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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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Obed, D., Salim, M., Schlottmann, F., Bingoel, A. S., Panayi, A. C., Dastagir, K., Vogt, P. M., & Könneker, S. (2022) · BMC Musculoskeletal Disorders · doi:10.1186/s12891-022-05894-6 · Cited by 14
“Point estimates of the effect sizes were used to rank treatments [16].”
Method
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Kuno, T., Ueyama, H. A., Takagi, H., & Bangalore, S. (2020) · American Heart Journal · doi:10.1016/j.ahj.2020.06.008 · Cited by 14
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de Melo, S. M., Marta, G. N., Latorraca, C. D. O. C., Martins, C. B., Efthimiou, O., & Riera, R. (2021) · PLoS ONE · doi:10.1371/journal.pone.0257384 · Cited by 14
“We used the p-score to rank the investigated hypofractionated schemes [22].”
BackgroundMethod
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Kunze, K. N., Farivar, D., Premkumar, A., Cross, M. B., Valle, A. G. D., & Pearle, A. D. (2021) · Journal of Orthopaedics · doi:10.1016/j.jor.2021.05.012 · Cited by 13
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Eisele‐Metzger, A., Schoser, D. S., Klein, M. D., Grummich, K., Schwarzer, G., Schwingshackl, L., Hermann, R. M., Biallas, B., Wilke, C., Meerpohl, J. J., et al. (2022) · Scandinavian Journal of Work Environment & Health · doi:10.5271/sjweh.4070 · Cited by 20
“In a second step, we conducted NMA using a fre - quentist approach (37) including all available interven - tions categorized as described above.”
Self-citation
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Malandris, K., Papandreou, S., Avgerinos, I., Karagiannis, T., Paschos, P., Michailidis, T., Liakos, A., Bekiari, E., Sinakos, E., & Τσάπας, Α. (2023) · HORMONES · doi:10.1007/s42000-023-00493-z · Cited by 13
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Mori, K., Yanagisawa, T., Fukuokaya, W., Iwatani, K., Matsukawa, A., Katayama, S., Pradère, B., Laukhtina, E., Rajwa, P., Moschini, M., et al. (2023) · International Journal of Urology · doi:10.1111/iju.15319 · Cited by 13
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Schmidt, J., Proesl, S., Schulz‐Kornas, E., Haak, R., Meyer‐Lueckel, H., Campus, G., & Esteves‐Oliveira, M. (2023) · Journal of Dentistry · doi:10.1016/j.jdent.2023.104776 · Cited by 14
Analyzing methods for reducing recurrence rates after EMR of large nonpedunculated colorectal polyps: an indirect pairwise comparison
Radadiya, D. K., Desai, M., Patel, H. K., Srinivasan, S., Chandrasekar, V. T., Hassan, C., Repici, A., Rex, D. K., & Sharma, P. (2023) · Gastrointestinal Endoscopy · doi:10.1016/j.gie.2023.11.060 · Cited by 13
Optimal combination of arthroplasty type, fixation method, and postoperative rehabilitation protocol for complex proximal humerus fractures in the elderly: a network meta-analysis
Colasanti, C. A., Anil, U., Rodriguez, K. A., Levin, J. M., Leucht, P., Simovitch, R. W., & Zuckerman, J. D. (2024) · Journal of Shoulder and Elbow Surgery · doi:10.1016/j.jse.2024.03.040 · Cited by 13
Comparative efficacy of biologics for patients with inadequately controlled asthma: A network meta-analysis
Kim, H., Kim, M. G., Kim, S., Lee, J., Byun, Y., Park, J., & Kim, K. (2024) · World Allergy Organization Journal · doi:10.1016/j.waojou.2024.100934 · Cited by 13
“24 In accordance with the basic NMA assumptions, outcomes were computed as multiple treatment comparisons only if a head-to-head trial existed; otherwise, an indirect treatment comparison was utilized.”
Method
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“3).”
EGFR-TKIs or EGFR-TKIs combination treatments for untreated advanced EGFR-mutated NSCLC: a network meta-analysis
Liu, A., Wang, X., Wang, L., Han, Z., Xiong, L., Gan, X., Wang, Q., & Tao, G. (2024) · BMC Cancer · doi:10.1186/s12885-024-13168-8 · Cited by 14
“Still, they do not directly quantify the certainty of one treatment being superior to another [44].”
Definitive Fixation Outcomes of Open Tibial Shaft Fractures: Systematic Review and Network Meta-analysis
Al-Hourani, K., Donovan, R. L., Stoddart, M. T., Foote, C. J., Kelly, M. B., & Tornetta, P. (2021) · Journal of Orthopaedic Trauma · doi:10.1097/bot.0000000000002090 · Cited by 13
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“A p-score of “one” is ranked as best, whereas “zero” is ranked as least.(35) A two-sided p-value of <0.”
BackgroundMethod
Quantifying and presenting overall evidence in network meta‐analysis
Lin, L. (2018) · Statistics in Medicine · doi:10.1002/sim.7905 · Cited by 14
“The treatment IDs are as follows: (1) usual control; (2) educational; (3) behavioral; (4) cognitive; (5) support; (6) educational + behavioral; (7) educational + cognitive; (8) educational + relaxation; (9) behavioral + cognitive; (10) behavioral + relaxation; (11) cognitive + relaxation; (12) cognitive + support; (13…”
Interventions for Actinic Keratosis in Nonscalp and Nonface Localizations: Results from a Systematic Review with Network Meta-Analysis
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“Forest plots and two-dimensional graphical presentations of the network structure were created with the same package in R (Rücker and Schwarzer, 2015).”
Method
Reporting of Cochrane systematic review protocols with network meta‐analyses—A scoping review
Wang, R., Dwan, K. M., Showell, M. G., van Wely, M., Mol, B. W., Askie, L. M., & Seidler, A. L. (2021) · Research Synthesis Methods · doi:10.1002/jrsm.1531 · Cited by 12
Network meta‐analysis and random walks
Davies, A. L., Papakonstantinou, T., Nikolakopoulou, A., Rücker, G., & Galla, T. (2022) · Statistics in Medicine · doi:10.1002/sim.9346 · Cited by 13
“635 (23) S2 = ( 2, 2) ∶ 2 = 1 ← → 3 ← → 2 2 = U (1-2) 1-3 U (1-2) 3-2 = 0.”
Self-citation
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Is Network Meta-analysis a Revolutionary Statistical Tool for Improving the Reliability of Clinical Trial Results? A Brief Overview and Emerging Issues Arising
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Herranz‐Gómez, A., Suso‐Martí, L., Varangot‐Reille, C., Barrachina-Gauchia, L., Casaña, J., López, L., Calatayud, J., & Cuenca‐Martínez, F. (2023) · Physical Therapy · doi:10.1093/ptj/pzad132 · Cited by 12
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“The SUCRA-based probabilistic ranking results ( Table 5 , Figure 5D ) indicated that QSYQDP + CWM (86.76”
MethodInfluential
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“The P-score, which is analogous to the surface under the cumulative ranking curve (SUCRA) and estimates the extent of certainty that a treatment is better than another treatment, was adopted to rank treatment arms [24].”
Short-term Dual Therapy or Mono Therapy With Acetaminophen and Ibuprofen for Fever: A Network Meta-Analysis
la Cruz-Mena, J. E. D., Veroniki, A.-A., Acosta-Reyes, J. L., Estupiñán-Bohorquez, A. F., Burgos, J. A. I., Pana, M., Sierra, J. M., & Flórez, I. D. (2024) · PEDIATRICS · doi:10.1542/peds.2023-065390 · Cited by 14
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“We generated P-scores to determine the relative ranking of interventions [17].”
A systematic review and network meta-analysis of interventions to preserve insulin-secreting beta cell function in people newly diagnosed with type 1 diabetes: results from randomised controlled trials of immunomodulatory therapies
Beese, S. E., Price, M. J., Tomlinson, C. L., Sharma, P., Harris, I. M., Adriano, A., Quinn, L. M., Gada, R., Horgan, T. J., Maggs, F., et al. (2025) · BMC Medicine · doi:10.1186/s12916-025-04201-z · Cited by 18
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Walter, M. A., Nesti, C., Spanjol, M., Kollár, A., Bütikofer, L., Gloy, V., Dumont, R. A., Seiler, C. A., Christ, E., Radojewski, P., et al. (2021) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013700.pub2 · Cited by 12
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“Other ranking metrics include the surface under the cumulative ranking curve (SUCRA), that averages across all ranking probabilities for each treatment, and its frequentist analogue, P-score, which is calculated analytically.(6,7) SUCRA and P-score can be interpreted as the mean extent of certainty that a treatment is…”
BackgroundMethodInfluential
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Kamarajah, S. K., Bundred, J., Littler, P., Reeves, H. L., Manas, D., & White, S. A. (2020) · HPB · doi:10.1016/j.hpb.2020.10.031 · Cited by 12
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“Yutani et al46 Japan R 40 HP 34 IDC, 2 MUC, 4 others NR NR 51 (25-86) B F Zhao et al47 China P 78 HP 66 IDC, 4 MC, 3 ILC, 3 MP, 1 MUC NR NR 52.”
Influential
Comparative Efficacy of Systemic Agents for Brain Metastases From Non-Small-Cell Lung Cancer With an EGFR Mutation/ALK Rearrangement: A Systematic Review and Network Meta-Analysis
Taslimi, S., Brar, K., Ellenbogen, Y., Deng, J., Hou, W., de Moraes, F. Y., Glantz, M., Zacharia, B. E., Tan, A. C., Ahluwalia, M. S., et al. (2021) · Frontiers in Oncology · doi:10.3389/fonc.2021.739765 · Cited by 12
“We then used the R̈cker & Schwarzer method to rank treatments (14).”
Method
Comparative efficacy of inhalers in mild-to-moderate asthma: systematic review and network meta-analysis
Park, H., Huh, J.-Y., Lee, J. S., Lee, J. S., Oh, Y., & Lee, S. W. (2022) · Scientific Reports · doi:10.1038/s41598-022-09941-z · Cited by 12
Intravenous iron versus oral iron versus no iron with or without erythropoiesis- stimulating agents (ESA) for cancer patients with anaemia: a systematic review and network meta-analysis
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Biologics for pediatric moderate‐to‐severe plaque psoriasis: a systematic review and network meta‐analysis
Huang, I., Yu, C., Tai, C., Tu, Y., & Chi, C. (2022) · JDDG Journal der Deutschen Dermatologischen Gesellschaft · doi:10.1111/ddg.14832 · Cited by 12
Multicriteria Decision-Making Methods for Optimal Treatment Selection in Network Meta-Analysis
Bellos, I. (2022) · Medical Decision Making · doi:10.1177/0272989x221126678 · Cited by 12
“Correspondingly, in the frequentist framework, the P-score has been proposed as a ranking tool, expressing the degree of certainty that a treatment is better than its alternatives.(4) Decision making in health care is multifactorial, since selecting an optimal treatment plan relies on the interplay of various factors,…”
Background
Antiplatelet therapy for secondary prevention of lacunar stroke: a systematic review and network meta-analysis
Hou, X., Cen, K., Cui, Y., Zhang, Y., & Xu, F. (2022) · European Journal of Clinical Pharmacology · doi:10.1007/s00228-022-03413-z · Cited by 11
“The value of the surface under the cumulative ranking (SUCRA) was used to represent the ranking of the efficacy of each antiplatelet therapy [16].”
Method
Pharmacotherapeutic efficacy on noninvasive fibrosis progression in nonalcoholic fatty liver disease: a systematic review and network meta-analysis
Kovalic, A. J., Gozar, M., Da, B. L., Bernstein, D., & Satapathy, S. K. (2022) · European Journal of Gastroenterology & Hepatology · doi:10.1097/meg.0000000000002463 · Cited by 13
Comparative efficacy and optimal duration of first-line antibiotic regimens for acute otitis media in children and adolescents: a systematic review and network meta-analysis of 89 randomized clinical trials
Kim, M. S., Kim, J. H., Ryu, S., Lee, S. W., Yon, D. K., Kim, E. Y., Koyanagi, A., Dragioti, E., Shin, J. I., & Smith, L. (2023) · World Journal of Pediatrics · doi:10.1007/s12519-023-00716-8 · Cited by 12
“We performed frequentist NMA, a method for comparing the efficacy of multiple interventions simultaneously by pooling direct and indirect comparisons [16].”

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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