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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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Predictive P-score for treatment ranking in Bayesian network meta-analysis
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“Pk = (K − Rk)/(K − 1) ; this corresponds to the findings by Rücker and Schwarzer [14].”
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“A ranking of intervention effectiveness was conducted based on P-scores (Rücker & Schwarzer, 2015), which are analogous to surface under cumulative ranking values in Bayesian NMA (Mbuagbaw et al., 2017).”
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“SUCRA values range from 0 to 100, and the closer it is to 100, the better the intervention (11).”
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Systematic review with network meta-analysis
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“NMA is used to compare three or more treatments for the same condition [24], to assess the relative effectiveness of two treatments when they have not been compared directly in a randomised trial but have each been compared to the similar control group [25].”
MethodAldin, A., Besiroglu, B., Adams, A., Monsef, I., Piechotta, V., Tomlinson, E., Hornbach, C., Dressen, N., Goldkuhle, M., Maisch, P., et al. (2023) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013798.pub2 · Cited by 40
Gao, Y., Liu, M., Yao, L., Yang, Z., Chen, Y., Niu, M., Sun, Y., Ji, C., Hou, L., Sun, F., et al. (2022) · Journal of Evidence-Based Medicine · doi:10.1111/jebm.12485 · Cited by 43
Lee, S. F., Kennedy, S. K. F., Caini, S., Wong, H. C. Y., Yip, P. L., Poortmans, P. M., Meattini, I., Kaidar‐Person, O., Recht, A., Hijal, T., et al. (2024) · BMJ · doi:10.1136/bmj-2023-079089 · Cited by 40
“29 All P values were two tailed, and we considered P values of 0.05 to be statistically significant.”
InfluentialAkter, S., Rahman, M. M., Rouyard, T., Aktar, S., Nsashiyi, R. S., & Nakamura, R. (2024) · Nature Human Behaviour · doi:10.1038/s41562-024-02002-7 · Cited by 49
You, W., Liu, M., Miao, J., Liao, Y., Song, Y.-B., Cai, D.-K., Gao, Y., & Peng, H. (2018) · Journal of Cancer · doi:10.7150/jca.22361 · Cited by 40
“A P-score, proposed by Rücker and Schwarzer [4] as a frequentist analog to surface under the cumulative ranking curve [5, 6] would be 0% for the worst treatment.”
MethodA generalized pairwise modelling framework for network meta-analysis
Doi, S. A. R., & Barendregt, J. J. (2018) · International Journal of Evidence-Based Healthcare · doi:10.1097/xeb.0000000000000140 · Cited by 40
Mavridis, D., Porcher, R., Nikolakopoulou, A., Salanti, G., & Ravaud, P. (2019) · Biometrical Journal · doi:10.1002/bimj.201900026 · Cited by 39
“Rücker and Schwarzer (2015) developed a measure called P-scores, which is equivalent to SUCRA but is not simulation-based and can be computed analytically.”
BackgroundInfluentialSayed, A. M., Morsy, S., Tawfik, G. M., Naveed, S., Duc, N. T. M., Hieu, T. H., Ali, Z. A., Shinkar, A., Doheim, M. F., Hashan, M. R., et al. (2020) · General Hospital Psychiatry · doi:10.1016/j.genhosppsych.2020.02.001 · Cited by 40
Tsai, S., Ding, Y., Shih, M., & Tu, Y. (2020) · Journal Of Clinical Periodontology · doi:10.1111/jcpe.13338 · Cited by 40
Phinyo, P., Koompawichit, P., Nochaiwong, S., Tovanabutra, N., Chiewchanvit, S., & Chuamanochan, M. (2020) · The Journal of Allergy and Clinical Immunology In Practice · doi:10.1016/j.jaip.2020.08.055 · Cited by 41
Gaitán‐Duarte, H., Álvarez, C., Rincón, C., González, N. Y., Cortés, J. A., Villar, J. C., Bravo-Ojeda, J. S., García-Peña, Á. A., Jaimes, W. A., Rodríguez, V., et al. (2021) · EClinicalMedicine · doi:10.1016/j.eclinm.2021.101242 · Cited by 42
Noninvasive respiratory support after extubation: a systematic review and network meta-analysis
Boscolo, A., Pettenuzzo, T., Sella, N., Zatta, M., Salvagno, M., Tassone, M., Pretto, C., Peralta, A., Muraro, L., Zarantonello, F., et al. (2023) · European Respiratory Review · doi:10.1183/16000617.0196-2022 · Cited by 39
“SUCRA represents the overall ranking of each treatment for the specified outcome and ranges from 0 (minimum) to 1 (maximum) [38, 39].”
Conservative Treatments in the Management of Acute Painful Vertebral Compression Fractures
Alimy, A., Anastasilakis, A. D., CAREY, J. J., D’Oronzo, S., Naciu, A. M., Paccou, J., Yavropoulou, M. P., Lems, W. F., & Rolvien, T. (2024) · JAMA Network Open · doi:10.1001/jamanetworkopen.2024.32041 · Cited by 45
Efficacy and safety of intranasal medications for allergic rhinitis: Network meta‐analysis
Sousa‐Pinto, B., Vieira, R. J., Bognanni, A., Gil‐Mata, S., Ferreira‐da‐Silva, R., Ferreira, A., Cardoso‐Fernandes, A., Ferreira‐Cardoso, H., Marques‐Cruz, M., Duarte, V. H., et al. (2024) · Allergy · doi:10.1111/all.16384 · Cited by 39
“12 We assessed transitivity (assumption that the different sets of included RCTs are similar in all important variables except the comparison of interventions being made) 3 by checking for consistency of patient and study characteristics across the studies.”
Nelson, A. D., Black, C. J., Houghton, L. A., Lugo‐Fagundo, N. S., Lacy, B. E., & Ford, A. C. (2021) · Alimentary Pharmacology & Therapeutics · doi:10.1111/apt.16437 · Cited by 39
Lewis, S. R., Macey, R., Stokes, J., Cook, J. A., Eardley, W. G., & Griffin, X. L. (2022) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013404.pub2 · Cited by 42
Geraldini, F., CASSAI, A. D., Diana, P., Correale, C., Boscolo, A., Zampirollo, S., Disarò, L., Carere, A., Cacco, N., Navalesi, P., et al. (2022) · Neurocritical Care · doi:10.1007/s12028-022-01493-4 · Cited by 39
Jung, Y. S., Park, C. H., Park, J. H., Nam, E., & Lee, H. L. (2017) · Helicobacter · doi:10.1111/hel.12389 · Cited by 39
Guo, G., Pan, C., Guo, W., Bai, S., Nie, H., Feng, Y., Li, G., Deng, H. X., Ma, Y., Zhu, S., et al. (2020) · Journal of NeuroInterventional Surgery · doi:10.1136/neurintsurg-2019-015362 · Cited by 39
Multiple treatment comparison in narcolepsy: a network meta-analysis
Lehert, P., & Falissard, B. (2018) · SLEEP · doi:10.1093/sleep/zsy185 · Cited by 38
“Thus, the ranking of P scores minimizes the gamma risk [23].”
BackgroundMethodInfluentialMori, K., Pradère, B., Moschini, M., Mostafaei, H., Laukhtina, E., Schuettfort, V. M., Motlagh, R. S., Soria, F., Teoh, J. Y., Egawa, S., et al. (2021) · European Journal of Cancer · doi:10.1016/j.ejca.2021.03.049 · Cited by 37
Hoang, N.-T.-T., Chen, S., & Chou, L. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph18158063 · Cited by 38
“The P-score of each treatment showed its ranking among the others; the most effective P-score is 1 and the worst is 0, and a higher score indicates a better effect [26].”
BackgroundKobeissi, H., Ghozy, S. A., Turfe, B., Bilgin, C., Kadirvel, R., Kallmes, D. F., Brinjikji, W., & Rabinstein, A. A. (2023) · Frontiers in Neurology · doi:10.3389/fneur.2023.1102463 · Cited by 38
“Treatments ranking was based on P-scores, which are the frequentist approach analog to surface under the cumulative ranking (SUCRA) (18).”
MethodKuno, T., Fujisaki, T., Shoji, S., Sahashi, Y., Tsugawa, Y., Iwagami, M., Takagi, H., Briasoulis, Α., Deharo, P., Cuisset, T., et al. (2022) · Circulation Cardiovascular Interventions · doi:10.1161/circinterventions.122.011990 · Cited by 37
Methods for Indirect Treatment Comparison: Results from a Systematic Literature Review
Macabeo, B., Quenéchdu, A., Aballéa, S., François, C., Boyer, L., & Laramée, P. (2024) · Journal of Market Access & Health Policy · doi:10.3390/jmahp12020006 · Cited by 37
“MAICs and STCs are also population-adjusted methods, designed for pairwise comparisons only, which can be of particular use in situations where heterogeneity exists across the trials within the network, as well as for incomplete evidence networks.”
MethodLi, Z., Lin, C., Cai, X., Lv, F., Yang, W., & Ji, L. (2024) · Alzheimer s Research & Therapy · doi:10.1186/s13195-024-01645-y · Cited by 44
“Moreover, the probability of being the best intervention was generated with the P-score and surface under the cumulative ranking curve (SUCRA) method [40, 41].”
Schwingshackl, L., Schwarzer, G., Rücker, G., & Meerpohl, J. J. (2019) · Advances in Nutrition · doi:10.1093/advances/nmz036 · Cited by 37
“SUCRA values can also be obtained in a frequentist framework, either through the use of resampling methods (80) or an analytic approach (P score), with corresponding interpretation and identical rankings (94).”
Self-citationPiechotta, V., Jakob, T., Langer, P. H., Monsef, I., Scheid, C., Estcourt, L. J., Ocheni, S., Theurich, S., Kuhr, K., Scheckel, B., et al. (2019) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd013487 · Cited by 35
Kuno, T., Ueyama, H. A., Fujisaki, T., Briasouli, A. A., Takagi, H., & Briasoulis, Α. (2020) · The American Journal of Cardiology · doi:10.1016/j.amjcard.2020.01.009 · Cited by 38
Comparative Efficacy of Bronchiolitis Interventions in Acute Care: A Network Meta-analysis
Elliott, S. A., Gaudet, L., Fernandes, R. M., Vandermeer, B., Freedman, S. B., Johnson, D. W., Plint, A. C., Klassen, T. P., Allain, D., & Hartling, L. (2021) · PEDIATRICS · doi:10.1542/peds.2020-040816 · Cited by 37
Jo, Y., Park, S., Oh, C., Pak, Y., Jeong, K., Yun, S., Noh, C., Chung, W., Kim, Y. H., Ko, Y., et al. (2021) · Korean Journal of Anesthesiology · doi:10.4097/kja.21330 · Cited by 37
“To rank the analgesic interventions in order, we reported the P score, which measures the level of certainty that an intervention is better than the competing interventions [22].”
BackgroundJuanJuan, W., Peng, P., Chen, P., Zeng, L., Pan, Q., Wei, W., & He, J. (2017) · Oncotarget · doi:10.18632/oncotarget.21633 · Cited by 36
“The P-scores that were based solely on the point estimates and standard errors of the network estimates were calculated to rank all probiotic regimens and the higher P-score value was correspond to better result for respective probiotic regimen [22].”
BackgroundDavey, M. S., Hurley, E. T., Anil, U., Moses, A. R., Thompson, K. A., Alaia, M. J., Strauss, E. J., & Campbell, K. A. (2021) · Arthroscopy The Journal of Arthroscopic and Related Surgery · doi:10.1016/j.arthro.2021.01.023 · Cited by 36
A systematic review and network meta‐analysis of interventions for subjective cognitive decline
Roheger, M., Hennersdorf, X.-S., Riemann, S., Flöel, A., & Meinzer, M. (2021) · Alzheimer s & Dementia Translational Research & Clinical Interventions · doi:10.1002/trc2.12180 · Cited by 35
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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