A novel approach to learning through categorical variables applicable to the classification of solitary pulmonary nodule malignancy

A novel approach to learning through categorical variables applicable to the classification of solitary pulmonary nodule malignancy | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article A novel approach to learning through categorical variables applicable to the classification of solitary pulmonary nodule malignancy Raquel Bosch-Romeu, Julian Librero, Marina Senent-Valero, Maria Carmen Sanfeliu-Alonso, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2502360/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background One of the main drawbacks in constructing a classification model is that some or all of the covariates are categorical variables. Classical methods either assign labels to each output of a categorical variable or are summarised measures (frequencies and percentages), which can be interpreted as probabilities. Methods We adopted a novel mathematical procedure to construct a classification model from categorical variables based on a non-classical probability approach. More specifically, we codified the variables following the categorical data representation from the Discriminant Correspondence Analysis before constructing a non-classical probability matrix system that represents an entangled system of dependent-independent variables. We then developed a disentangled procedure to obtain an empirical density function for each representative class (minimum of two classes). Finally, we constructed our classification model using the density functions. Results We applied the proposed procedure to build a classification model of the malignancy of Solitary Pulmonary Nodule (SPN) after five years of follow up using routine clinical data. First, with 2/3 (270) of the sample of 404 patients with SPN, we constructed the classification model, and then validated it with the remaining 1/3 (134) we validated it. We tested the procedure’s stability by repeating the analysis randomly 1000 times. We obtained a model accuracy of 0.74, an F1 score of 0.58, a Cohen’s Kappa value of 0.41 and a Matthews Correlation Coefficient of 0.45. Finally, the area under the ROC curve was 0.86. Conclusion The proposed procedure provides a machine learning classification model with an acceptable performance of a classification model of solitary pulmonary nodule malignancy constructed from routine clinical data and mainly composed of categorical variables. It provides an acceptable performance, which could be used by clinicians as a tool to classify SPN malignancy in routine clinical practice. Classification methods Non-classical probabilities Solitary Pulmonary Nodule Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2502360","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":169842195,"identity":"51cf59f7-3eb4-4d9a-b545-9a2c7e95eaa7","order_by":0,"name":"Raquel Bosch-Romeu","email":"","orcid":"","institution":"CEU Cardinal Herrera University","correspondingAuthor":false,"prefix":"","firstName":"Raquel","middleName":"","lastName":"Bosch-Romeu","suffix":""},{"id":169842197,"identity":"cce39c78-1e41-4cca-a2db-8bbc8844e90e","order_by":1,"name":"Julian Librero","email":"","orcid":"","institution":"NavarraBiomed","correspondingAuthor":false,"prefix":"","firstName":"Julian","middleName":"","lastName":"Librero","suffix":""},{"id":169842199,"identity":"f62d85e9-5f30-41b5-ad71-42e4fd67ce68","order_by":2,"name":"Marina Senent-Valero","email":"","orcid":"","institution":"Hospital General Universitario de Alicante","correspondingAuthor":false,"prefix":"","firstName":"Marina","middleName":"","lastName":"Senent-Valero","suffix":""},{"id":169842200,"identity":"b1326904-68d7-4daf-a37f-29c2d301c938","order_by":3,"name":"Maria Carmen Sanfeliu-Alonso","email":"","orcid":"","institution":"CEU Cardinal Herrera University","correspondingAuthor":false,"prefix":"","firstName":"Maria","middleName":"Carmen","lastName":"Sanfeliu-Alonso","suffix":""},{"id":169842201,"identity":"2988bd71-fdb7-4612-8442-139276546e1e","order_by":4,"name":"Jose Maria Salinas-Serrano","email":"","orcid":"","institution":"Hospital Universitari Sant Joan d'Alacant","correspondingAuthor":false,"prefix":"","firstName":"Jose","middleName":"Maria","lastName":"Salinas-Serrano","suffix":""},{"id":169842202,"identity":"e6acbe4d-9b75-4149-a541-878d56a0e961","order_by":5,"name":"Jaume Forés-Martos","email":"","orcid":"","institution":"CEU Cardinal Herrera University","correspondingAuthor":false,"prefix":"","firstName":"Jaume","middleName":"","lastName":"Forés-Martos","suffix":""},{"id":169842203,"identity":"4f4d671b-1dac-4d26-a0f2-c13bc1434995","order_by":6,"name":"Beatriz Suay-Garcia","email":"","orcid":"","institution":"CEU Cardinal Herrera University","correspondingAuthor":false,"prefix":"","firstName":"Beatriz","middleName":"","lastName":"Suay-Garcia","suffix":""},{"id":169842204,"identity":"1258c259-285a-42a5-aac5-17c5073d7bf9","order_by":7,"name":"Joan Climent","email":"","orcid":"","institution":"CEU Cardinal Herrera University","correspondingAuthor":false,"prefix":"","firstName":"Joan","middleName":"","lastName":"Climent","suffix":""},{"id":169842205,"identity":"a60d0379-764d-4c60-b826-cf39fcbd7631","order_by":8,"name":"Antonio Falco","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYDAC5gOMBxgYbBgYJIjWwpbAANSSRrqWwyRo4W9jfnDgR8X5xP7ZzQ8f8zDY2BPUInGMzeBgz5nbiTPuHDM25mFIS2wgqOd+g8FhxrbbiRskctikeRgOJxDUIX+M/QNQyzmQFvbfPAz/CTvM4BgPyJYDYFuYeRgOMBJ0mOExngKgX5KNZ9xIM5acY5BM2C9yx9g3PvhRYSfbPyP54Yc3FXaEHYbuTlI1jIJRMApGwSjACgAaBT1GsFXwVgAAAABJRU5ErkJggg==","orcid":"","institution":"CEU Cardinal Herrera University","correspondingAuthor":true,"prefix":"","firstName":"Antonio","middleName":"","lastName":"Falco","suffix":""},{"id":169842206,"identity":"180324c2-a88a-4696-90c5-82477be65cde","order_by":9,"name":"Maria Pastor-Valero","email":"","orcid":"","institution":"Miguel Hernandez University","correspondingAuthor":false,"prefix":"","firstName":"Maria","middleName":"","lastName":"Pastor-Valero","suffix":""}],"badges":[],"createdAt":"2023-01-21 12:59:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2502360/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2502360/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":41482868,"identity":"d94a1855-e49c-4afc-9dd4-25b592e875e9","added_by":"auto","created_at":"2023-08-13 03:22:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":426625,"visible":true,"origin":"","legend":"","description":"","filename":"Archivocomprimido.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2502360/v1_covered_fb50faaf-0e35-4f7c-8796-f5461b050739.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A novel approach to learning through categorical variables applicable to the classification of solitary pulmonary nodule malignancy","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Classification methods, Non-classical probabilities, Solitary Pulmonary Nodule","lastPublishedDoi":"10.21203/rs.3.rs-2502360/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2502360/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e One of the main drawbacks in constructing a classification model is that some or all of the covariates are categorical variables. Classical methods either assign labels to each output of a categorical variable or are summarised measures (frequencies and percentages), which can be interpreted as probabilities.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods \u003c/strong\u003eWe adopted a novel mathematical procedure to construct a classification model from categorical variables based on a non-classical probability approach. More specifically, we codified the variables following the categorical data representation from the Discriminant Correspondence Analysis before constructing a non-classical probability matrix system that represents an entangled system of dependent-independent variables. We then developed a disentangled procedure to obtain an empirical density function for each representative class (minimum of two classes). Finally, we constructed our classification model using the density functions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e We applied the proposed procedure to build a classification model of the malignancy of Solitary Pulmonary Nodule (SPN) after five years of follow up using routine clinical data. First, with 2/3 (270) of the sample of 404 patients with SPN, we constructed the classification model, and then validated it with the remaining 1/3 (134) we validated it. We tested the procedure’s stability by repeating the analysis randomly 1000 times. We obtained a model accuracy of 0.74, an F1 score of 0.58, a Cohen’s Kappa value of 0.41 and a Matthews Correlation Coefficient of 0.45. Finally, the area under the ROC curve was 0.86.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusion \u003c/strong\u003eThe proposed procedure provides a machine learning classification model with an acceptable performance of a classification model of solitary pulmonary nodule malignancy constructed from routine clinical data and mainly composed of categorical variables. It provides an acceptable performance, which could be used by clinicians as a tool to classify SPN malignancy in routine clinical practice.\u003c/p\u003e","manuscriptTitle":"A novel approach to learning through categorical variables applicable to the classification of solitary pulmonary nodule malignancy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-01-24 15:03:50","doi":"10.21203/rs.3.rs-2502360/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0df992bd-2ba2-43db-b541-2150b6a9c9d8","owner":[],"postedDate":"January 24th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-08-13T03:14:17+00:00","versionOfRecord":[],"versionCreatedAt":"2023-01-24 15:03:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2502360","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2502360","identity":"rs-2502360","version":["v1"]},"buildId":"J0_U0BvcaRcwD8yVFaRlm","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}