Recommendations for examining and interpreting funnel plot asymmetry in meta-analyses of randomised controlled trials
Open accessAbstract
Funnel plots, and tests for funnel plot asymmetry, have been widely used to examine bias in the results of meta-analyses. Funnel plot asymmetry should not be equated with publication bias, because it has a number of other possible causes. This article describes how to interpret funnel plot asymmetry, recommends appropriate tests, and explains the implications for choice of meta-analysis model
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The non-significant tendencies to asymmetry and small study effects identified by the Eggers and Begg tests, presumably caused by the similar SEM of most of the studies, can be assumed to be trustworthy.
“so the non-significant tendencies to asymmetry and small study effects identified by the Eggers and Begg tests, presumably caused by the similar SEM of most of the studies, can be assumed to be trustworthy [30].”
From Are Dietary Proteins the Key to Successful Body Weight Management? A Systematic Review and Meta-Analysis of Studies Assessing Body Weight Outcomes after Interventions with Increased Dietary Protein (2021) · cites this paper as [30]
Box 2 says asymmetry tests should not be used when studies’ standard errors are all similar. The Statistical tests for funnel plot asymmetry section also says these tests have low power and that a non-significant result cannot exclude bias. The paper therefore does not support treating the reported test results as trustworthy because the studies had similar SEMs. (LLM, conf=0.90)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredPublication bias was not assessed because no forest plot had at least ten studies.
“publication bias was not assessed in this review because there was no forest plot with at least ten studies (Sterne et al. 2011).”
From The Effect of Mindfulness-Based and Acceptance Commitment Therapy-Based Interventions to Improve the Mental Well-Being Among Parents of Children with Developmental Disabilities: A Systematic Review and Meta-Analysis. (2022) · cites this paper as Sterne et al. 2011
Box 2 recommends against tests for funnel plot asymmetry when a meta-analysis has fewer than 10 studies, because such tests usually have too little power. It does not say that publication bias cannot be assessed by other means, and the citing review’s study counts are its own finding, not a finding of this source. (LLM, conf=0.86)
Experimental — accuracy not yet measuredPublication bias was assessed using funnel plot analysis and Egger's test where the number of studies for the outcome of interest was at least 10.
“Publication bias was assessed using funnel plot analysis and Egger's test where the number of studies for the outcome of interest was ≥10”
From IVF/ICSI or surgery as first approach for the treatment of infertility associated with ovarian and deep infiltrating endometriosis? A systematic review and meta-analysis. (2026) · cites this paper as Sterne et al., 2011
Box 2 recommends against tests for funnel-plot asymmetry with fewer than 10 studies and says Egger’s test may be used for continuous outcomes. It also cautions that some analyses need more than 10 studies, that other tests may be preferable for dichotomous outcomes, and that asymmetry does not necessarily indicate publication bias. The source supports the cited threshold as a rule of thumb, not as a sufficient condition for using Egger’s test to assess publication bias in every outcome. (LLM, conf=0.85)
Experimental — accuracy not yet measuredPublication bias was assessed by visual inspection of funnel plot asymmetry for comparisons with data from at least ten studies.
“For those comparisons in which data were obtained from at least ten studies (Sterne et al. 2011), publication bias was assessed by visual inspection of funnel plot asymmetry.”
From Analysis of sex-based differences in energy substrate utilization during moderate-intensity aerobic exercise (2022) · cites this paper as Sterne et al. 2011
Box 2 recommends avoiding statistical tests for funnel plot asymmetry when a meta-analysis has fewer than ten studies and says test results should be interpreted alongside visual inspection. It does not set ten studies as a threshold specifically for visual inspection. Box 2 also cautions that asymmetry has causes other than publication bias, so visual inspection alone cannot establish publication bias. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe asymmetry likely represents a 'small study bias', where methodological approaches inherent in small studies lead to stronger effects with greater variance.
“Instead, the asymmetry likely represents a ‘small study bias’, where methodological approaches inherent in small studies lead to stronger effects with greater variance (Peters et al., 2008; Sterne et al., 2011).”
From The Distributed Practice Effect on Classroom Learning: A Meta-Analytic Review of Applied Research (2025) · cites this paper as Sterne et al., 2011
The Heterogeneity section (page not specified in our copy) says smaller studies tend to use less rigorous methods and that lower-quality trials tend to show larger effects. The Reporting bias section says smaller studies have more sampling error. But the Discussion describes multiple possible causes of funnel plot asymmetry; the paper does not establish that methodological bias is the likely cause of the particular asymmetry described here. (LLM, conf=0.86)
Experimental — accuracy not yet measured
Publication bias was assessed by visual inspection of a funnel plot, Egger test for asymmetry, and Begg test for small-study effects.
“Publication bias was assessed by visual inspection of funnel plot and by Egger test to assess asymmetry, as well as by Begg test to assess small study effects [29,30,31].”
From Are Dietary Proteins the Key to Successful Body Weight Management? A Systematic Review and Meta-Analysis of Studies Assessing Body Weight Outcomes after Interventions with Increased Dietary Protein (2021) · cites this paper as [30]
The paper’s section on interpreting funnel plot asymmetry discusses visual inspection, and Box 2 recommends Egger’s test for asymmetry under specified conditions. Our copy does not describe a Begg test for small-study effects; Begg appears only in the references. The paper also cautions that funnel plot asymmetry is not necessarily publication bias. (LLM, conf=0.86)
Experimental — accuracy not yet measuredIf a meta-analysis had adequate power (≥10 cohorts), funnel plots were generated and Egger test used to assess small study effects.
“If a meta-analysis of a medication adherence measure had adequate power (ie, ≥10 cohorts), funnel plots were generated and visually inspected, and the Egger test was used to assess for small study effects (funnel plot asymmetry) potentially caused by reporting bias.30”
From Adherence to PCSK9 Inhibitors in Clinical Practice (2026) · cites this paper as [30]
Box 2 recommends avoiding asymmetry tests with fewer than 10 studies and interpreting results alongside visual inspection of funnel plots. It permits Egger’s test for continuous outcomes, but the guidance concerns randomised controlled trials, not cohorts, and notes that even 10 studies may be insufficient when heterogeneity is substantial. It does not establish that the citing authors’ analyses had adequate power. (LLM, conf=0.86)
Experimental — accuracy not yet measuredBias statistics were only calculated if the total number of correspondence audits for a given analysis equalled or exceeded ten, because otherwise statistical power could be too low to detect asymmetry.
“we only calculated bias statistics if the total number of correspondence audits for a given analysis equalled or exceeded ten, otherwise, the statistical power could be too low to detect asymmetry.”
From The state of hiring discrimination: A meta-analysis of (almost) all recent correspondence experiments (2023) · cites this paper as Sterne et al., 2011
Box 2 recommends not testing funnel plot asymmetry when a meta-analysis has fewer than 10 studies, because test power is usually too low. The citing sentence applies that threshold to correspondence audits rather than studies; the source does not establish that it applies in that setting. No page number is provided in our copy. (LLM, conf=0.86)
Experimental — accuracy not yet measuredBecause the symmetry of funnel plots could be influenced by various factors, such as publication bias, and/or small-study effects, it was difficult to figure out the cause of asymmetry, especially when the sample size of each comparison was less than ten.
“Because the symmetry of funnel plots could be influence by various factors, such as publication bias, and/or small-study effects, it was difficult to figure out the cause of asymmetry, especially when the sample size of each comparison was less than ten [82].”
From Efficacy and safety of curcuminoids alone in alleviating pain and dysfunction for knee osteoarthritis: a systematic review and meta-analysis of randomized controlled trials (2022) · cites this paper as [82]
Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredPublication bias was assessed by plotting each trial's effect against standard errors, creating one effect size per study per outcome.
“To assess risk of publication bias, we plotted each trial's effect against the standard errors (Sterne et al., 2011), creating a single effect size per study per outcome.”
From Shared Picture Book Reading Interventions for Child Language Development: A Systematic Review and Meta-Analysis (2020) · cites this paper as Sterne et al., 2011
Heterogeneity can influence funnel plot asymmetry.
“Notably, heterogeneity can also influence funnel plot asymmetry (Sterne et al., 2011).”
From The Distributed Practice Effect on Classroom Learning: A Meta-Analytic Review of Applied Research (2025) · cites this paper as Sterne et al., 2011
The Egger test was not employed to formally assess funnel plot asymmetry because it is not recommended for small numbers of studies.
“Consequently, the Egger test was not employed to formally assess funnel plot asymmetry, as it is not recommended for such small numbers of studies [25].”
The review was not able to explore possible publication bias through a funnel plot because it did not combine a sufficient number of trials.
“We were not able to explore possible publication bias through a funnel plot (Sterne 2011), as we did not combine a sufficient number of trials.”
From Mobile technologies to support healthcare provider to healthcare provider communication and management of care (2020) · cites this paper as Sterne 2011
Funnel plots were generated for visual assessment for asymmetry and potential publication bias.
“Funnel plots were generated for visual assessment for asymmetry and potential publication bias 31 (see Figures S20–S29).”
From Systematic review and meta-analysis of protein intake to support muscle mass and function in healthy adults (2022) · cites this paper as [31]
Tests for funnel plot asymmetry should only be used where there are at least 10 studies in each meta-analysis.
“Typically tests for funnel plot asymmetry should only be used where there are at least 10 studies in each meta-analysis (Sterne et al., 2011).”
From Nature-based outdoor activities for mental and physical health: Systematic review and meta-analysis (2021) · cites this paper as Sterne et al., 2011
Publication bias was assessed with funnel plots, Rosenthal's fail-safe N, and Egger's regression intercept.
“Presence of publication bias was assessed with funnel plots, 22 Rosenthal's fail-safe N , 23 and Egger's regression intercept. 24”
From Light Therapy for Patients With Bipolar Depression: Systematic Review and Meta-Analysis of Randomized Controlled Trials (2020) · cites this paper as [22]
A funnel plot and Egger's test for asymmetry was used to explore publication and small study biases where at least 10 different-sized studies were pooled.
“To explore publication and small study biases, a funnel plot and Egger ' s test for asymmetry was used where at least 10 different-sized studies were pooled. 62”
From High-velocity power training has similar effects to traditional resistance training for functional performance in older adults: a systematic review (2023) · cites this paper as [62]
Small study effects (e.g. publication bias) were assessed when there were 10 or more studies in the meta-analysis by visually examining the funnel plot, supplemented by Egger's test and Duval and Tweedie's trim and fill.
“Small study effects (e.g. publication bias) were assessed when there were 10 or more studies in the meta-analysis by visually examining the funnel plot, supplemented by Egger’s test of funnel plot asymmetry [39, 40]. Duval and Tweedie’s trim and fill procedure was used to estimate the effect size after imputing potentially missing studies [41].”
From Systematic review and meta-analysis of Mental Health First Aid training: Effects on knowledge, stigma, and helping behaviour (2018) · cites this paper as [40]
The asymmetry in the sleep outcome could exist due to chance, as the analysis contained few studies with few participants.
“this asymmetry could exist due to chance, as the analysis contained few studies with few participants (Sterne et al., 2011).”
From The effects of physical activity on cortisol and sleep: A systematic review and meta-analysis. (2022) · cites this paper as Sterne et al., 2011
For each risk factor, no meta-analysis included more than ten studies, so funnel plots and Egger's test were not assessed to calculate risk of bias.
“However, for each risk factor, no one included more than ten studies; these numbers were too small so that the test efficacy of funnel plots and egger's test was insufficient [31]. Therefore, funnel plots and Egger's test were not assessed to calculate the risk of bias.”
From Preoperative Risk Factors for Short-Term Postoperative Mortality of Acute Mesenteric Ischemia after Laparotomy: A Systematic Review and Meta-Analysis (2020) · cites this paper as [31]
Publication bias or other small study effects were assessed using the Egger test if there were ≥10 eligible studies.
“We assessed the latter for evidence of asymmetry, and therefore possible publication bias or other small study effects, using the Egger test, 35 if there were suf fi cient ( 10) eligible studies included in the meta-analysis, in line with recommendations. 36”
From Efficacy of Probiotics in Irritable Bowel Syndrome: Systematic Review and Meta-analysis (2023) · cites this paper as [36]
It is not recommended to use tests for funnel plot asymmetry when the number of studies included in a meta-analysis is less than 10, because statistical power is usually too low to distinguish chance from real asymmetry.
“According to Sterne et al. (2011) it is not recommended to use tests for funnel plot asymmetry when the number of studies included in the meta-analysis is <10 as statistical power is usually too low to distinguish chance from real asymmetry.”
From The effect of internet-delivered cognitive behavioral therapy for depression and anxiety on quality of life: A meta-analysis of randomized controlled trials (2023) · cites this paper as Sterne et al., 2011
Not all asymmetric funnel plots are due to issues that impact meta-analytic inference.
“However, not all asymmetric funnel plots are due to issues that impact meta-analytic inference (Sterne et al., 2011).”
From Can MRI measure myelin? Systematic review, qualitative assessment, and meta-analysis of studies validating microstructural imaging with myelin histology (2021) · cites this paper as Sterne et al., 2011
Publication bias was not formally assessed using funnel plots or asymmetry tests due to the small number of included studies.
“Due to the small number of included studies, publication bias was not formally assessed using funnel plots or asymmetry tests, as these methods have low statistical power under such conditions (Sterne et al., 2011).”
From Efficacy and safety of small interfering RNA (siRNA) therapies for hypertriglyceridemia and mixed dyslipidemia: an updated systematic review and meta-analysis (2026) · cites this paper as Sterne et al., 2011
Egger's test was not performed because testing for publication bias is not advised for fewer than 10 studies.
“Because the test for a publication is not advised for fewer than 10 studies, Egger’s test was not performed.20”
Risk of bias was assessed with the Cochrane Collaboration's Rob2 tool, independently rated by two authors, with discrepancies resolved through discussion.
“To assess risk of bias, the Cochrane Collaboration's risk-of-bias tool (Rob2) was used (Sterne et al., 2011).”
From Effects of voluntary slow breathing on heart rate and heart rate variability: A systematic review and a meta-analysis (2022) · cites this paper as Sterne et al., 2011
The paper’s Reporting bias and Interpreting funnel plot asymmetry sections discuss biases in meta-analyses, not the Rob2 risk-of-bias tool. Searches for Rob2 and for the described assessment procedure found no passage identifying this paper as the tool or documenting its use. (LLM, conf=0.78)
Experimental — accuracy not yet measuredIncluded studies exceeded the minimum number of effect sizes to be pooled.
“Included studies exceeded the minimum number of effect sizes to be pooled [98].”
From Estimating the Effect of Aerobic Exercise Training on Novel Lipid Biomarkers: A Systematic Review and Multivariate Meta-Analysis of Randomized Controlled Trials (2023) · cites this paper as [98]
Box 2 (page unavailable) recommends a rule-of-thumb minimum of 10 studies for testing funnel plot asymmetry, not a minimum number of effect sizes required for pooling. The source does not report how many studies or effect sizes the citing analysis included, so it cannot establish that they exceeded a minimum. (LLM, conf=0.78)
Experimental — accuracy not yet measuredFunnel plot asymmetry may be due to true heterogeneity, selection bias, bias in design or analysis, or chance.
“This may be due to several reasons, including true heterogeneity (i.e., smaller studies differ from larger ones in terms of study population, exposure levels, etc.), selection bias (i.e., the selective publication of small studies showing an effect), bias in design or analysis, or chance [77,78].”
From COSMOS-E: Guidance on conducting systematic reviews and meta-analyses of observational studies of etiology (2019) · cites this paper as [77]
Publication bias was examined by inspecting the funnel plot and conducting the Egger test, and Duval and Tweedie's trim and fill procedure was used to adjust the effect size for missing studies.
“Publication bias was examined by inspecting the funnel plot [44] and conducting the Egger test of the intercept with a one-tailed significance level of α=.05 [45]. In addition, we used Duval and Tweedie’s trim and fill procedure [46] to adjust the effect size for missing studies.”
Based on current recommendations, at least 10 studies are needed to examine reporting bias using funnel plots, and if heterogeneity is high, the minimum number of studies may be substantially more than 10.
“Based on current recommendations, at least 10 studies are needed to examine reporting bias using funnel plots and, if the heterogeneity is high, the minimum number of studies may be substantially more than 10. 34”
From Global prevalence of sarcopenia and severe sarcopenia: a systematic review and meta‐analysis (2022) · cites this paper as [34]
Trialists may deliver interventions less thoroughly in larger trials, which could explain more positive findings in smaller trials.
“Trialists may have implemented interventions less thoroughly in larger trials, thus explaining the more positive results in smaller trials 57 .”
From Investigating and dealing with publication bias and other reporting biases in meta-analyses of health research: a review (2021) · cites this paper as [57]
Small trials usually precede larger trials, and standard control treatments may improve over time, reducing the experimental treatment's relative efficacy.
“Small trials generally are conducted before larger trials are established, and in the intervening years standard, control treatments may have improved, which can reduce the relative efficacy of the experimental treatment.”
From Investigating and dealing with publication bias and other reporting biases in meta-analyses of health research: a review (2021) · cites this paper as [57]
Brief contact interventions reduce the number of suicide attempts per person but not the total number of suicide attempts or suicide deaths.
“Brief contact interventions reduce the number of suicide attempts per person but not the total number of suicide attempts or suicide deaths.9”
Funnel plots were constructed for only 1 analysis because fewer than 10 studies were included in each analysis.
“We constructed funnel plots for only 1 analysis due to the small number of studies included in each analysis (n<10) [63,64].”
From Tailored web-based interventions for pain: Systematic review and meta-analysis (2017) · cites this paper as [64]
Several reviews could not evaluate the presence of publication bias because of the small number of studies in the meta-analyses.
“Several reviews could not evaluate the presence of publication bias because of the small number of studies in the meta-analyses”
From Association between the reproductive health of young women and cardiovascular disease in later life: umbrella review (2020) · cites this paper as [123]
The Begg's and Egger's tests were not used because there were not more than 10 subjects in each group.
“The Begg’s and Egger’s tests were not used because there were not more than 10 subjects in each group.15”
From A comprehensive analysis of the efficacy and safety of COVID-19 vaccines (2021) · cites this paper as [15]
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- Authors
- Sterne, J. A. C., Sutton, A. J., Ioannidis, J. P. A., Terrin, N., Jones, D. R., Lau, J., Carpenter, J., Rucker, G., Harbord, R. M., Schmid, C. H., Tetzlaff, J., Deeks, J. J., Peters, J., Macaskill, P., Schwarzer, G., Duval, S., Altman, D. G., Moher, D., & Higgins, J. P. T.
- Affiliations
- University of Bristol (GB)
- University of Leicester (GB)
- Stanford Medicine (US)
- Tufts University (US)
- London School of Hygiene & Tropical Medicine (GB)
- Ottawa Hospital Research Institute (CA)
- University of Birmingham (GB)
- University of Exeter (GB)
- The University of Sydney (AU)
- University of Freiburg (DE)
- University of Minnesota (US)
- University of Oxford (GB)
- Corresponding author
- Sterne, J. A. C.
- ORCID
- Venue
- BMJ
- Publisher
- BMJ
- Published
- 2011-07-22
- Volume
- 343
- Issue
- jul22 1
- Pages
- d4002-d4002
- ISSN
- 0007-1447 (ISSN-L)
- 0959-8138
- 1468-5833
- OpenAlex
- W2119605658
- Semantic Scholar
- 660168dbe48731c1dae7dfd14a0525404d8e59e5
- Cited by
- 7,709
- References
- 45
- Citations by year
- 2026: 967 · 2025: 792 · 2024: 824 · 2023: 766 · 2022: 786 · 2021: 687 · 2020: 610 · 2019: 492 · 2018: 447 · 2017: 377 · 2016: 304 · 2015: 241 · 2014: 197 · 2013: 122 · 2012: 74
- FWCI
- 136.80
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- BMJ (publishedVersion)
- PubMed (publishedVersion)
- Bristol Research (University of Bristol) (publishedVersion)
- LSHTM Research Online (London School of Hygiene and Tropical Medicine) (acceptedVersion)
- Leicester Research Archive (University of Leicester) (submittedVersion)
- HighWire Press Open Archive (submittedVersion)
- University of Birmingham Research Portal (University of Birmingham) (submittedVersion)
- Explore Bristol Research (submittedVersion)
- Funders
- Cancer Research UK
- Deutsche Forschungsgemeinschaft (FOR 534)
- Canadian Institutes of Health Research
- Medical Research Council (U1052.00.011)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- funnel plot asymmetry, publication bias, meta-analysis bias, randomized controlled trials, heterogeneity
- MeSH terms
- Statistics as Topic, Meta-Analysis as Topic, Selection Bias, Randomized Controlled Trials as Topic
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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