Estimating a change-point of baseline age in the longitudinal trajectories of biomarkers: application to an imaging study of preclinical Alzheimer disease

Estimating a change-point of baseline age in the longitudinal trajectories of biomarkers: application to an imaging study of preclinical Alzheimer disease | 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 Estimating a change-point of baseline age in the longitudinal trajectories of biomarkers: application to an imaging study of preclinical Alzheimer disease Chengjie Xiong, Folasade Agboola, Jingqin Luo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6681661/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Feb, 2026 Read the published version in BMC Medical Research Methodology → Version 1 posted 12 You are reading this latest preprint version Abstract Background Biomarkers are routinely measured from human biospecimens and imaging scans in Alzheimer disease (AD) research. Age is a well-known risk factor for AD. Detecting the age at which the longitudinal change in biomarkers starts to accelerate, i.e., a change-point in age, is important to design preventive interventions. Methods We analyzed longitudinal biomarker data by a random intercept and random slope model where the slope (longitudinal rate of change) was modeled as a piecewise linear and continuous function of baseline age. We proposed to estimate the intersection of the two linear functions, i.e., the change-point in age by multiple methods: maximum (profile) likelihood, minimum squared pseudo bias, minimum variance, minimum mean square error (MSE), and a two-stage method. We simulated large numbers of data sets to evaluate the performance of these estimators and implemented them to analyze the longitudinal white matter hypointensity from brain magnetic resonance imaging scans in an AD cohort study of 616 participants to estimate the age when the longitudinal rate of change starts to accelerate. Results Our simulations indicated that performance was universally poor for all point estimators and CI estimates when the true change-point was near the boundary or when sample size was small (N = 100). Yet, the proposed change-point estimators became approximately unbiased and showed relatively small MSE when sample size increased (N > 200) and the true change-point was away from boundary. The 95% CIs from these methods also provided good nominal coverage with large sample sizes if the change-point was away from boundary. When applied to the AD biomarker study, we found that almost all methods yielded similar estimates to the change-point from 59.19 years to 65.78 years, but the profile likelihood approach led to a much later estimate. Conclusions Our proposed estimators for the change-point performed reasonably well, especially when it is away from the boundary and the sample sizes are large. Our methods revealed a largely consistent age when the longitudinal change in white matter hypointensity started to accelerate. Further research is needed to tackle more complex challenges, i.e., multiple change-points that may depend on other AD risk factors. Trial registration: N/A Alzheimer disease biomarker change-point point and confidence interval estimators Full Text Additional Declarations Competing interest reported. Work citing NIH grant AG067505 requires an institutional disclosure. Washington University School of Medicine in St. Louis has a financial interest in C2N Diagnostics and may financially benefit if the company is successful in marketing its product(s) that are related to this research. Supplementary Files StatisticalInferenceonLongitudinalChangePointSupplementalFigures5152025.docx Cite Share Download PDF Status: Published Journal Publication published 24 Feb, 2026 Read the published version in BMC Medical Research Methodology → Version 1 posted Editorial decision: Revision requested 10 Jul, 2025 Reviews received at journal 30 Jun, 2025 Reviews received at journal 28 Jun, 2025 Reviewers agreed at journal 22 Jun, 2025 Reviews received at journal 22 Jun, 2025 Reviewers agreed at journal 19 Jun, 2025 Reviewers agreed at journal 10 Jun, 2025 Reviewers invited by journal 10 Jun, 2025 Editor assigned by journal 09 Jun, 2025 Editor invited by journal 21 May, 2025 Submission checks completed at journal 21 May, 2025 First submitted to journal 21 May, 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-6681661","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":469721960,"identity":"d1581ad5-62a6-4856-b860-edc2aa6f6316","order_by":0,"name":"Chengjie Xiong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYDACCRDBI8HAD+YVAPEBYrVINoBUGxCtBQgMDhCrhX9287GHX2Qs5Ixv5Bh//mDAIMd3I4GAJXeOpRvL8EgYm93IMZMA2mIsSUiLgUSOmbQEj0Titts5ZiCHJW4grCX/G0hL/ebZOcYfgFrqidCSwyb5gUciwUA6xwDksAQDgn65kWYmDQxkwxn3n5VJnDGQMJx55gF+Lfwzkp9J/uypk+fvObz5Q0WFjTzfcQK2gAAzbw/CVsLKQYDxxw/iFI6CUTAKRsEIBQBsIEGcCeoygwAAAABJRU5ErkJggg==","orcid":"","institution":"Washington University School of Medicine","correspondingAuthor":true,"prefix":"","firstName":"Chengjie","middleName":"","lastName":"Xiong","suffix":""},{"id":469721962,"identity":"0bf12e37-45c9-44f2-92ff-102a0ad53ea9","order_by":1,"name":"Folasade Agboola","email":"","orcid":"","institution":"Washington University School of Medicine","correspondingAuthor":false,"prefix":"","firstName":"Folasade","middleName":"","lastName":"Agboola","suffix":""},{"id":469721963,"identity":"d3bdae14-d2d8-442a-b16e-9aa7e673ca19","order_by":2,"name":"Jingqin Luo","email":"","orcid":"","institution":"Washington University School of Medicine","correspondingAuthor":false,"prefix":"","firstName":"Jingqin","middleName":"","lastName":"Luo","suffix":""}],"badges":[],"createdAt":"2025-05-16 14:38:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6681661/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6681661/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12874-026-02806-3","type":"published","date":"2026-02-24T15:58:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":103765751,"identity":"eb0a8cb5-6d9f-423a-a964-184126b508f9","added_by":"auto","created_at":"2026-03-02 16:08:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1474498,"visible":true,"origin":"","legend":"","description":"","filename":"StatisticalInferenceonLongitudinalChangePoint5202025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6681661/v1_covered_f6e31e55-91e4-4db2-b7af-e8e5718e627f.pdf"},{"id":84450530,"identity":"23c4126e-a229-4c74-a972-9a0ea1df35eb","added_by":"auto","created_at":"2025-06-12 06:44:35","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":127850,"visible":true,"origin":"","legend":"","description":"","filename":"StatisticalInferenceonLongitudinalChangePointSupplementalFigures5152025.docx","url":"https://assets-eu.researchsquare.com/files/rs-6681661/v1/2cfdf59ed5cfc86965d85256.docx"}],"financialInterests":"Competing interest reported. Work citing NIH grant AG067505 requires an institutional disclosure. Washington University School of Medicine in St. Louis has a financial interest in C2N Diagnostics and may financially benefit if the company is successful in marketing its product(s) that are related to this research.","formattedTitle":"Estimating a change-point of baseline age in the longitudinal trajectories of biomarkers: application to an imaging study of preclinical Alzheimer disease","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":"bmc-medical-research-methodology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmrm","sideBox":"Learn more about [BMC Medical Research Methodology](http://bmcmedresmethodol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmrm/default.aspx","title":"BMC Medical Research Methodology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Alzheimer disease, biomarker, change-point, point and confidence interval estimators","lastPublishedDoi":"10.21203/rs.3.rs-6681661/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6681661/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eBiomarkers are routinely measured from human biospecimens and imaging scans in Alzheimer disease (AD) research. Age is a well-known risk factor for AD. Detecting the age at which the longitudinal change in biomarkers starts to accelerate, i.e., a change-point in age, is important to design preventive interventions.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eWe analyzed longitudinal biomarker data by a random intercept and random slope model where the slope (longitudinal rate of change) was modeled as a piecewise linear and continuous function of baseline age. We proposed to estimate the intersection of the two linear functions, i.e., the change-point in age by multiple methods: maximum (profile) likelihood, minimum squared pseudo bias, minimum variance, minimum mean square error (MSE), and a two-stage method. We simulated large numbers of data sets to evaluate the performance of these estimators and implemented them to analyze the longitudinal white matter hypointensity from brain magnetic resonance imaging scans in an AD cohort study of 616 participants to estimate the age when the longitudinal rate of change starts to accelerate.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eOur simulations indicated that performance was universally poor for all point estimators and CI estimates when the true change-point was near the boundary or when sample size was small (N\u0026thinsp;=\u0026thinsp;100). Yet, the proposed change-point estimators became approximately unbiased and showed relatively small MSE when sample size increased (N\u0026thinsp;\u0026gt;\u0026thinsp;200) and the true change-point was away from boundary. The 95% CIs from these methods also provided good nominal coverage with large sample sizes if the change-point was away from boundary. When applied to the AD biomarker study, we found that almost all methods yielded similar estimates to the change-point from 59.19 years to 65.78 years, but the profile likelihood approach led to a much later estimate.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eOur proposed estimators for the change-point performed reasonably well, especially when it is away from the boundary and the sample sizes are large. Our methods revealed a largely consistent age when the longitudinal change in white matter hypointensity started to accelerate. Further research is needed to tackle more complex challenges, i.e., multiple change-points that may depend on other AD risk factors.\u003c/p\u003e\u003ch2\u003eTrial registration:\u003c/h2\u003e \u003cp\u003eN/A\u003c/p\u003e","manuscriptTitle":"Estimating a change-point of baseline age in the longitudinal trajectories of biomarkers: application to an imaging study of preclinical Alzheimer disease","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-12 06:44:31","doi":"10.21203/rs.3.rs-6681661/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-10T17:42:51+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-30T18:15:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-29T00:06:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"310205027860641990194041863164581152530","date":"2025-06-22T15:55:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-22T05:47:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"225741967587236633079736571032156175045","date":"2025-06-19T14:17:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"89061034492239107724384683414031016671","date":"2025-06-11T00:26:59+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-10T16:49:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-09T17:36:58+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-05-21T20:01:11+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-21T16:14:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Research Methodology","date":"2025-05-21T16:13:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-research-methodology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmrm","sideBox":"Learn more about [BMC Medical Research Methodology](http://bmcmedresmethodol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmrm/default.aspx","title":"BMC Medical Research Methodology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"75f683d1-8402-4ef7-8720-26e1f6a42fdf","owner":[],"postedDate":"June 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-02T16:05:46+00:00","versionOfRecord":{"articleIdentity":"rs-6681661","link":"https://doi.org/10.1186/s12874-026-02806-3","journal":{"identity":"bmc-medical-research-methodology","isVorOnly":false,"title":"BMC Medical Research Methodology"},"publishedOn":"2026-02-24 15:58:22","publishedOnDateReadable":"February 24th, 2026"},"versionCreatedAt":"2025-06-12 06:44:31","video":"","vorDoi":"10.1186/s12874-026-02806-3","vorDoiUrl":"https://doi.org/10.1186/s12874-026-02806-3","workflowStages":[]},"version":"v1","identity":"rs-6681661","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6681661","identity":"rs-6681661","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}