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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Publication bias was explored using comparison-adjusted funnel plots and Egger's regression test.
“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]
Small-study effect (publication bias) was evaluated using comparison-adjusted funnel plots.
“We evaluated the presence of small-study effect (publication bias) by means of comparison-adjusted funnel plots [13].”
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netmeta: Network Meta-Analysis using Frequentist Methods
Rücker, G., Krahn, U., König, J., Efthimiou, O., Davies, A. L., Papakonstantinou, T., & Schwarzer, G. (2013) · doi:10.32614/cran.package.netmeta · Cited by 117 · see citing works
Davies, C., Radua, J., Cipriani, A., Stahl, D., Provenzani, U., McGuire, P., & Fusar-Poli, P. (2018) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2018.00187 · Cited by 107 · see citing works
Burschinski, A., Schneider-Thoma, J., Chiocchia, V., Schestag, K., Wang, D., Siafis, S., Bighelli, I., Wu, H., Hansen, W.-P., Priller, J., et al. (2023) · World Psychiatry · doi:10.1002/wps.21036 · Cited by 102 · see citing works
Self-citationMa, H., Lin, Y., Dai, L.-Z., Lin, C., Huang, Y., & Liu, S.-Y. (2023) · BMJ Open · doi:10.1136/bmjopen-2022-061807 · Cited by 115 · see citing works
Karagiannis, T., Malandris, K., Avgerinos, I., Stamati, A., Kakotrichi, P., Liakos, A., Vasilakou, D., Kakaletsis, N., Tsapas, A., & Bekiari, E. (2024) · Diabetologia · doi:10.1007/s00125-024-06144-1 · Cited by 102 · see citing works
“We evaluated the presence of small-study effect (publication bias) by means of compari-son-adjusted funnel plots [13].”
Association of Umbilical Cord Management Strategies With Outcomes of Preterm Infants
Jasani, B., Torgalkar, R., Ye, X. Y., Syed, S., & Shah, P. S. (2021) · Archives of Pediatrics and Adolescent Medicine · doi:10.1001/jamapediatrics.2021.0102 · Cited by 97 · see citing works
Wang, Y., Ye, Z., Ge, L., Siemieniuk, R. A. C., Wang, X., Wang, Y., Hou, L., Ma, Z., Agoritsas, T., Vandvik, P. O., et al. (2020) · BMJ · doi:10.1136/bmj.l6744 · Cited by 96 · see citing works
Management of people with early- or very early-stage hepatocellular carcinoma
Majumdar, A., Roccarina, D., Thorburn, D., Davidson, B. R., Tsochatzis, E. A., & Gurusamy, K. S. (2017) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd011650.pub2 · Cited by 94 · see citing works
Maneiro, J. R., Souto, A., & Gómez-Reino, J. J. (2017) · Seminars in Arthritis and Rheumatism · doi:10.1016/j.semarthrit.2017.02.007 · Cited by 93 · see citing works
Efficacy, Safety, and Acceptability of Pharmacologic Treatments for Pediatric Migraine Prophylaxis
Locher, C., Kossowsky, J., Koechlin, H., Lam, T. L., Barthel, J., Berde, C. B., Gaab, J., Schwarzer, G., Linde, K., & Meißner, K. (2020) · Archives of Pediatrics and Adolescent Medicine · doi:10.1001/jamapediatrics.2019.5856 · Cited by 95 · see citing works
Comparison of Amitriptyline and US Food and Drug Administration–Approved Treatments for Fibromyalgia
Farag, H., Yunusa, I. U., Goswami, H. H., Sultan, I., Doucette, J. A., & Eguale, T. (2022) · JAMA Network Open · doi:10.1001/jamanetworkopen.2022.12939 · Cited by 92 · see citing works
Sehmbi, H., Brull, R., Ceballos, K. R., Shah, U. J., Martin, J. E., Tobı́as, A., Solo, K., & Abdallah, F. W. (2020) · Anaesthesia · doi:10.1111/anae.15288 · Cited by 89 · see citing works
Akshintala, V. S., Weiland, C. J. S., Bhullar, F. A., Kamal, A., Kanthasamy, K. A., Kuo, A., Tomasetti, C., Gürakar, M., Drenth, J. P. H., Yadav, D. K., et al. (2021) · The Lancet. Gastroenterology & hepatology · doi:10.1016/s2468-1253(21)00170-9 · Cited by 86 · see citing works
Chaimani, A., Vasiliadis, H. S., Pandis, N., Schmid, C. H., Welton, N. J., & Salanti, G. (2013) · International Journal of Epidemiology · doi:10.1093/ije/dyt074 · Cited by 82 · see citing works
Self-citationThe efficacy of powered toothbrushes: A systematic review and network meta‐analysis
Thomassen, T. M. J. A., van der Weijden, G. A., & Slot, D. E. (2021) · International Journal of Dental Hygiene · doi:10.1111/idh.12563 · Cited by 81 · see citing works
Tang, H., Li, G., Zhao, Y. J., Wang, F., Gower, E. W., Shi, L., & Wang, T. (2018) · Diabetes Obesity and Metabolism · doi:10.1111/dom.13232 · Cited by 81 · see citing works
“Finally, a comparison-adjusted funnel plot was used to assess small study effects within a network of interventions.(24) We performed a regression analysis to examine the relationship between trial characteristics and effect size using the following factors: duration of diabetes, difference in change in glycaemic cont…”
MethodLinden, A., Best, L., Elise, F., Roberts, D., Branagan, A., Tay, Y. B. E., Crane, L., Cusack, J., Davidson, B., Davidson, I., et al. (2023) · Autism · doi:10.1177/13623613221117931 · Cited by 78 · see citing works
“…the risk of bias in the studies, sample size, or the control group used over time), we judged this reporting bias by the completeness of the search (Chaimani & Salanti, 2012) (i.e. identify completed but unpublished trials from the trial registry for which we are unable to obtain data from the…”
MethodEvaluation of Comparative Efficacy and Safety of Surgical Approaches for Total Hip Arthroplasty
Yan, L., Ge, L., Dong, S., Saluja, K., Li, D., Reddy, K. S., Wang, Q., Yao, L., Li, J. J., da Costa, B. R., et al. (2023) · JAMA Network Open · doi:10.1001/jamanetworkopen.2022.53942 · Cited by 81 · see citing works
Sekercioglu, N., Thabane, L., Martinez, J. P. D., NESRALLAH, G. E., Longo, C. J., Busse, J. W., Akhtar‐Danesh, N., Agarwal, A., Khalifah, R. A. A., Iorio, A., et al. (2016) · PLoS ONE · doi:10.1371/journal.pone.0156891 · Cited by 80 · see citing works
“Publication bias was considered undetected unless the effect measure was asymmetrically distributed around the pooled effect [24, 25].”
BackgroundBest, L. M., Freeman, S. C., Sutton, A. J., Cooper, N. J., Tng, E.-L., Csenar, M., Hawkins, N., Pavlov, C. S., Davidson, B. R., Thorburn, D., et al. (2019) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013103.pub2 · Cited by 78 · see citing works
“If there is no meaningful way in which to rank these studies (i.e. there was no specific change in the risk of bias in the studies, sample size, or the control group used over time), we will judge the reporting bias by the completeness of the search (Chaimani 2012).”
Wangdi, K., Furuya‐Kanamori, L., Clark, J. M., Barendregt, J. J., Gatton, M. L., Banwell, C. L., Kelly, G. C., Doi, S. A. R., & Clements, A. (2018) · Parasites & Vectors · doi:10.1186/s13071-018-2783-y · Cited by 81 · see citing works
“small-study effects, we expect the studies to form an inverted funnel centred at zero [33].”
BackgroundA selection model for accounting for publication bias in a full network meta‐analysis
Mavridis, D., Welton, N. J., Sutton, A. J., & Salanti, G. (2014) · Statistics in Medicine · doi:10.1002/sim.6321 · Cited by 75 · see citing works
“We re-analyzed the data from a network that has been recently used to illustrate the extension of the Copas model to multi-arm trials [24] and the use of network meta-regression to evaluate the existence of smallstudy effects [37].”
MethodSelf-citationFarhat, L. C., Behling, E., Landeros‐Weisenberger, A., Levine, J. L. S., de Barros, P. M. F., Wang, Z., & Bloch, M. H. (2022) · The Lancet Child & Adolescent Health · doi:10.1016/s2352-4642(22)00316-9 · Cited by 75 · see citing works
Zufferey, P. J., Chaux, R., Lachaud, P.-A., Capdevila, X., Lanoiselée, J., & Ollier, É. (2024) · British Journal of Anaesthesia · doi:10.1016/j.bja.2023.12.021 · Cited by 75 · see citing works
Pharmacological interventions for non-alcohol related fatty liver disease (NAFLD)
Lombardi, R., Onali, S., Thorburn, D., Davidson, B. R., Gurusamy, K. S., & Tsochatzis, E. A. (2017) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd011640.pub2 · Cited by 74 · see citing works
Tang, H., Fang, Z., Wang, T., Cui, W., Zhai, S., & Song, Y. (2016) · The American Journal of Cardiology · doi:10.1016/j.amjcard.2016.08.061 · Cited by 73 · see citing works
New generation antidepressants for depression in children and adolescents: a network meta-analysis
Hetrick, S. E., Meader, N., Bailey, A. P., Badcock, P. B., Moller, C. I., Cox, G., Merry, S., & McKenzie, J. E. (2020) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013674 · Cited by 73 · see citing works
Yunitri, N., Chu, H., Kang, X. L., Wiratama, B. S., Lee, T., Chang, L., Liu, D., Kustanti, C. Y., Chiang, K., Chen, R., et al. (2023) · Psychological Medicine · doi:10.1017/s0033291722003737 · Cited by 73 · see citing works
“Ninik Yunitri et al. lower scores of DIC suggests a better model fit compared with the other NMA model (Chaimani & Salanti, 2012).”
ResultTang, H., Li, D., Zhang, J., Li, Y., Wang, T., Zhai, S., & Song, Y. (2017) · Diabetes Obesity and Metabolism · doi:10.1111/dom.12917 · Cited by 72 · see citing works
“Finally, a comparison-adjusted funnel plot was used to assess small-study effects within a network of interventions, with symmetry around the summary effect line indicating the absence of small-study effects.(27)”
MethodCuijpers, P. J., Oud, M., Karyotaki, E., Noma, H., Quero, S., Cipriani, A., Arroll, B., & Furukawa, T. A. (2021) · The Annals of Family Medicine · doi:10.1370/afm.2676 · Cited by 71 · see citing works
Maintenance immunosuppression for adults undergoing liver transplantation: a network meta-analysis
Rodríguez‐Perálvarez, M., Misas, M. G., Thorburn, D., Davidson, B. R., Tsochatzis, E. A., & Gurusamy, K. S. (2017) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd011639.pub2 · Cited by 70 · see citing works
Michopoulos, I., Furukawa, T. A., Noma, H., Kishimoto, S., Onishi, A., Ostinelli, E. G., Ciharova, M., Miguel, C., Karyotaki, E., & Cuijpers, P. (2021) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2020.12.012 · Cited by 69 · see citing works
Wewege, M. A., Bagg, M. K., Jones, M. D., Ferraro, M. C., Cashin, A. G., Rizzo, R. R. N., Leake, H. B., Hagstrom, A. D., Sharma, S., McLachlan, A. J., et al. (2023) · BMJ · doi:10.1136/bmj-2022-072962 · Cited by 66 · see citing works
Hao, J., He, Z., Yu, X., & Remis, A. (2023) · Neurological Sciences · doi:10.1007/s10072-023-06742-8 · Cited by 64 · see citing works
Komolafe, O., Roberts, D. A., Freeman, S. C., Wilson, P., Sutton, A. J., Cooper, N. J., Pavlov, C. S., Milne, E., Hawkins, N., Cowlin, M., et al. (2020) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013125.pub2 · Cited by 61 · see citing works
Planer, D., Yanko, S., Matok, I., Paltiel, O., Zmiro, R., Rotshild, V., Amir, O., Elbaz‐Greener, G., & Raccah, B. H. (2023) · Canadian Medical Association Journal · doi:10.1503/cmaj.220960 · Cited by 60 · see citing works
Comparison of First-Line Treatments for Patients With Extensive-Stage Small Cell Lung Cancer
Zhou, T., Zhang, Z., Luo, F., Zhao, Y., Hou, X., Liu, T., Wang, K., Zhao, H., Huang, Y., & Zhang, L. (2020) · JAMA Network Open · doi:10.1001/jamanetworkopen.2020.15748 · Cited by 59 · see citing works
Dong, S., Schneider-Thoma, J., Bighelli, I., Siafis, S., Wang, D., Burschinski, A., Schestag, K., Samara, M., & Leucht, S. (2024) · European Archives of Psychiatry and Clinical Neuroscience · doi:10.1007/s00406-023-01654-2 · Cited by 68 · see citing works
“…effects and publication bias for the primary outcome with funnel plots of pairwise meta-analysis if ten or more studies were included, as well as comparison-adjusted funnel plots [28, 29] ordering the antipsychotics from the newest to the oldest and from the best to the worst in efficacy [30].”
Kim, J. Y., Jang, M., Kim, D., Park, S., & Han, D. H. (2021) · The Journal of Allergy and Clinical Immunology In Practice · doi:10.1016/j.jaip.2021.08.018 · Cited by 56 · see citing works
“7 (18-60) 24 96,600 IR SS Wang (2016)(39) China 25 R without A 6-14 12 NR SS, MS Xian (2020)(10) China 27 R with or without A 24.”
BackgroundInfluentialYe, Z., Wang, Y., Ge, L., Guyatt, G. H., Collister, D., Alhazzani, W. A., Bagshaw, S. M., Belley‐Côté, E. P., Fang, F., Hou, L., et al. (2021) · Critical Care Explorations · doi:10.1097/cce.0000000000000399 · Cited by 55 · see citing works
“We assessed small-study effects with a comparison-adjusted funnel plot of treatment estimates for each outcome (17).”
MethodPharmacological interventions for primary biliary cholangitis
Saffioti, F., Gurusamy, K. S., Eusebi, L. H., Tsochatzis, E. A., Davidson, B. R., & Thorburn, D. (2017) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd011648.pub2 · Cited by 54 · see citing works
Comparative efficacy and safety of lipid-lowering agents in patients with hypercholesterolemia
Zhao, Z., Du, S., Shen, S., Luo, P., Ding, S., Wang, G., & Wang, L. (2019) · Medicine · doi:10.1097/md.0000000000014400 · Cited by 55 · see citing works
“Third, we utilized the design-by-treatment interaction model of Higgins and colleagues to check the consistency of the entire network.([31]) Network meta-regression was used to further evaluate the possible existence of small-study effects in network of interventions.”
MethodTsiami, A. P., Chaimani, A., Mavridis, D., Siskou, M., Assimakopoulos, E., & Sotiriadis, A. (2016) · Ultrasound in Obstetrics and Gynecology · doi:10.1002/uog.15900 · Cited by 51 · see citing works
Self-citationAssessing Confidence in the Results of Network Meta-Analysis (Cinema)Preprint
Nikolakopoulou, A., Higgins, J. P. T., Papakonstantinou, T., Chaimani, A., Giovane, C. D., Egger, M., & Salanti, G. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/597047 · Cited by 49 · see citing works
“trial registries do not indicate important discrepancies with published reports 209 - Empirical examination of patterns of results between small and large studies, using the 210 comparison-adjusted funnel plot (31,32), regression models (33) or selection models 211 (34) do not indicate that results from small studies…”
ResultSelf-citationKiesswetter, E., Stadelmaier, J., Πετροπούλου, Μ., Morze, J., Grummich, K., Roux, I., Lay, R., Himmelsbach, L., Kussmann, M., Roeger, C., et al. (2023) · Advances in Nutrition · doi:10.1016/j.advnut.2023.03.004 · Cited by 49 · see citing works
“When the number of studies was more than 10, a comparison-adjusted funnel plot was drawn to assess publication bias and small study effects [38,39].”
MethodSalahuddin, N. H., Schütz, A., Pitschel‐Walz, G., Mayer, S. F., Chaimani, A., Siafis, S., Priller, J., Leucht, S., & Bighelli, I. (2024) · The Lancet Psychiatry · doi:10.1016/s2215-0366(24)00136-6 · Cited by 48 · see citing works
Self-citationBonovas, S., Nikolopoulos, G. K., Lytras, T., Fiorino, G., Peyrin‐Biroulet, L., & Danese, S. (2017) · British Journal of Clinical Pharmacology · doi:10.1111/bcp.13456 · Cited by 47 · see citing works
Statin therapy on glycemic control in type 2 diabetic patients: A network meta-analysis
Cui, J. Y., Zhou, R., Han, S., Wang, T., Wang, L., & Xie, X. (2018) · Journal of Clinical Pharmacy and Therapeutics · doi:10.1111/jcpt.12690 · Cited by 47 · see citing works
Medications for adults with type 2 diabetes: a living systematic review and network meta-analysis
Nong, K., Jeppesen, B. T., Shi, Q., Agoritsas, T., Guyatt, G. H., White, H., Gao, Y., Agarwal, A., Macdonald, H., Zou, X., et al. (2025) · BMJ · doi:10.1136/bmj-2024-083039 · Cited by 48 · see citing works
“…we assess publication bias from two sources: global publication bias reflecting network estimates, evaluated using comparison-adjusted funnel plots 29 ; and local publication bias reflecting each pairwise direct comparison, evaluated using Harbord’s score test for binary outcomes and Egger’s…”
Lifestyle modifications for non-alcohol related fatty liver disease: a network meta-analysis
Buzzetti, E., Linden, A. H., Best, L. M., Madden, A. M., Roberts, D. A., Chase, T. J. G., Freeman, S. C., Cooper, N. J., Sutton, A. J., Fritche, D., et al. (2018) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013156 · Cited by 48 · see citing works
Boutron, I., Chaimani, A., Devane, D., Meerpohl, J. J., Rada, G., Hróbjartsson, A., Tovey, D., Grasselli, G., & Ravaud, P. (2020) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013769 · Cited by 41 · see citing works
Self-citationBergman, H., Walker, D., Nikolakopoulou, A., Soares‐Weiser, K., & Adams, C. E. (2017) · Health Technology Assessment · doi:10.3310/hta21430 · Cited by 45 · see citing works
Jung, A., Eschke, R.-C., Struss, J., Taucher, W. K., & Luedtke, K. (2022) · Cephalalgia · doi:10.1177/03331024221082073 · Cited by 45 · see citing works
“An examination of publication bias using a comparisonadjusted funnel plot (17) and linear regression test of funnel plot asymmetry (Egger test) were considered if there were more than 10 studies included in NMA for each outcome (18).”
MethodLewis, S. R., Macey, R., Lewis, J., Stokes, J. R., Gill, J. R., Cook, J. A., Eardley, W., Parker, M. J., & Griffin, X. L. (2022) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013405.pub2 · Cited by 46 · see citing works
Avgerinos, I., Manolopoulos, A., Michailidis, T., Kitsios, K., Liakos, A., Karagiannis, T., Dimitrakopoulos, K., Matthews, D. R., Τσάπας, Α., & Bekiari, E. (2020) · Diabetes Obesity and Metabolism · doi:10.1111/dom.14291 · Cited by 44 · see citing works
“We investigated the presence of small-study effects for the primary outcome utilizing comparison-adjusted funnel plots.(19)”
MethodAdams, M., Gordt, K., Bongartz, M., Zimmermann, S., Seide, S., Braun, V., & Schwenk, M. (2023) · Sports Medicine - Open · doi:10.1186/s40798-023-00606-3 · Cited by 48 · see citing works
“We investigated the presence of small study effects using funnel plots for the outcomes of overall strength and balance together with Egger’s regression test [43].”
Method
- 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
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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