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Using network meta‐analysis to evaluate the existence of small‐study effects in a network of interventions
Abstract
Suggested methods for exploring the presence of small‐study effects in a meta‐analysis and the possibility of publication bias are associated with important limitations. When a meta‐analysis comprises only a few studies, funnel plots are difficult to interpret, and regression‐based approaches to test and account for small‐study effects have low power. Assuming that the cause of funnel plot asymmetry is likely to affect an entire research field rather than only a particular comparison of interventions, we suggest that network meta‐regression is employed to account for small‐study effects in a set of related meta‐analyses. We present several possible models for the direction and distribution of small‐study effects and we describe the methods by re‐analysing two published networks. Copyright © 2012 John Wiley & Sons, Ltd.
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“Potential small-study effects, including possible publication bias, were explored using ‘comparison-adjusted’ funnel plots.”
From The Effect of Different Psychological Interventions on Athletes' Competitive Anxiety: A Systematic Review and Bayesian Network Meta-Analysis. (2026) · cites this paper as [43]
In the citing paper
“We evaluated the presence of small-study effect (publication bias) by means of comparison-adjusted funnel plots [13].”
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“To assess the presence of small-study effects in the network for the primary outcomes we drew ‘comparisonadjusted’ funnel plots considering that small trials might give more favorable results for the sponsored drugs than larger trials and used network meta-regression models with the variance of the trials as a covaria…”
ResultSelf-citationSchwingshackl, L., Nitschke, K., Zähringer, J., Bischoff, K., Lohner, S., Torbahn, G., Schlesinger, S., Schmucker, C. M., & Meerpohl, J. J. (2020) · Advances in Nutrition · doi:10.1093/advances/nmaa056 · Cited by 46
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“In addition, a comparison-adjusted funnel plot was used to assess smallstudy effects within a network of interventions, with symmetry around the summary effect line indicating the absence of small-study effects (13).”
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“10 was considered to indicate significant asymmetry and publication bias [29, 37].”
BackgroundPharmacological interventions for alcoholic liver disease (alcohol-related liver disease)
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“Therefore, a comparison-adjusted funnel plot with accompanying Egger test for asymmetry was conducted [24].”
MethodNury, E., Stadelmaier, J., Morze, J., Nagavci, B., Grummich, K., Schwarzer, G., HOFFMANN, G. E., Angele, C. M., Steinacker, J. M., Wendt, J., et al. (2022) · BMJ Medicine · doi:10.1136/bmjmed-2022-000346 · Cited by 34
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“For analyses with 10 or more trials, we assessed for publication bias using comparison-adjusted funnel plots and the Egger test (22).”
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“As there is often a dilemma in choosing between analyzing all trials or a subset that is believed to be less prone to bias, the methods used provide a compromise where all trials are used but the results are adjusted for SSEs or PB.”
BackgroundInfluentialSelf-citationAttauabi, M., Steenholdt, C., Poulsen, A., Gubatan, J. M. B., Burisch, J. M., Nielsen, O. H., & Seidelin, J. B. (2024) · Alimentary Pharmacology & Therapeutics · doi:10.1111/apt.18110 · Cited by 25
“26”
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Pharmacological interventions for acute hepatitis B infection
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“910) demonstrated no small-study effects and bias concerning fatigue scores (67, 68).”
BackgroundBioactive glass for periodontal regeneration: a systematic review
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“As there was no concrete methodology to evaluate the publication bias between studies in network meta-analysis, we used the comparisonadjusted funnel plots to assess the publication bias among treatment comparisons (Chaimani and Salanti, 2012).”
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“publication bias for all treatment comparisons.(25) Comparison-adjusted funnel plots are scatter plots of effect size versus precision, and substantial asymmetry around the effect estimate line in the funnel plot would suggest likely publication bias.”
MethodInterventions for Glaucoma Medication Adherence Improvement
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Induction immunosuppression in adults undergoing liver transplantation: a network meta-analysis
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“…funnel plot, it is necessary to rank the studies in a meaningful way as asymmetry may be due to small sample sizes in newer studies (comparing newer treatments with older treatments) or higher risk of bias in older studies (comparing older treatments with placebo) (Chaimani 2012).”
MethodResultInfluentialZhang, J., Zhang, Y., Huang, X., Lan, K., Hu, L., Chen, Y., & Yu, H. (2020) · Evidence-based Complementary and Alternative Medicine · doi:10.1155/2020/8363027 · Cited by 23
“Potential small study effects within the network were detected using comparison-adjusted funnel plots [17].”
MethodMultivariate network meta‐analysis to mitigate the effects of outcome reporting bias
Hwang, H., & DeSantis, S. M. (2018) · Statistics in Medicine · doi:10.1002/sim.7815 · Cited by 22
Elmakaty, I., Abdo, R., Elsabagh, A. A., Elsayed, A., & Malki, M. I. (2023) · Cancer Cell International · doi:10.1186/s12935-023-02941-7 · Cited by 22
“Visual inspection of comparison-adjusted funnel plots for NMA was used to assess publication bias [27].”
MethodDai, P., Xie, W., Yu, X., Sun, J., Wang, S., & Kawuki, J. (2021) · International Immunopharmacology · doi:10.1016/j.intimp.2021.107376 · Cited by 21
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“(7 )”
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Self-citationAdverse effects of immunotherapies for multiple sclerosis: a network meta-analysis
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“The comparison-adjusted funnel plot was used for the presence of small-study effects (Chaimani and Salanti, 2012).”
MethodPharmacological interventions for primary sclerosing cholangitis
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Network meta-analysis reaches nutrition research
Schwingshackl, L., Buyken, A. E., & Chaimani, A. (2018) · European Journal of Nutrition · doi:10.1007/s00394-018-1849-0 · Cited by 20
Self-citationBayesian Mixed Treatment Comparisons Meta-Analysis for Correlated Outcomes Subject to Reporting Bias
Liu, Y., DeSantis, S. M., & Chen, Y. (2017) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12220 · Cited by 19
“An asymmetric ‘comparison-adjusted’ funnel plot may indicate the existence of small study effects (Chaimani and Salanti, 2012; Chaimani et al., 2013).”
BackgroundNonpharmacological Interventions for Pediatric Migraine: A Network Meta-analysis
Koechlin, H., Kossowsky, J., Lam, T. L., Barthel, J., Gaab, J., Berde, C. B., Schwarzer, G., Linde, K., Meißner, K., & Locher, C. (2021) · PEDIATRICS · doi:10.1542/peds.2019-4107 · Cited by 19
Liu, H., Wang, X., Gong, T., Xu, S., Zhang, J., Li, Y., Zeng, Y., Yi, M., & Qian, Y. (2024) · Journal of Anxiety Disorders · doi:10.1016/j.janxdis.2024.102912 · Cited by 19
Solmi, M., Fornaro, M., Caiolo, S., Lussignoli, M., Caiazza, C., Prisco, M. D., Solini, N., de Bartolomeis, A., Iasevoli, F., Pigato, G., et al. (2024) · Molecular Psychiatry · doi:10.1038/s41380-024-02733-z · Cited by 18
“Publication bias was visually inspected with a funnel plot and Egger ’ s test [23] for the co-primary outcomes.”
Schneider‐Thoma, J., Kapfhammer, A., Wang, D., Bighelli, I., Siafis, S., Wu, H., Hansen, W., Davis, J. M., Salanti, G., & Leucht, S. (2021) · Systematic Reviews · doi:10.1186/s13643-021-01760-z · Cited by 18
“Publication bias We will explore the association between study size and effect size with a comparison-adjusted funnel plot and with a contour enhanced funnel plot of all active drugs versus placebo (when at least 10 studies are available per outcome) [52].”
MethodSelf-citationRossano, F., Caiazza, C., Sobrino, A., Solini, N., Vellucci, A., Zotti, N., Fornaro, M., Gillman, P. K., Cattaneo, C. I., den Eynde, V. V., et al. (2023) · European Neuropsychopharmacology · doi:10.1016/j.euroneuro.2023.03.012 · Cited by 19
Fornaro, M., Caiazza, C., Solini, N., Prisco, M. D., Billeci, M., Vannini, M., Shorr, R., Caiolo, S., Lussignoli, M., Siskind, D. J., et al. (2023) · Molecular Psychiatry · doi:10.1038/s41380-023-02266-x · Cited by 18
“Publication bias was assessed by visual inspection of the funnel plot and Egger ’ s test [25].”
Management of people with intermediate-stage hepatocellular carcinoma
Roccarina, D., Majumdar, A., Thorburn, D., Davidson, B. R., Tsochatzis, E. A., & Gurusamy, K. S. (2017) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd011649.pub2 · Cited by 18
Bonovas, S., Nikolopoulos, G. K., Piovani, D., González‐Lorenzo, M., Pantavou, K. G., Lytras, T., Peyrin‐Biroulet, L., & Danese, S. (2019) · British Journal of Clinical Pharmacology · doi:10.1111/bcp.14051 · Cited by 19
“Small‐study effects or publication bias were examined with funnel graphs appropriately adjusted for inclusion of studies that compare different pairs of treatments.(19,20,31)”
MethodLiu, S., Hu, J., Zhao, C., Liu, H., & He, C. (2025) · Frontiers in Endocrinology · doi:10.3389/fendo.2025.1513641 · Cited by 17
Furuya‐Kanamori, L., Walker, R., Gillespie, B. M., Clark, J. M., Doi, S. A. R., & Thalib, L. (2018) · Journal of the American Medical Directors Association · doi:10.1016/j.jamda.2018.10.010 · Cited by 17
Montes-Andujar, L., Tinoco, E., Pravia, O. V. B., Saborido, C. M., Blanco-Schweizer, P., Segura, C., Silva, E. P., Reyes, V., Cobo, A. R., Zurdo, C., et al. (2021) · Thorax · doi:10.1136/thoraxjnl-2019-214054 · Cited by 19
Classifying information-sharing methods
Nikolaidis, G. F., Woods, B. S., Palmer, S., & Soares, M. O. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01292-z · Cited by 17
“Examples of parameters to which randomeffects have been applied include: comparison-specific meta-regression slopes [34, 38, 41, 42, 50], comparisonspecific between-trial variances [39, 40], and studyspecific baseline-risks [34, 54].”
MethodLee, Y. J., Ha, A., Kang, D., Shim, S. R., Jeoung, J. W., Park, K. H., & Kim, Y. K. (2023) · International Journal of Surgery · doi:10.1097/js9.0000000000000283 · Cited by 17
Kong, W., Deng, T., Li, S., Shu, Y., & Wu, Y. (2023) · BMC Infectious Diseases · doi:10.1186/s12879-023-08209-9 · Cited by 17
Adams, A., Jakob, T., Huth, A., Monsef, I., Ernst, M., Kopp, M., Caro-Valenzuela, J., Wöckel, A., & Skoetz, N. (2024) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013451.pub2 · Cited by 17
Wang, H., Xu, X., Lu, Z., Zhai, Z., Shao, L., Song, X., & Zhang, Y. (2024) · European Archives of Oto-Rhino-Laryngology · doi:10.1007/s00405-024-08903-7 · Cited by 20
“…and the closer the value is to 100%, the better the efficacy of the intervention is indicated, with a value of P < 0.05,and P < 0.05 as the difference is significant, and finally a comparative corrective funnel was performed on the outcome indicators to test for small sample effects [22].”
InfluentialPang, L., Liu, J., & Lv, X. (2019) · Medicine · doi:10.1097/md.0000000000016325 · Cited by 17
“If feasible, we will also employ the statistical model, suggested by Chaimani,[38] to explore the possible existence of small-study effects in the network.”
Gupta, S. K., Belley‐Côté, E. P., Panchal, P., Pandey, A. K., Basha, A., Pallo, L. P., Rochwerg, B. N., Mehta, S. R., Schwalm, J. D., & Whitlock, R. P. (2020) · Interactive Cardiovascular and Thoracic Surgery · doi:10.1093/icvts/ivaa115 · Cited by 18
Desborough, M., Estcourt, L. J., Chaimani, A., Doree, C. J., Hopewell, S., Trivella, M., Hadjinicolaou, A. V., Vyas, P., & Stanworth, S. J. (2016) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd012055 · Cited by 17
Self-citationCharitakis, E., Karlsson, L., Rizas, K. D., Almroth, H., Jönsson, A. H., Schweiler, J., Sideris, S. K., Tsartsalis, D., Dragioti, E., & Chaimani, A. (2020) · BMJ Open · doi:10.1136/bmjopen-2020-041819 · Cited by 16
“…for the primary outcomes will be tested by analysing 1 only studies with low RoB (as reported in RoB section) 2 only studies with head to head comparison of two different CA ablation approaches excluding studies that have drugs as comparing arm 3 Only studies that include patients with non-PAF.”
MethodSelf-citationLuo, Z., Wang, Y., Zhang, T., & Wang, J. (2025) · Frontiers in Bioengineering and Biotechnology · doi:10.3389/fbioe.2025.1660524 · Cited by 21
Schneider‐Thoma, J., Zhu, Y., Qin, M., Dong, Y., Guan, S., Wang, J., Tian, J., Lin, X., Rodolico, A., Siafis, S., et al. (2026) · The Lancet · doi:10.1016/s0140-6736(25)02365-7 · Cited by 16
Self-citationCaro, P., Turner, W., Caldwell, D. M., & Macdonald, G. M. (2023) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013361.pub2 · Cited by 19
Jiang, Z., Zou, Y. L., Li, G., Zhao, S., & Zhang, W. (2024) · Frontiers in Pharmacology · doi:10.3389/fphar.2024.1376262 · Cited by 17
Zhao, Y., Guo, Y., Pan, X., Zhang, X., Yu, F., & Cao, X. (2024) · Pain and Therapy · doi:10.1007/s40122-024-00648-9 · Cited by 16
“The small-study effect and publication bias were judged using comparison-adjusted funnel plots [26] with Egger’s test [27].”
MethodRosenblat, M. A., Watt, J. A., Arnold, J. I., Treff, G., Sandbakk, Ø. B., Esteve-Lanao, J., Festa, L., Filipas, L., Galloway, S. D. R., Muñoz‐Pérez, I., et al. (2025) · Sports Medicine · doi:10.1007/s40279-024-02149-3 · Cited by 25
“A comparison adjusted funnel plot was used to visually assess small study effects for the NMA [43].”
Furukawa, T. A., Schramm, E., Weitz, E. S., Salanti, G., Efthimiou, O., Michalak, J., Watanabe, N., Cipriani, A., Keller, M. B., Kocsis, J. H., et al. (2016) · BMJ Open · doi:10.1136/bmjopen-2016-011769 · Cited by 16
“meta-analyses if more than 10 studies per treatment comparison are available,(48) and comparison-adjusted funnel plots for network meta-analyses.(49) If evidence of publication bias is found, we will incorporate this in the”
BackgroundSelf-citationZhang, Z., Zhao, Y., Lu, F., Hou, X., Ma, Y., Luo, F., Zeng, K., Zhao, S., Zhang, Y., Zhou, T., et al. (2019) · Annals of Translational Medicine · doi:10.21037/atm.2019.08.51 · Cited by 16
Metadata
- Authors
- Chaimani, A., & Salanti, G.
- Affiliations
- University of Ioannina (GR)
- Corresponding author
- Salanti, Georgia
- Venue
- Research Synthesis Methods
- Publisher
- Wiley
- Published
- 2012-06
- Volume
- 3
- Issue
- 2
- Pages
- 161-176
- ISSN
- 1759-2879 (ISSN-L)
- 1759-2887
- OpenAlex
- W2121796373
- Cited by
- 521
- References
- 35
- Citations by year
- 2026: 59 · 2025: 48 · 2024: 55 · 2023: 59 · 2022: 50 · 2021: 60 · 2020: 58 · 2019: 37 · 2018: 28 · 2017: 29 · 2016: 17 · 2015: 4 · 2014: 8 · 2013: 7 · 2012: 2
- FWCI
- 8.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Research Synthesis Methods (publishedVersion)
- PubMed (publishedVersion)
- Funders
- uropean Research Council (IMMA 260559)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Keywords
- small-study effects, publication bias, network meta-regression, network meta-analysis, funnel plot asymmetry
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