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Ranking treatments in frequentist network meta-analysis works without resampling methods
Open accessAbstract
BACKGROUND: Network meta-analysis is used to compare three or more treatments for the same condition. Within a Bayesian framework, for each treatment the probability of being best, or, more general, the probability that it has a certain rank can be derived from the posterior distributions of all treatments. The treatments can then be ranked by the surface under the cumulative ranking curve (SUCRA). For comparing treatments in a network meta-analysis, we propose a frequentist analogue to SUCRA which we call P-score that works without resampling. METHODS: P-scores are based solely on the point estimates and standard errors of the frequentist network meta-analysis estimates under normality assumption and can easily be calculated as means of one-sided p-values. They measure the mean extent of certainty that a treatment is better than the competing treatments. RESULTS: Using case studies of network meta-analysis in diabetes and depression, we demonstrate that the numerical values of SUCRA and P-Score are nearly identical. CONCLUSIONS: Ranking treatments in frequentist network meta-analysis works without resampling. Like the SUCRA values, P-scores induce a ranking of all treatments that mostly follows that of the point estimates, but takes precision into account. However, neither SUCRA nor P-score offer a major advantage compared to looking at credible or confidence intervals.
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“This approach is often misleading, as it considers only the point estimate of effect and not the associated precision or certainty of evidence and ignores absolute differences between treatment alternatives.[56][57][58]”
From Management of chronic pain secondary to temporomandibular disorders: a systematic review and network meta-analysis of randomised trials (2023) · cites this paper as [57]
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“P-scores (ranging from 0 to 1) were used to rank interventions, with higher scores indicating a greater likelihood of a treatment being the most effective [16].”
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“A higher P-score (value range 0–1) translated into best ranking (treatment hierarchy) [33].”
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Answering complex hierarchy questions in network meta-analysis
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“18 The P scores measure the ranking of an intervention as being better than the others, averaged over all competing interventions.”
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“Notes: P-score: the extent of certainty that a treatment is superior to its comparators (closest score to 1 being the “best”) [25].”
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Dou, M., Liang, H., Liu, Y., Zhang, Q., Li, R., Chen, S., & Shi, B. (2023) · Journal of Cancer Research and Clinical Oncology · doi:10.1007/s00432-023-04658-6 · Cited by 10
“The P-score was applied as the counter-part of the SUCRA to assess the relative efficacy as ranked in the frequentist model (Rücker and Schwarzer 2015).”
MethodRegional analgesia techniques for lumbar spine surgery: a frequentist network meta-analysis
Hong, B., Baek, S.-J., Kang, H., Oh, C., Jo, Y., Lee, S., & Park, S. (2023) · International Journal of Surgery · doi:10.1097/js9.0000000000000270 · Cited by 10
Antibiotic Prophylaxis in Reduction Mammaplasty: A Network Meta-Analysis
Seretis, K. G., Bounas, N., & Papaspyrou, F. (2023) · Aesthetic Plastic Surgery · doi:10.1007/s00266-023-03313-2 · Cited by 10
“The probability of the most efficient intervention was estimated and ranked using the P-Score, which measures the certainty that one treatment is better than the other, averaged over all competing treatments, and the closer the P-Score is to 1, the better the therapeutic effect of the intervention may be [12].”
MethodZhu, Y., Liu, K., Zhu, H., Cao, H., & Zhou, Y. (2023) · Therapeutic Advances in Medical Oncology · doi:10.1177/17588359231206147 · Cited by 10
“25,26 The primary efficacy analyses were focused on comparing serplulimab plus chemotherapy with all other treatments and comparing all treatments with chemotherapy alone.”
MethodKirkland, S. W., Visser, L., Meyer, J., Junqueira, D. R., Campbell, S., Villa‐Roel, C., Friedman, B. W., Essel, N. O. M., & Rowe, B. H. (2024) · Headache The Journal of Head and Face Pain · doi:10.1111/head.14704 · Cited by 9
Kamarajah, S. K., Bundred, J., Alessandri, G., Robinson, S. M., Wilson, C. H., French, J., & Pandanaboyana, S. (2020) · World Journal of Surgery · doi:10.1007/s00268-020-05459-5 · Cited by 10
The ANiMALIA investigators, Wewege, M. A., Bagg, M. K., Jones, M. D., & McAuley, J. H. (2020) · Systematic Reviews · doi:10.1186/s13643-020-01506-3 · Cited by 10
“We will rank the effect of all interventions on pain intensity and safety using P-scores, a method for estimating treatment rankings that does not require resampling methods [71].”
MethodChan, S.-K., Choi, C., & Lee, V. H.-F. (2022) · JTO Clinical and Research Reports · doi:10.1016/j.jtocrr.2022.100322 · Cited by 10
“Although regimens in this study were usefully ranked with respect to OS, PFS, and grade greater than or equal to 3 AEs, they were primarily calculated using point estimates, which in this study were HRs and ORs.(51) Therefore, to accurately and”
MethodInfluentialFeng, F., Zhang, T., Yin, F., Liu, C., Zhuang, J., Qi, L., Wang, X., Li, J., Wang, L., Tian, J., et al. (2019) · OncoTargets and Therapy · doi:10.2147/ott.s187739 · Cited by 10
“The SUCRA value would be 100%, indicating that the regimen is always the best, and 0%, indicating that the regimen is always the worst.(25) As there is a loop in three arms, the node-splitting method was used to evaluate the inconsistency between direct and indirect comparisons.”
MethodNetwork meta-analysis as a tool in clinical practice guidelines
Antoniou, S. A., Mavridis, D., Tsokani, S., Morales‐Conde, S., Ortenzi, M., Vettoretto, N., Carrano, F. M., Preda, S. D., & Arulampalam, T. (2022) · Surgical Endoscopy · doi:10.1007/s00464-022-09772-z · Cited by 11
altmeta: Alternative Meta-Analysis Methods
Lin, L., & Chu, H. (2016) · doi:10.32614/cran.package.altmeta · Cited by 10
Yang, F.-A., Lee, T.-H., Huang, S., Liou, T., Escorpizo, R. S., & Chen, H. (2022) · Clinical Rehabilitation · doi:10.1177/02692155221137698 · Cited by 9
“The P score is used to measure the extent of certainty that a treatment is better than other treatments, averaged over all competing treatments.(29) The P score is measured on a scale from 0 (worst) to 1 (best).”
MethodPharmaceutical administration for severe hypertension during pregnancy: Network meta-analysis
Deng, N., Xian‐Yu, C., Han, R.-Z., Huang, C.-Y., Ma, Y.-T., Li, H., Gao, T., Liu, X., & Zhang, C. (2023) · Frontiers in Pharmacology · doi:10.3389/fphar.2022.1092501 · Cited by 9
“By definition, SUCRA values reflected the efficacy of an intervention and, thus, a rank plot with larger SUCRA scores implied more effective interventions (Rücker and Schwarzer, 2015).”
BackgroundWalsh, G. S., Delextrat, A. A., & Bibbey, A. (2023) · Maturitas · doi:10.1016/j.maturitas.2023.107790 · Cited by 9
“Exercise interventions were ranked according to P-score, the mean probability that a treatment with a larger P-score is more effective than treatments with lower P-scores [27].”
MethodRomadlon, D. S., Tu, Y., Chen, Y., Hasan, F., & Chiu, H. (2023) · Diabetes Obesity and Metabolism · doi:10.1111/dom.15227 · Cited by 9
“hierarchy was determined based on P score between 0 and 1, with higher values indicating superior treatment.(29) We assessed global inconsistencies by using the design-by-treatment interaction test and local inconsistencies by adopting the node-splitting inconsistency test.”
MethodDharnipragada, R., Denduluri, L. S., Naik, A., Bertogliat, M. J., Awad, M., Ikramuddin, S. S., & Park, M. C. (2023) · Parkinsonism & Related Disorders · doi:10.1016/j.parkreldis.2023.105809 · Cited by 9
Chen, J., Jin, Z., Luo, B., Wang, Y.-Q., Li, R., Zhu, H., & Teng, G. (2023) · Journal of Clinical and Translational Hepatology · doi:10.14218/jcth.2023.00188 · Cited by 9
“17, 21, and 25).”
Hu, L., Deng, X., Wei, B., Wang, J., & Hou, D. (2023) · Journal of Orthopaedic Surgery and Research · doi:10.1186/s13018-023-04463-4 · Cited by 9
“The interventions were ranked using the surface under the cumulative ranking (SUCRA), ranging from 0 to 1 with higher scores indicating better outcomes, and the most frequent analog of the SUCRA curve was determined [34–36].”
MethodHe, L., Li, Y., Jin, J., Cheng, M., Bai, Y., & Xu, J. (2024) · BMC Nephrology · doi:10.1186/s12882-024-03460-x · Cited by 9
“We used STATA software (Version 17) to perform a multivariate network meta-analysis within a frequentist framework [24] according to current PRISMA NMA guidelines.”
MethodHaghbin, H., Zakirkhodjaev, N., Fatima, R., Kamal, F., & Aziz, M. (2024) · Journal of Clinical Medicine · doi:10.3390/jcm13051298 · Cited by 9
“The treatment groups were then ranked using P-score, with higher values denoting decreased recurrence and/or adverse events [24].”
MethodHsieh, P., Yang, T., Kang, E. Y.-N., Lee, P., Luo, J., Huang, Y., Hou, M., & Huang, S. (2024) · Journal of Internal Medicine · doi:10.1111/joim.13782 · Cited by 9
“In summarizing the network meta-analysis findings, both p -best value and p -score were calculated [29, 30]. p - best involves determining probabilities for parameter distribution, with each treatment i prioritized based on expected effect size, and gives a proportion p ( i = 1) to show a specific…”
Weninger, V., Agócs, G., Kovács, N., Váncsa, S., Hergár, L., Baek, C. J., Hegyi, P., Holnapy, G., & Skaliczki, G. (2024) · Arthroscopy The Journal of Arthroscopic and Related Surgery · doi:10.1016/j.arthro.2024.03.035 · Cited by 9
Zhang, S., Zhou, L., Yi, L., Chen, X., Zhang, Y., Li, J., Zhang, Y., & Hu, X. (2024) · Journal of Nursing Scholarship · doi:10.1111/jnu.12974 · Cited by 10
Huang, M., Yang, J., Wang, Y., & Wu, J. (2024) · Frontiers in Physiology · doi:10.3389/fphys.2024.1428723 · Cited by 12
“A higher SUCRA value indicates a higher probability that a speci fi c intervention will be the most effective (Rücker and Schwarzer, 2015).”
Laperrousaz, B., Levast, B., Fontaine, M., Nancey, S., Déchelotte, P., Dore, J. M., & Lehert, P. (2024) · BMC Gastroenterology · doi:10.1186/s12876-024-03487-2 · Cited by 10
“Treatment ranking by P-scores measured the extent of certainty that any one treatment was better than another, averaged over all competing treatments [15].”
BackgroundLuca, B. D., Canozzi, A., Mosconi, C., Gastaldon, C., Papola, D., Metelli, A., Tedeschi, F., Amaddeo, F., Purgato, M., Solmi, M., et al. (2025) · The British Journal of Psychiatry · doi:10.1192/bjp.2025.18 · Cited by 12
“40 If a comparison included ten studiesormore,weassessedpublicationbiasbyvisuallyinspectingthe funnelplot,testedthemforasymmetrywiththeEgger ’ sregressiontest and investigated possible reasons for funnel plot asymmetry.”
Huang, K., Zhang, G., Gains, H., He, R., Jiao, Y., Jia, Y., & Chen, L. (2025) · Journal of the American Medical Directors Association · doi:10.1016/j.jamda.2025.105583 · Cited by 15
Zhou, J., Jiang, W., Wang, J., & Dou, J. (2025) · Journal of Psychiatric Research · doi:10.1016/j.jpsychires.2025.05.028 · Cited by 9
Wei, M., He, S., Zhang, X., Meng, D., Yang, G., & Wang, Z. (2025) · BMC Geriatrics · doi:10.1186/s12877-025-06529-w · Cited by 9
“We chose the Bayesian model over the frequentist model for network meta-analysis because it allows us to incorporate prior information and uncertainty, and to obtain posterior distributions and probabilities for each pairwise comparison in the network [50].”
Efficacy and Safety of Oral Antihistamines for Allergic Rhinitis: Network Meta-Analysis
Vieira, R. J., Gil‐Mata, S., Ferreira, A., Serra, P. R., Bognanni, A., Duarte, V. H., Viegas, H., Pereira, A. M., Ferreira‐da‐Silva, R., Ferreira‐Cardoso, H., et al. (2026) · The Journal of Allergy and Clinical Immunology In Practice · doi:10.1016/j.jaip.2025.12.034 · Cited by 9
Metadata
- Authors
- Rücker, G., & Schwarzer, G.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Rücker, Gerta
- Venue
- BMC Medical Research Methodology
- Published
- 2015-07-31
- Volume
- 15
- Issue
- 1
- Pages
- 58-58
- ISSN
- 1471-2288 (ISSN-L)
- PMC
- PMC4521472
- OpenAlex
- W2111999709
- Cited by
- 1,732
- References
- 32
- Citations by year
- 2026: 249 · 2025: 253 · 2024: 267 · 2023: 229 · 2022: 226 · 2021: 191 · 2020: 148 · 2019: 76 · 2018: 52 · 2017: 32 · 2016: 8 · 2015: 1
- FWCI
- 28.58
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- BMC Medical Research Methodology (publishedVersion, other-oa)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- FreiDok plus (Universitätsbibliothek Freiburg) (submittedVersion)
- Funders
- Deutsche Forschungsgemeinschaft (RU1747/1-1)
- 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 › Sociology and Political Science › Delphi Technique in Research
- Keywords
- treatment ranking, P-score, surface under the cumulative ranking curve, confidence intervals, diabetes mellitus, depression
- MeSH terms
- Algorithms, Bayes Theorem, Biometry, Data Interpretation, Statistical, Humans, Review Literature as Topic, Meta-Analysis as Topic, Reproducibility of Results, Biomedical Research
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