NOTEARS-M: Causal Bayesian Network Structure Learning of Mixed Type Data and Its Application in Identifying Disease Risk Factors

NOTEARS-M: Causal Bayesian Network Structure Learning of Mixed Type Data and Its Application in Identifying Disease Risk Factors | 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 Research Article NOTEARS-M: Causal Bayesian Network Structure Learning of Mixed Type Data and Its Application in Identifying Disease Risk Factors Yuanyuan Zhao, Jinzhu Jia This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5644505/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Jun, 2025 Read the published version in BMC Medical Research Methodology → Version 1 posted 11 You are reading this latest preprint version Abstract Background Identifying and understanding disease risk factors is crucial in epidemiology, particularly for chronic and noncommunicable diseases that often have complex interrelationships. Traditional statistical methods struggle to capture these complexities, necessitating more sophisticated analytical frameworks. Bayesian networks and directed acyclic graphs (DAGs) provide powerful tools for exploring the complex relationships between variables. However, existing DAG structure learning algorithms still have limitations in handling mixed-type data (including continuous and discrete variables), which restricts their practical utility. Therefore, developing DAG structure learning methods that can effectively handle mixed data is highly important for obtaining an in-depth understanding of disease risk factors and pathogenic mechanisms. Methods This study proposes an extension of the NOTEARS algorithm, termed NOTEARS-M, which is designed for Bayesian network structure learning with mixed-type data. The algorithm integrates continuous and categorical variables through a tailored loss function, enhancing its applicability to real-world epidemiological datasets. Results Extensive simulations were conducted across eight distinct scenarios, specifically, variations in the number of nodes, changes in the proportion of categorical nodes, different sample sizes, levels of categorical nodes, variations in edge sparsity, adjustments to the weight scale, different graph types, and diverse noise distributions. These scenarios demonstrate that NOTEARS-M consistently outperforms existing methods such as MMHC, mDAG, and DAGBagM across key metrics, including precision, recall, F1 score, and structural Hamming distance (SHD). Furthermore, the robustness of NOTEARS-M is validated through its application to the National Health and Nutrition Examination Survey (NHANES) dataset, revealing critical causal relationships among risk factors for CHD and diabetes. Conclusions NOTEARS-M provides a powerful and scalable tool for uncovering causal relationships in complex disease networks, with significant implications for risk factor identification and public health research. Bayesian networks (BNs) Directed cyclic graphs (DAGs) Causal inference Risk factor Full Text Additional Declarations No competing interests reported. Supplementary Files AdditionalFile1.docx Additional file 1: Supplementary figures. AdditionalFile2.docx Additional file 2: Supplementary results. Cite Share Download PDF Status: Published Journal Publication published 06 Jun, 2025 Read the published version in BMC Medical Research Methodology → Version 1 posted Editorial decision: Revision requested 05 Feb, 2025 Reviews received at journal 20 Jan, 2025 Reviews received at journal 12 Jan, 2025 Reviewers agreed at journal 09 Jan, 2025 Reviewers agreed at journal 08 Jan, 2025 Reviewers agreed at journal 06 Jan, 2025 Reviewers invited by journal 27 Dec, 2024 Editor invited by journal 19 Dec, 2024 Editor assigned by journal 18 Dec, 2024 Submission checks completed at journal 18 Dec, 2024 First submitted to journal 14 Dec, 2024 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. 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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-5644505","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":392517543,"identity":"3d5598f9-343d-4751-a51e-571484906833","order_by":0,"name":"Yuanyuan Zhao","email":"","orcid":"","institution":"Peking University","correspondingAuthor":false,"prefix":"","firstName":"Yuanyuan","middleName":"","lastName":"Zhao","suffix":""},{"id":392517547,"identity":"cf70525c-7091-4e00-bf89-b4310a0ad6e7","order_by":1,"name":"Jinzhu 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