -- a visibly asymmetric funnel. That pattern is consistent with (but does not by itself prove) publication bias: it is equally consistent with genuine clinical heterogeneity between the small and large trials, or with methodological weaknesses concentrated in the smaller studies. The next step is a formal asymmetry test and a sensitivity analysis, not a conclusion.
- Is an instance
Egger's test, a linear-regression-based test for funnel-plot asymmetry, regresses each study's standardized effect estimate against its precision; a statistically significant intercept indicates asymmetry. The Cochrane Handbook recommends against relying on Egger's test (or any funnel-plot asymmetry test) with fewer than about 10 studies in the meta-analysis, since power to distinguish real asymmetry from chance is too low below that threshold.
Counter-examples
Looks similar, but isn't
- Not an instance
A symmetric funnel plot does not rule out publication bias. If small studies with unfavorable or null results are suppressed at roughly the same rate regardless of their precision, or if there are simply too few studies to see a pattern, the plot can look symmetric even though selective reporting is occurring. Symmetry is reassuring, not conclusive.
- Not an instance
Asymmetry driven by a single very large, methodologically distinct trial (for example, one multi-site trial with a different patient population than the smaller single-site trials) reflects genuine clinical heterogeneity, not publication bias -- inspecting which studies drive the asymmetry, not just the summary shape, is part of correct interpretation.
Editorial commentary
What a funnel plot shows
A funnel plot is a diagnostic chart used in meta-analysis and systematic review to look for signs of small-study effects — the tendency for smaller studies to report systematically different, usually larger, effects than larger studies in the same body of evidence. Each point on the plot represents one included study: its effect estimate (for example, a log odds ratio, risk ratio, or mean difference) is plotted on the x-axis, and a measure of its precision — most commonly standard error, plotted so precision increases up the y-axis — is plotted on the y-axis. Sample size is sometimes used in place of standard error. In the absence of bias or meaningful heterogeneity, the resulting scatter should resemble an inverted funnel: small, imprecise studies scatter widely near the bottom, and large, precise studies cluster narrowly near the top, close to the pooled effect estimate.
What asymmetry does and does not prove
A visibly lopsided, asymmetric funnel plot is a widely used signal that something may be distorting the body of evidence — but funnel-plot asymmetry is not synonymous with, or proof of, publication bias. The Cochrane Handbook is explicit on this point: asymmetry can arise from several distinct causes, and a funnel plot alone cannot distinguish between them:
- Publication or reporting bias — smaller studies with null or unfavorable results are less likely to be published or fully reported, leaving a gap in the funnel.
- Genuine clinical or methodological heterogeneity — smaller studies may have been conducted in different populations, settings, or with different intervention intensities than larger studies, producing real differences in effect that have nothing to do with selective reporting.
- Poor methodological quality correlated with study size — smaller studies are, on average, more likely to have design weaknesses (inadequate blinding or allocation concealment) that inflate effect estimates, independent of any publishing decision.
- Chance — with a small number of studies, an asymmetric-looking pattern can simply be a product of random variation.
Because of this, funnel-plot asymmetry should be treated as a prompt for further investigation, not a finding to report on its own.
Egger’s test
Egger’s test is a regression-based statistical test for funnel-plot asymmetry: it regresses each study’s standardized effect estimate against its precision, and a statistically significant non-zero intercept indicates asymmetry. It formalizes what the plot shows visually, but carries the same interpretive caveat — a significant result flags asymmetry, not its cause. The Cochrane Handbook recommends against relying on Egger’s test, or most other funnel-plot asymmetry tests, when a meta-analysis includes fewer than about 10 studies, since statistical power to distinguish genuine asymmetry from chance is too low below that threshold.
Trim-and-fill
Trim-and-fill (Duval and Tweedie’s method) is a sensitivity-analysis technique that estimates how many studies would need to be ‘missing’ from one side of the funnel to restore symmetry, imputes those studies, and recalculates the pooled effect including them. It is used to gauge how sensitive the meta-analysis’s conclusion is to a publication-bias explanation for observed asymmetry — it is an exploratory adjustment, not a bias-free corrected result, and its own estimates depend on assumptions that can be wrong when asymmetry has a non-bias cause.
When a funnel plot is (and isn’t) appropriate
Funnel plots and their associated asymmetry tests are only meaningfully interpretable with a reasonable number of studies — the Cochrane Handbook’s general guidance is at least 10 — and are not recommended as a primary tool when the included studies are highly heterogeneous in design, since heterogeneity itself can produce funnel-plot asymmetry unrelated to publication bias. See CASRAI’s guides on detecting and assessing publication bias and peer reviewing a systematic review or meta-analysis for how funnel plots fit into a broader bias-assessment workflow, and the forest plot entry for the companion visualization used to display the pooled result itself rather than assess bias in it.
Machine-readable encodings
Use in your systems
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