{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T11:03:00Z","timestamp":1788865380149,"version":"build-2803163510"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,11,10]],"date-time":"2017-11-10T00:00:00Z","timestamp":1510272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2017,11,10]],"date-time":"2017-11-10T00:00:00Z","timestamp":1510272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we use Bayesian networks to determine and visualise the interactions among various Class III malocclusion maxillofacial features during growth and treatment. We start from a sample of 143 patients characterised through a series of a maximum of 21 different craniofacial features. We estimate a network model from these data and we test its consistency by verifying some commonly accepted hypotheses on the evolution of these disharmonies by means of Bayesian statistics. We show that untreated subjects develop different Class III craniofacial growth patterns as compared to patients submitted to orthodontic treatment with rapid maxillary expansion and facemask therapy. Among treated patients the <jats:italic>CoA<\/jats:italic> segment (the maxillary length) and the <jats:italic>ANB<\/jats:italic> angle (the antero-posterior relation of the maxilla to the mandible) seem to be the skeletal subspaces that receive the main effect of the treatment.<\/jats:p>","DOI":"10.1038\/s41598-017-15293-w","type":"journal-article","created":{"date-parts":[[2017,11,6]],"date-time":"2017-11-06T09:27:56Z","timestamp":1509960476000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Bayesian Networks Analysis of Malocclusion Data"],"prefix":"10.1038","volume":"7","author":[{"given":"Marco","family":"Scutari","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pietro","family":"Auconi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guido","family":"Caldarelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lorenzo","family":"Franchi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,11,10]]},"reference":[{"key":"15293_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1197\/jamia.M2853","volume":"17","author":"M Scotch","year":"2010","unstructured":"Scotch, M., Duggal, M., Brandt, C., Lin, Z. & Shiffman, R. Use of Statistical Analysis in the Biomedical Informatics Literature. Journal of the American Medical Informatics Association \n                           17, 3\u20135 (2010).","journal-title":"Journal of the American Medical Informatics Association"},{"key":"15293_CR2","unstructured":"Ravindra, N. & Uribe, R. A. Atlas of Complex Orthodontics (Elsevier, 2016)."},{"key":"15293_CR3","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1080\/00207450590914464","volume":"115","author":"DW Zaidel","year":"2005","unstructured":"Zaidel, D. W. & Cohen, J. A. The Face, Beauty, and Symmetry: Perceiving Asymmetry in Beautiful Faces. The International Journal of Neuroscience \n                           115, 1165\u201373 (2005).","journal-title":"The International Journal of Neuroscience"},{"key":"15293_CR4","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1053\/j.sodo.2007.05.006","volume":"13","author":"T Baccetti","year":"2007","unstructured":"Baccetti, T., Franchi, L. & McNamara, J. A. Growth in the Untreated Class III Subject. Seminars in Orthodontics \n                           13, 130\u2013142 (2007).","journal-title":"Seminars in Orthodontics"},{"key":"15293_CR5","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1093\/ejo\/cjq052","volume":"33","author":"P Fudalej","year":"2011","unstructured":"Fudalej, P., Dragan, M. & Wedrychowska-Szulc, B. Prediction of the Outcome of Orthodontic Treatment of Class III Malocclusions\u2013a Systematic Revie. w. European Journal of Orthodontics \n                           33, 190\u2013197 (2011).","journal-title":"w. European Journal of Orthodontics"},{"key":"15293_CR6","unstructured":"Silver, N. The Signal and the Noise: Why So Many Predictions Fail\u2013but Some Don\u2019t (Penguin, 2015)."},{"key":"15293_CR7","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1177\/0956797613504966","volume":"25","author":"G Cumming","year":"2014","unstructured":"Cumming, G. The New Statistics: Why and How. Psychological Science \n                           25, 7\u201329 (2014).","journal-title":"Psychological Science"},{"key":"15293_CR8","doi-asserted-by":"crossref","unstructured":"Pearl, J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann Publishers Inc., 1988).","DOI":"10.1016\/B978-0-08-051489-5.50008-4"},{"key":"15293_CR9","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1098\/rstl.1763.0053","volume":"1683-1775","author":"T Bayes","year":"1763","unstructured":"Bayes, T. & Price, M. An Essay Towards Solving a Problem in the Doctrine of Chances. Philosophical Transactions \n                           1683\u20131775, 370\u2013418 (1763).","journal-title":"Philosophical Transactions"},{"key":"15293_CR10","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1214\/ss\/1177013621","volume":"1","author":"PS Laplace","year":"1986","unstructured":"Laplace, P. S. Memoir on the Probability of the causes of Events (1774) Translated from French. Statistical Science \n                           1, 364\u2013378 (1986).","journal-title":"Statistical Science"},{"key":"15293_CR11","doi-asserted-by":"crossref","unstructured":"Berry, S. M., Carlin, B. P., Lee, J. J. & M\u00fcller, P. Bayesian Adaptive Methods for Clinical Trials (Chapman & Hall, 2011).","DOI":"10.1201\/EBK1439825488"},{"key":"15293_CR12","doi-asserted-by":"crossref","unstructured":"Nagarajan, R., Scutari, M. & L\u00e8bre, S. Bayesian Networks in R with Applications in Systems Biology. Use R! series (Springer, 2013).","DOI":"10.1007\/978-1-4614-6446-4"},{"key":"15293_CR13","doi-asserted-by":"crossref","unstructured":"Pearl, J. Causality: Models, Reasoning and Inference, 2nd edn (Cambridge University Press, 2009).","DOI":"10.1017\/CBO9780511803161"},{"key":"15293_CR14","doi-asserted-by":"crossref","unstructured":"Caldarelli, G. Scale-Free Networks: Complex Webs in Nature and Technology (Oxford University Press, 2007).","DOI":"10.1093\/acprof:oso\/9780199211517.001.0001"},{"key":"15293_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v035.i03","volume":"35","author":"M Scutari","year":"2010","unstructured":"Scutari, M. Learning Bayesian Networks with the bnlearn R Package. Journal of Statistical Software \n                           35, 1\u201322 (2010).","journal-title":"Journal of Statistical Software"},{"key":"15293_CR16","doi-asserted-by":"publisher","first-page":"115017","DOI":"10.1088\/1367-2630\/16\/11\/115017","volume":"16","author":"A Scala","year":"2014","unstructured":"Scala, A. et al. Complex Networks for Data-Driven Medicine: the Case of Class III Dentoskeletal Disharmony. New Journal of Physics \n                           16, 115017 (2014).","journal-title":"New Journal of Physics"},{"key":"15293_CR17","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1111\/j.1601-6343.2011.01523.x","volume":"14","author":"P Auconi","year":"2011","unstructured":"Auconi, P., Caldarelli, G., Scala, A., Ierardo, G. & Polimeni, A. A Network Approach to Orthodontic Diagnosis. Orthodontics & Craniofacial Research \n                           14, 189\u2013197 (2011).","journal-title":"Orthodontics & Craniofacial Research"},{"key":"15293_CR18","doi-asserted-by":"crossref","unstructured":"Young, G. A. & Smith, R. L. Essentials of Statistical Inference (Cambridge University Press, 2005).","DOI":"10.1017\/CBO9780511755392"},{"key":"15293_CR19","unstructured":"Lee, P. M. Bayesian Statistics: an Introduction, 2nd edn (Wiley, 2012)."},{"key":"15293_CR20","unstructured":"Weisberg, S. Applied Linear Regression, 4th edn (Wiley, 2013)."},{"key":"15293_CR21","unstructured":"Hoyle, R. H. Structural Equation Modeling: Concepts, Issues, and Applications (SAGE, 1995)."},{"key":"15293_CR22","doi-asserted-by":"publisher","first-page":"e114","DOI":"10.1371\/journal.pgen.0020114","volume":"2","author":"R Li","year":"2006","unstructured":"Li, R. et al. Structural Model Analysis of Multiple Quantitative Traits. PLoS Genetics \n                           2, e114 (2006).","journal-title":"PLoS Genetics"},{"key":"15293_CR23","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1186\/1297-9686-43-6","volume":"43","author":"GJM Rosa","year":"2011","unstructured":"Rosa, G. J. M. et al. Inferring Causal Phenotype Networks Using Structural Equation Models. Genomic Selection Evolution \n                           43, 6 (2011).","journal-title":"Genomic Selection Evolution"},{"key":"15293_CR24","unstructured":"Koller, D. & Friedman, N. Probabilistic Graphical Models: Principles and Techniques (MIT Press, 2009)."},{"key":"15293_CR25","doi-asserted-by":"crossref","unstructured":"Scutari, M. & Denis, J.-B. Bayesian Networks with Examples in R (Chapman & Hall, 2014).","DOI":"10.1201\/b17065"},{"key":"15293_CR26","doi-asserted-by":"crossref","unstructured":"Draper, N. R. & Smith, H. Applied Regression Analysis, 3rd edn(Wiley, 1998).","DOI":"10.1002\/9781118625590"},{"key":"15293_CR27","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz, G. Estimating the Dimension of a Model. The Annals of Statistics \n                           6, 461\u2013464 (1978).","journal-title":"The Annals of Statistics"},{"key":"15293_CR28","unstructured":"Russell, S. J. & Norvig, P. Artificial Intelligence: A Modern Approach, 3rd edn (Prentice Hall, 2009)."},{"key":"15293_CR29","doi-asserted-by":"crossref","unstructured":"Auconi, P. et al. Understanding Interactions among Cephalometrics Variables During Growth in Untreated Class III Subjects. European Journal of Orthodontics (2017).","DOI":"10.1093\/ejo\/cjw084"},{"key":"15293_CR30","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.artmed.2012.12.006","volume":"57","author":"M Scutari","year":"2013","unstructured":"Scutari, M. & Nagarajan, R. On Identifying Significant Edges in Graphical Models of Molecular Networks. Artificial Intelligence in Medicine \n                           57, 207\u2013217 (2013).","journal-title":"Artificial Intelligence in Medicine"},{"key":"15293_CR31","unstructured":"Claeskens, G. & Hjort, N. L. Model Selection and Model Averaging (Cambridge University Press, 2008)."},{"key":"15293_CR32","doi-asserted-by":"crossref","unstructured":"Efron, B. & Tibshirani, R. An Introduction to the Bootstrap (Chapman & Hall, New York, 1993).","DOI":"10.1007\/978-1-4899-4541-9"},{"key":"15293_CR33","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R. & Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer, 2009), 2nd edn.","DOI":"10.1007\/978-0-387-84858-7"},{"key":"15293_CR34","unstructured":"R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2016)."},{"key":"15293_CR35","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1093\/ejo\/cju038","volume":"37","author":"P Auconi","year":"2015","unstructured":"Auconi, P., Scazzocchio, M., Cozza, P., McNamara, J. A. & Franchi, L. Prediction of Class III Treatment Outcomes Through Orthodontic Data Mining. European Journal of Orthodontics \n                           37, 257\u2013267 (2015).","journal-title":"European Journal of Orthodontics"},{"issue":"Suppl. 2","key":"15293_CR36","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2105-8-S2-S3","volume":"8","author":"R Opgen-Rhein","year":"2007","unstructured":"Opgen-Rhein, R. & Strimmer, K. Learning Causal Networks from Systems Biology Time Course Data: an Effective Model Selection Procedure for the Vector Autoregressive Process. BMC Bioinformatics \n                           8(Suppl. 2), S3 (2007).","journal-title":"BMC Bioinformatics"},{"key":"15293_CR37","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.artmed.2003.11.001","volume":"30","author":"PJF Lucas","year":"2004","unstructured":"Lucas, P. J. F., van der Gaag, L. C. & Abu-Hanna, A. Bayesian Networks in Biomedicine and Health-Care. Artificial Intelligence in Medicine \n                           30, 201\u2013214 (2004).","journal-title":"Artificial Intelligence in Medicine"},{"key":"15293_CR38","doi-asserted-by":"publisher","first-page":"14313","DOI":"10.1073\/pnas.0802272105","volume":"105","author":"S Mukherjee","year":"2008","unstructured":"Mukherjee, S. & Speed, T. P. Network Inference Using Informative Priors. Proceedings of the National Academy of Sciences \n                           105, 14313\u201314318 (2008).","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"15293_CR39","doi-asserted-by":"crossref","unstructured":"Ness, R. O., Sachs, K., Mallick, P. & Vitek, O. A Bayesian Active Learning Experimental Design for Inferring Signaling Networks. In Proceedings of the 21st Annual International Conference on Research in Computational Molecular Biology, 134\u2013156 (Springer, 2017).","DOI":"10.1007\/978-3-319-56970-3_9"},{"key":"15293_CR40","doi-asserted-by":"publisher","DOI":"10.1186\/s12918-014-0102-6","volume":"8","author":"E Pauwels","year":"2014","unstructured":"Pauwels, E., Lajaunie, C. & Vert, J.-P. A Bayesian Active Learning Strategy for Sequential Experimental Design in Systems Biology. BMC Systems Biology \n                           8, 102 (2014).","journal-title":"BMC Systems Biology"},{"key":"15293_CR41","unstructured":"Bathia, S. N. & Leighton, B. C. A Manual of Facial Growth (Oxford University Press, 1993)."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-017-15293-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-017-15293-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-017-15293-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T13:23:58Z","timestamp":1671801838000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-017-15293-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,10]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["15293"],"URL":"https:\/\/doi.org\/10.1038\/s41598-017-15293-w","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,10]]},"assertion":[{"value":"10 February 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 November 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"15236"}}