Cited by 1,732Meta-analysis and systematic reviewsStatistical Methods in Clinical TrialsDelphi Technique in Research

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Ranking treatments in frequentist network meta-analysis works without resampling methods

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Rücker, Gerta, Schwarzer, Guido·2015·BMC Medical Research Methodology

DOI 10.1186/s12874-015-0060-8PMC PMC4521472

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Abstract

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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Fig. 1 Fictitious example. Two normal posterior distributions following N(0,1) (dashed) and N(0.5, 22) (continuous) with credible intervals. The probability that treatment A, corresponding to the flat distribution, is better than treatment B, corresponding to the steep distribution, is 59 %CC BY · PubMed Central

Fig. 2 Fictitious example: ROC curve. ROC curve and area under the curve (AUC) corresponding to the example of Fig. 1 (AUC = 0.59)CC BY · PubMed Central

Fig. 3 Diabetes data, analyzed with WinBUGS. Diabetes data, analyzed with WinBUGS and ordered by treatment effects (REM = random effects model, MCMC = Markov Chain Monte Carlo analysis with 3 chains, 40000 iterations, 10000 burn in iterations discarded). CI = credible interval (median and 2.5 % / 97.5 % quantiles). The estimated common variance between studies was σ 2=0.1221CC BY · PubMed Central

Fig. 4 Diabetes data, analyzed with R package netmeta. Diabetes data, analyzed with R package netmeta and ordered by treatment effects (REM = random effects model, CI = confidence interval). The estimated common between study variance was τ 2=0.1087CC BY · PubMed Central

Fig. 5 Depression data, analyzed with WinBUGS. Depression data, analyzed with WinBUGS (REM = random effects model, MCMC = Markov Chain Monte Carlo analysis with 3 chains, 40000 iterations, 10000 burn in iterations discarded). CI = credible interval (median and 2.5 % / 97.5 % quantiles). The estimated common between study variance was σ 2=0.2011CC BY · PubMed Central

Fig. 6 Depression data, analyzed with R package netmeta. Depression data, analyzed with R package netmeta (REM = random effects model, CI = confidence interval). The estimated common between study variance was τ 2=0.1875CC BY · PubMed Central

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“21,22 The variety of interventions was considered among the best if p -score was ≥0.66; when p -score was 0.65 to 0.33, the combination was judged inferior to the best/better than the worst; when p -score was <0.33, the combination was considered among the worst.”
MethodInfluential
Comparative efficacy of five approved Janus kinase inhibitors as monotherapy and combination therapy in patients with moderate-to-severe active rheumatoid arthritis: a systematic review and network meta-analysis of randomized controlled trials
Cai, W., Tong, R., Sun, Y., Yao, Y., & Zhang, J. (2024) · Frontiers in Pharmacology · doi:10.3389/fphar.2024.1387585 · Cited by 30
Effects of Resistance Training Volume on Physical Function, Lean Body Mass and Lower-Body Muscle Hypertrophy and Strength in Older Adults: A Systematic Review and Network Meta-analysis of 151 Randomised Trials
Radaelli, R., Rech, A., Molinari, T., Markarian, A. M., Πετροπούλου, Μ., Granacher, U., Hortobágyi, T., & López, P. (2024) · Sports Medicine · doi:10.1007/s40279-024-02123-z · Cited by 37
“Intervention effects were ranked according to P -scores [49].”
Cardiovascular safety of Janus kinase inhibitors in inflammatory bowel disease: a systematic review and network meta-analysis
Yang, H., An, T., Zhao, Y., Shi, X., Wang, B., & Zhang, Q. (2025) · Annals of Medicine · doi:10.1080/07853890.2025.2455536 · Cited by 30
“Given that P-score took precision into account [25] and sUcRa were unstable based on simulations, we preferentially ranked interventions with P-score like another study [26] and also compared the potential differences between sUcRa and P-score. the key characteristics of included Rcts were…”
Pharmacologic Treatment of Heart Failure With Reduced Ejection Fraction
van Essen, B. J., Ceelen, D. C. H., Ouwerkerk, W., Teng, T. K., Tharshana, G. N., Hew, F. M., Butler, J., Zannad, F. M., Lam, C. S. P., Ezekowitz, J. A., et al. (2025) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2025.08.054 · Cited by 35
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Uhlig, A., Uhlig, J., Trojan, L., Hinterthaner, M., von Hammerstein-Equord, A. F., & Strauß, A. (2019) · BMC Urology · doi:10.1186/s12894-019-0544-7 · Cited by 31
Progress and challenges of network meta‐analysis
Tian, J., Gao, Y., Zhang, J., Yang, Z., Dong, S., Zhang, T., Sun, F., Wu, S., Wu, J., Wang, J., et al. (2021) · Journal of Evidence-Based Medicine · doi:10.1111/jebm.12443 · Cited by 29
Efficacy and safety of antiviral treatments for symptomatic COVID-19 outpatients: Systematic review and network meta-analysis
Zur, M., Peselev, T., Yanko, S., Rotshild, V., & Matok, I. (2023) · Antiviral Research · doi:10.1016/j.antiviral.2023.105768 · Cited by 30
Efficacy of first-line treatments for multiple myeloma patients not eligible for stem cell transplantation: a network meta-analysis
Blommestein, H. M., van Beurden-Tan, C. H. Y., Franken, M. G., Groot, C. A. U., Sonneveld, P., & Zweegman, S. (2019) · Haematologica · doi:10.3324/haematol.2018.206912 · Cited by 30
“MP} NMSG MP 74 179 14 32 42 NCT00218855 (11-18) Beksac 2010 Treatment 122 MPT 69 60 n/r 0.”
No difference in outcomes between femoral fixation methods with hamstring autograft in anterior cruciate ligament reconstruction – A network meta-analysis
Hurley, E. T., Gianakos, A. L., Anil, U., Strauss, E. J., & Gonzalez-Lomas, G. P. (2019) · The Knee · doi:10.1016/j.knee.2019.01.015 · Cited by 30
Computerized Cognitive Training in Cognitively Healthy Older Adults: A Systematic Review and Network Meta-AnalysisPreprint
Lampit, A., Gavelin, H. M., Sabatés, J., Launder, N. H., Hallock, H., Finke, C., Krohn, S., & Peeters, G. M. E. E. (2020) · medRxiv · doi:10.1101/2020.10.07.20208306 · Cited by 33
“Ranking of treatments were estimated using P-scores, representing the extent of certainty that an intervention is more effective than another intervention 19 .”
Method
The effects of active workstations on reducing work-specific sedentary time in office workers: a network meta-analysis of 23 randomized controlled trials
Zhou, L., Deng, X., Xu, M., Wu, Y., Shang, X., Fenfen, E., Wang, Y., Liang, S., Yang, K., & Li, X. (2023) · International Journal of Behavioral Nutrition and Physical Activity · doi:10.1186/s12966-023-01467-5 · Cited by 33
“SUCRA is an index that can be used as a reference to evaluate the relative position of each treatment and account for inconsistencies between studies [32, 33].”
Method
Integrating Evidence to Guide Use of Biologics and Small Molecules for Inflammatory Bowel Diseases
Dulai, P. S., Singh, S., Jairath, V., Wong, E. C. L., & Narula, N. (2023) · Gastroenterology · doi:10.1053/j.gastro.2023.10.033 · Cited by 32
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Vuyyuru, S. K., Nguyen, T. M., Murad, M. H., Narula, N., Bessissow, T., Zou, G., McCurdy, J. D., Peyrin‐Biroulet, L., Danese, S., Ma, C., et al. (2024) · Clinical Gastroenterology and Hepatology · doi:10.1016/j.cgh.2023.12.023 · Cited by 29
Efficacy and safety of antibody-drug conjugates in pretreated HER2-low metastatic breast cancer: A systematic review and network meta-analysis
Schettini, F., Nucera, S., Pascual, T., Martínez‐Sáez, O., Sánchez-Bayona, R., Conte, B., Buono, G., Lambertini, M., Punie, K., Cejalvo, J. M., et al. (2024) · Cancer Treatment Reviews · doi:10.1016/j.ctrv.2024.102865 · Cited by 29
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“A P score of 1 indicates that the treatment is certain to be the most effective/safest treatment in the network, while a P score of 0 indicates that the treatment is certain to be the least effective/safe in the network [25].”
Background
UEG and EAES rapid guideline: Update systematic review, network meta‐analysis, CINeMA and GRADE assessment, and evidence‐informed European recommendations on surgical management of GERD
Markar, S. R., Andreou, A., Bonavina, L., Flórez, I. D., Huo, B., Kontouli, K., Low, D. E., Mavridis, D., Maynard, N., Moss, A., et al. (2022) · United European Gastroenterology Journal · doi:10.1002/ueg2.12318 · Cited by 28
“We ranked all the available treatments in each outcome, from best to worst, using P‐ scores.(33) A value close to 1 means that the intervention is very efficacious, whereas a value close to 0 means the opposite.”
Method
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Wang, Z., Zhou, Z., Zhang, L., Li, X., Li, M., Pan, Y., Jiao, T., Shi, X., Liu, Q., Wang, C., et al. (2023) · European journal of medical research · doi:10.1186/s40001-022-00968-6 · Cited by 29
“The larger the percentage is, it means that the intervention has the highest probability and possibility of becoming the most preferred option, and a value of 0 indicates that the intervention may be completely ineffective [23, 24].”
Background
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Ballesio, A., Zagaria, A., Vacca, M., Pariante, C. M., & Lombardo, C. (2023) · Brain Behavior and Immunity · doi:10.1016/j.bbi.2023.05.006 · Cited by 30
“A hierarchy of competing interventions on the basis of their efficacy was established using P-scores, which are considered a frequentist equivalent to the Bayesian network surface under the cumulative ranking curves (SUCRA; Rücker and Schwarzer, 2015).”
Head-to-head drug comparisons in multiple sclerosis
Tur, C., Kalinčík, T., Oh, J., Sormani, M. P., Tintoré, M., Butzkueven, H., & Montalbán, X. (2019) · Neurology · doi:10.1212/wnl.0000000000008319 · Cited by 29
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“49 Comparisons were made when more than one study was included for each comparator and were considered statistically significant when the 95% CI did not include the value of zero.”
Background
Comparative efficacy, safety and benefit/risk of alerting agents for excessive daytime sleepiness in patients with obstructive sleep apnoea: a network meta-analysis
Pépin, J., Lehert, P., Messaoud, R. B., Joyeux-faure, M., Caussé, C., Asin, J., Barbé, F., Bonsignore, M., Randerath, W., Verbraecken, J., et al. (2024) · EClinicalMedicine · doi:10.1016/j.eclinm.2024.102843 · Cited by 28
“51 Pi is de ﬁ ned as the mean of all 1 – Pj (Pj = one-sided p value of accepting the alternative hypothesis that ti > tj).”
Background
Comparative effectiveness of different therapies for Clostridioides difficile infection in adults: a systematic review and network meta-analysis of randomized controlled trials
Bednárik, D. S., Földvári-Nagy, K. C., Simon, V., Rancz, A., Gede, N., Veres, D. S., Paraskevopoulos, P., Schnabel, T., Erőss, B. M., Hegyi, P., et al. (2025) · The Lancet Regional Health - Europe · doi:10.1016/j.lanepe.2024.101151 · Cited by 30
“P-scores 23 were calculated to indicate which treatments were more or less likely to have the most signi ﬁ cant bene ﬁ ts or negligible adverse effects; the score ranged from 0 to 1, representing the theoretically worst and best treatments, respectively, compared to the other treatments.”
Which are the best Chinese herbal injections combined with XELOX regimen for gastric cancer?
Zhang, D., Wu, J., Wang, K., Duan, X., Liu, S., & Zhang, B. (2018) · Medicine · doi:10.1097/md.0000000000010127 · Cited by 28
Topically applied treatments for external genital warts in nonimmunocompromised patients: a systematic review and network meta‐analysis
Jung, J. M., Jung, C. J., Lee, W. J., Won, C. H., Lee, M. W., Choi, J. H., & Chang, S. E. (2019) · British Journal of Dermatology · doi:10.1111/bjd.18638 · Cited by 28
Agreement between ranking metrics in network meta-analysis: an empirical study
Chiocchia, V., Nikolakopoulou, A., Papakonstantinou, T., Egger, M., & Salanti, G. (2020) · BMJ Open · doi:10.1136/bmjopen-2020-037744 · Cited by 30
A Markov chain approach for ranking treatments in network meta‐analysis
Chaimani, A., Porcher, R., Sbidian, É., & Mavridis, D. (2020) · Statistics in Medicine · doi:10.1002/sim.8784 · Cited by 27
Pain Control After Shoulder Arthroscopy: A Systematic Review of Randomized Controlled Trials With a Network Meta-analysis
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“The P-score represents the probability that the nerve block is the ideal block for optimal pain control, and it provides a method for ranking the possible options.(81) However, the optimal method of comparing treatments should be to look at the odds ratio and confidence interval.”
MethodInfluential
Pain management in shoulder arthroplasty: a systematic review and network meta-analysis of randomized controlled trials
Xiao, M. X., Cohen, S., Cheung, E. V., Freehill, M. T., & Abrams, G. D. (2021) · Journal of Shoulder and Elbow Surgery · doi:10.1016/j.jse.2021.06.008 · Cited by 28
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“Higher P-score scores correspond to a greater weaning success rate, lower proportion requiring reintubation and lower mortality (26).”
Background
The effect of Varenicline and Bupropion on smoking cessation: A network meta-analysis of 20 randomized controlled trials
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“We used P-scores to rank exercise types on the basis of the degree of improvement in each balance outcome categories [31].”
Method
EAES, SAGES, and ESCP rapid guideline: bowel preparation for minimally invasive colorectal resection
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“The SUCRA value ranged from 0 to 100%, with a larger SUCRA value indicating a better treatment option (Rücker and Schwarzer, 2015; Trinquart et al., 2016).”
Background
A Practical Guide for Application of Network Meta-Analysis in Evidence Synthesis
Antoniou, S. A., Koelemay, M. J. W., Antoniou, G. A., & Mavridis, D. (2018) · European Journal of Vascular and Endovascular Surgery · doi:10.1016/j.ejvs.2018.10.023 · Cited by 27
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Srisurapanont, M., Suttajit, S., Kosachunhanun, N., Likhitsathian, S., Suradom, C., & Maneeton, B. (2022) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2022.104731 · Cited by 31
Mineralocorticoid receptor antagonists in heart failure with reduced ejection fraction: a systematic review and network meta-analysis of 32 randomized trials
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Adjuvant bisphosphonates or RANK-ligand inhibitors for patients with breast cancer and bone metastases: A systematic review and network meta-analysis
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Ciclosporin or Infliximab as Rescue Therapy in Acute Glucorticosteroid-Refractory Ulcerative Colitis: Systematic Review and Network Meta-Analysis
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Self-citation

Authors: Rücker, G., & Schwarzer, G.
Affiliations: University of Freiburg (DE)
Corresponding author: Rücker, Gerta
ORCID: Rücker, Gerta
Schwarzer, Guido
Venue: BMC Medical Research Methodology
Publisher: Springer Science and Business Media LLC
Published: 2015-07-31
Volume: 15
Issue: 1
Pages: 58-58
ISSN: 1471-2288 (ISSN-L)
DOI: 10.1186/s12874-015-0060-8
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: other-oa
creativecommons.org/licenses/by/4.0 (unspecified)
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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Ranking treatments in frequentist network meta-analysis works without resampling methods

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