Debiased machine learning  for logistic  partially linear mediation models with high-dimensional confounders

Debiased machine learning for logistic partially linear mediation models with high-dimensional confounders | 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 Debiased machine learning for logistic partially linear mediation models with high-dimensional confounders Lei Wang, Yining Wu, Jichen Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7449255/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Jan, 2026 Read the published version in Statistics and Computing → Version 1 posted 10 You are reading this latest preprint version Abstract In this paper, we propose debiased machine learning strategies for estimating direct effect, indirect effect and total effect in logistic partially linear mediation models with high-dimensional confounders. To obtain asymptotically efficient estimators for the effects of interest,two Neyman-orthogonal score functions are proposed to remove regularization biascaused by the estimation of the nuisance functions.To address nonlinearity and unextractability of the logit link, double data splitting is applied to estimate nuisance functions and mitigate potential overfitting. Theoretically, we establish rigorous asymptotic properties for the proposed estimators of all three effects and derive their asymptotic normal distributions. The satisfactoryperformance of our proposed estimators is demonstrated by simulation results and a real-world PM2.5 concentration data from Beijing. Double data splitting Logistic partially linear models Machine learning Neymanorthogonal score function Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 27 Jan, 2026 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 08 Oct, 2025 Reviews received at journal 07 Oct, 2025 Reviews received at journal 25 Sep, 2025 Reviewers agreed at journal 12 Sep, 2025 Reviewers agreed at journal 03 Sep, 2025 Reviewers agreed at journal 27 Aug, 2025 Reviewers invited by journal 26 Aug, 2025 Editor assigned by journal 25 Aug, 2025 Submission checks completed at journal 25 Aug, 2025 First submitted to journal 24 Aug, 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. 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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-7449255","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":508231774,"identity":"94c8e852-a5ca-4d7c-ac99-19ce061c0c7b","order_by":0,"name":"Lei Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/klEQVRIiWNgGAWjYBACPjiLvQFIHGDgAZIGeLWwQSgDBh6eAyRrkUgAa2EgrEUi+dnDL3/+yNtLvj34ueCMnQwDe/M2CYaaO3i0pJkby7YZGPZI5yVLz7iRzMPAc6xMguHYM9xapBPMpCUbDBh7pHMMpHk+MPMwSOSYSTA2HMajJf2btMQfA/seyTPGv3k+1PMwyL8hpCXHTPIDm0FijwSPmTTPjcNAW3gIaJF/UybN2Gac3HMmx8ya58xxHjaetGKLhGO4tfDzHN8m+eOPnG17+xnj2zzHqu352Q9vvPGhBrcWEGDmQbEXRCTg1cDAwPiDgIJRMApGwSgY4QAAuh9JLYUTRRUAAAAASUVORK5CYII=","orcid":"","institution":"Nankai University","correspondingAuthor":true,"prefix":"","firstName":"Lei","middleName":"","lastName":"Wang","suffix":""},{"id":508231775,"identity":"ed679bc4-52ba-4630-9a4f-1b2f28fe2d3f","order_by":1,"name":"Yining Wu","email":"","orcid":"","institution":"Nankai University","correspondingAuthor":false,"prefix":"","firstName":"Yining","middleName":"","lastName":"Wu","suffix":""},{"id":508231776,"identity":"1530d17c-f333-49ba-bd95-17ff8d4db779","order_by":2,"name":"Jichen Yang","email":"","orcid":"","institution":"Nankai University","correspondingAuthor":false,"prefix":"","firstName":"Jichen","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2025-08-25 03:23:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7449255/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7449255/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11222-026-10822-y","type":"published","date":"2026-01-27T15:58:46+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":101690498,"identity":"095673ef-41af-44aa-9af4-0ae75d53f296","added_by":"auto","created_at":"2026-02-02 16:04:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":834448,"visible":true,"origin":"","legend":"","description":"","filename":"SCLPLMMs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7449255/v1_covered_44729c89-f0b6-46db-bcc9-8fce5cd2922f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Debiased machine learning for logistic partially linear mediation models with high-dimensional confounders","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Double data splitting, Logistic partially linear models, Machine learning, Neymanorthogonal score function","lastPublishedDoi":"10.21203/rs.3.rs-7449255/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7449255/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" In this paper, we propose debiased machine learning strategies for estimating direct effect, indirect effect and total effect in logistic partially linear mediation models with high-dimensional confounders. 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