HiDiNet: High-Dimensional Interpretive Network forModeling Aging Health and Survival

HiDiNet: High-Dimensional Interpretive Network forModeling Aging Health and Survival | 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 Article HiDiNet: High-Dimensional Interpretive Network forModeling Aging Health and Survival Hannah Guan, Aashish Dhanani, Yu Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8310550/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 14 You are reading this latest preprint version Abstract Aging is a high-dimensional and stochastic process through various pathways in which healthy functioning can change withtime. While many studies focused on prediction of aging cross-sectionally, few methodologies have been developed to modellongitudinal aging process. Modeling longitudinal data with a Stochastic Differential Equation (SDE) is an emerging area ofaging research. There are frameworks that have been proposed, but have only implemented for few health variables or limitedto binary values. We propose HiDiNet (High-Dimensional Interpretive Network), a framework for predicting individual healthtrajectories and survival over continuous time. Unlike traditional sequential models that operate on fixed, discrete timesteps,HiDiNet uses stochastic differential equations (SDEs) to represent health evolution and integrates Multi-Visit Attention tocapture long-range temporal dependencies among irregular clinical visits. A three-dimensional interaction network supportsinterpretability by visualizing cross-variable effects and pairwise correlations. Evaluated on the English Longitudinal Study ofAging (ELSA; 10 waves, 1998–2019), HiDiNet outperforms Recurrent Neural Network (RNN) and Elastic-Net models (Brierscore 0.33 vs 0.42 vs 0.70; C-index 0.968 vs 0.951 vs 0.700) and achieves more reliable calibration than a Transformer-onlymodel (D-calibration p = 0.932 vs 0.280), while maintaining comparable discrimination (C-index 0.968 vs 0.978). We alsocompare HiDiNet to latent space models with varying dimensions to demonstrate that HiDiNet is comparable to other high-dimensional models in prediction. Finally, we demonstrate HiDiNet’s interpretability through a visualized pairwise correlationnetwork of the various health variables. HiDiNet is the first three-dimensional interaction network to uncover high dimensionalinteractions among health variables during the aging process while capturing its stochasticity in longitudinal data. It canbe applied to a wide range of high-dimensional health data and ultimately improve our understanding of aging process and transform health policy approaches for aging populations. Biological sciences/Computational biology and bioinformatics Health sciences/Health care Physical sciences/Mathematics and computing Stochastic Differential Equation Transformer Aging Interpretability Survival Analysis Longitudinal Modeling Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 10 May, 2026 Reviews received at journal 05 May, 2026 Reviews received at journal 04 May, 2026 Reviewers agreed at journal 26 Apr, 2026 Reviewers agreed at journal 24 Apr, 2026 Reviewers agreed at journal 22 Apr, 2026 Reviewers agreed at journal 22 Apr, 2026 Reviews received at journal 09 Feb, 2026 Reviewers agreed at journal 18 Jan, 2026 Reviewers invited by journal 15 Jan, 2026 Editor assigned by journal 15 Jan, 2026 Editor invited by journal 11 Dec, 2025 Submission checks completed at journal 10 Dec, 2025 First submitted to journal 10 Dec, 2025 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-8310550","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":576232681,"identity":"01670e2e-8866-40db-baa1-5774babbf711","order_by":0,"name":"Hannah Guan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDklEQVRIiWNgGAWjYBACAzBZwcDAxw5mHYAI8zAwMDbg1XKGgYGNmSQtjG2kaDHnX2P4uXCenRwbM/PhFx8Y7sibz0h+9uENg43shgPYtVjOeGMsPXNbsjEbM1ua5QyGZ4ZzbqQZz5zDkGaMS4vBjTMG0rzbDiS2MfOYGfMwHGacwXPAmBnISMSjxfg37xyQFv5vxn8YDtvP4Dn+GajlP24t53vMpHkbwLYwP2YAGj6DvQdkywE8trCVWfMcA/vFjLHH4HAyUEsx4xyDZOOZOG05vPk2T42dHD978+MPPyoO285gZt/M8KbCTrYPhxYGiQQ4k00CGrMMDAgGFsCPMIv5Ax51o2AUjIJRMIIBALV9Wq/i67XZAAAAAElFTkSuQmCC","orcid":"","institution":"Harvard University","correspondingAuthor":true,"prefix":"","firstName":"Hannah","middleName":"","lastName":"Guan","suffix":""},{"id":576232682,"identity":"eed9f105-cfd8-4eae-9707-78897bd87e3c","order_by":1,"name":"Aashish Dhanani","email":"","orcid":"","institution":"Trinity University","correspondingAuthor":false,"prefix":"","firstName":"Aashish","middleName":"","lastName":"Dhanani","suffix":""},{"id":576232683,"identity":"0bf67460-37c3-4895-b29d-2720de2732d9","order_by":2,"name":"Yu Zhang","email":"","orcid":"","institution":"Trinity University","correspondingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2025-12-08 18:53:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8310550/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8310550/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100715869,"identity":"2871e226-0cbe-4555-a3a8-1fd9ba1ee5bb","added_by":"auto","created_at":"2026-01-20 18:50:08","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5842,"visible":true,"origin":"","legend":"","description":"","filename":"6ccbd82fe2de46a58a1b9e8a6895c808.json","url":"https://assets-eu.researchsquare.com/files/rs-8310550/v1/fc4cf3e0e423da05dd0dd26b.json"},{"id":100725571,"identity":"d66a819a-0d1e-42c1-be52-71e580817d44","added_by":"auto","created_at":"2026-01-20 20:14:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4177500,"visible":true,"origin":"","legend":"","description":"","filename":"HiDiNetPaperGuanDhananiZhang.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8310550/v1_covered_dcbd7a80-6673-4ba2-ae2e-854777924fe7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"HiDiNet: High-Dimensional Interpretive Network forModeling Aging Health and Survival","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Stochastic Differential Equation, Transformer, Aging, Interpretability, Survival Analysis, Longitudinal Modeling","lastPublishedDoi":"10.21203/rs.3.rs-8310550/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8310550/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Aging is a high-dimensional and stochastic process through various pathways in which healthy functioning can change withtime. While many studies focused on prediction of aging cross-sectionally, few methodologies have been developed to modellongitudinal aging process. Modeling longitudinal data with a Stochastic Differential Equation (SDE) is an emerging area ofaging research. There are frameworks that have been proposed, but have only implemented for few health variables or limitedto binary values. We propose HiDiNet (High-Dimensional Interpretive Network), a framework for predicting individual healthtrajectories and survival over continuous time. Unlike traditional sequential models that operate on fixed, discrete timesteps,HiDiNet uses stochastic differential equations (SDEs) to represent health evolution and integrates Multi-Visit Attention tocapture long-range temporal dependencies among irregular clinical visits. A three-dimensional interaction network supportsinterpretability by visualizing cross-variable effects and pairwise correlations. Evaluated on the English Longitudinal Study ofAging (ELSA; 10 waves, 1998–2019), HiDiNet outperforms Recurrent Neural Network (RNN) and Elastic-Net models (Brierscore 0.33 vs 0.42 vs 0.70; C-index 0.968 vs 0.951 vs 0.700) and achieves more reliable calibration than a Transformer-onlymodel (D-calibration p = 0.932 vs 0.280), while maintaining comparable discrimination (C-index 0.968 vs 0.978). We alsocompare HiDiNet to latent space models with varying dimensions to demonstrate that HiDiNet is comparable to other high-dimensional models in prediction. Finally, we demonstrate HiDiNet’s interpretability through a visualized pairwise correlationnetwork of the various health variables. HiDiNet is the first three-dimensional interaction network to uncover high dimensionalinteractions among health variables during the aging process while capturing its stochasticity in longitudinal data. It canbe applied to a wide range of high-dimensional health data and ultimately improve our understanding of aging process and transform health policy approaches for aging populations.","manuscriptTitle":"HiDiNet: High-Dimensional Interpretive Network forModeling Aging Health and Survival","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-20 15:36:46","doi":"10.21203/rs.3.rs-8310550/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-11T03:53:02+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-06T02:32:07+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-05T03:32:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"181165126147433983813589435347564859064","date":"2026-04-26T08:10:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"338926139102914646626521457772595525786","date":"2026-04-24T17:06:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"20081601841654756249069539966576739122","date":"2026-04-22T16:57:35+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"44845060855928850752984914697709757345","date":"2026-04-22T15:34:53+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-09T07:34:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"55449046440187235520753118287296019298","date":"2026-01-18T07:49:06+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-16T01:23:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-16T01:21:38+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-12T04:29:15+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-10T15:15:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-12-10T15:12:52+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ce3feae1-5385-4ad2-93ef-22aa3b17e064","owner":[],"postedDate":"January 20th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-11T03:53:02+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-06T02:32:07+00:00","index":137,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-05T03:32:44+00:00","index":136,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":61311703,"name":"Biological sciences/Computational biology and bioinformatics"},{"id":61311704,"name":"Health sciences/Health care"},{"id":61311705,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-11T04:08:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-20 15:36:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8310550","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8310550","identity":"rs-8310550","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}