Survey-Weighted Bayesian Logistic Regression for Measurement Error in Cross-Sectional Data Health Surveys

Survey-Weighted Bayesian Logistic Regression for Measurement Error in Cross-Sectional Data Health Surveys | 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 Short Report Survey-Weighted Bayesian Logistic Regression for Measurement Error in Cross-Sectional Data Health Surveys Romuald Daniel BOY-NGBOGBELE, Nisreen Osman E. Ahmed Osman E. Ahmed, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9361219/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: Low- and middle-income nations employ cross-sectional health surveys like the Demographic and Health Surveys (DHS) to estimate population health indicators. These estimates may be invalidated by measurement error in explanatory factors and complicated survey design with uneven sample probability. Traditional logistic regression models neglect these difficulties, resulting in skewed parameter estimates and poor inference. Aims: This study aims to develop and evaluate a survey-weighted Bayesian logistic regression framework that simultaneously accounts for measurement error and complex survey design in cross-sectional health survey data. Methods: A Bayesian hierarchical model with pseudo-posterior likelihood combines sampling weights and interprets observed covariates as noisy measurements of latent true variables. Markov Chain Monte Carlo (MCMC) techniques are used for posterior inference over regression coefficient and measurement error variance prior distributions. A simulation study compares the proposed model to a standard unweighted model utilizing parameter estimation metrics and predictive performance indicators. Results: The simulation results show that the survey-weighted Bayesian model produces lower bias, reduced root mean square error, and coverage probabilities closer to the nominal level. In addition, the corrected model demonstrates improved predictive performance, with higher accuracy (0.836 vs.\ 0.724), precision (0.933 vs.\ 0.857), recall (0.948 vs.\ 0.696), F1-score (0.900 vs.\ 0.796), and AUC (0.844 vs.\ 0.745) compared to the unweighted model. Conclusion: Incorporating survey weights and correcting for measurement error within a Bayesian framework improves both parameter estimation and predictive performance. The proposed model provides a robust methodological approach for analyzing complex cross-sectional health survey data and supports more reliable population-level inference. Bayesian inference Measurement error models Survey-weighted regression Demographic and Health Surveys Health survey analysis Cross-sectional data 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. 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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-9361219","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Short Report","associatedPublications":[],"authors":[{"id":620892984,"identity":"c1d23f0d-a360-4232-939a-c532c589659b","order_by":0,"name":"Romuald Daniel BOY-NGBOGBELE","email":"data:image/png;base64,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","orcid":"","institution":"Pan African University","correspondingAuthor":true,"prefix":"","firstName":"Romuald","middleName":"Daniel","lastName":"BOY-NGBOGBELE","suffix":""},{"id":620892985,"identity":"2ef99b75-ed14-4898-be03-8cdf2f89553c","order_by":1,"name":"Nisreen Osman E. 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These estimates may be invalidated by measurement error in explanatory factors and complicated survey design with uneven sample probability. Traditional logistic regression models neglect these difficulties, resulting in skewed parameter estimates and poor inference. Aims: This study aims to develop and evaluate a survey-weighted Bayesian logistic regression framework that simultaneously accounts for measurement error and complex survey design in cross-sectional health survey data.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMethods: A Bayesian hierarchical model with pseudo-posterior likelihood combines sampling weights and interprets observed covariates as noisy measurements of latent true variables. Markov Chain Monte Carlo (MCMC) techniques are used for posterior inference over regression coefficient and measurement error variance prior distributions. A simulation study compares the proposed model to a standard unweighted model utilizing parameter estimation metrics and predictive performance indicators.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eResults: The simulation results show that the survey-weighted Bayesian model produces lower bias, reduced root mean square error, and coverage probabilities closer to the nominal level. In addition, the corrected model demonstrates improved predictive performance, with higher accuracy (0.836 vs.\\ 0.724), precision (0.933 vs.\\ 0.857), recall (0.948 vs.\\ 0.696), F1-score (0.900 vs.\\ 0.796), and AUC (0.844 vs.\\ 0.745) compared to the unweighted model.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eConclusion: Incorporating survey weights and correcting for measurement error within a Bayesian framework improves both parameter estimation and predictive performance. The proposed model provides a robust methodological approach for analyzing complex cross-sectional health survey data and supports more reliable population-level inference.\u003c/p\u003e","manuscriptTitle":"Survey-Weighted Bayesian Logistic Regression for Measurement Error in Cross-Sectional Data Health Surveys","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-15 03:43:26","doi":"10.21203/rs.3.rs-9361219/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":"1ba22c7d-f76f-43bf-b1d6-b2cd09aaac8d","owner":[],"postedDate":"April 15th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-11T09:28:41+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-15 03:43:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9361219","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9361219","identity":"rs-9361219","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}