{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T19:33:31Z","timestamp":1791660811851,"version":"4.3.4"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,1,7]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n               <jats:p>SARS-CoV-2\u2013infected individuals have reported a diverse collection of persistent and often debilitating symptoms commonly referred to as long COVID or post-acute sequelae of SARS-CoV-2 (PASC). Identifying PASC and its subphenotypes is challenging because available data are \u201cnegative-unlabeled\u201d as uninfected individuals must be PASC negative, but those with prior infection have unknown PASC status. Moreover, feature selection among many potentially informative characteristics can facilitate reaching a concise and easily interpretable PASC definition. Therefore, to characterize PASC and the spectrum of PASC subphenotypes while identifying a minimal set of features, we propose a Bernoulli mixture model with novel parameterization to accommodate negative-unlabeled data and Bayesian priors to induce sparsity. We present an efficient expectation-maximization algorithm for estimation, and a grid search procedure to select the number of clusters and level of sparsity. We evaluate the proposed method with a simulation study and an analysis of data on self-reported symptoms from the ongoing Researching COVID to Enhance Recovery-Adult Cohort study.<\/jats:p>","DOI":"10.1093\/biomtc\/ujaf021","type":"journal-article","created":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T14:36:26Z","timestamp":1741790186000},"source":"Crossref","is-referenced-by-count":2,"title":["Sparse Bernoulli mixture modeling with negative-unlabeled data: an approach to identify and characterize long COVID"],"prefix":"10.1093","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4210-7127","authenticated-orcid":false,"given":"Tingyi","family":"Cao","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA 02115 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Harrison T","family":"Reeder","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Massachusetts General Hospital , Somerville, MA 02145 ,","place":["United States"]},{"name":"Department of Medicine, Harvard Medical School , Boston, MA 02115 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea S","family":"Foulkes","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA 02115 ,","place":["United States"]},{"name":"Department of Biostatistics, Massachusetts General Hospital , Somerville, MA 02145 ,","place":["United States"]},{"name":"Department of Medicine, Harvard Medical School , Boston, MA 02115 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,3,12]]},"reference":[{"key":"2025031214361605300_bib1","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/TCBB.2015.2478454","article-title":"Supervised, unsupervised, and semi-supervised feature selection: a review on gene selection","volume":"13","author":"Ang","year":"2016","journal-title":"IEEE\/ACM Transactions on Computational Biology and Bioinformatics"},{"key":"2025031214361605300_bib2","first-page":"19","article-title":"Semi-supervised clustering by seeding","volume-title":"Proceedings of 19th International Conference on Machine Learning (ICML-2002)","author":"Basu","year":"2002"},{"key":"2025031214361605300_bib3","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1007\/978-0-387-30164-8_547","article-title":"Mixture Model","volume-title":"Encyclopedia of Machine Learning","author":"Baxter","year":"2011"},{"key":"2025031214361605300_bib4","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.csda.2009.07.013","article-title":"On multivariate binary data clustering and feature weighting","volume":"54","author":"Bouguila","year":"2010","journal-title":"Computational Statistics & Data Analysis"},{"key":"2025031214361605300_bib5","doi-asserted-by":"crossref","first-page":"851","DOI":"10.2466\/pr0.1966.18.3.851","article-title":"Hierarchical cluster analysis","volume":"18","author":"Bridges","year":"1966","journal-title":"Psychological Reports"},{"key":"2025031214361605300_bib6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s00357-001-0004-3","article-title":"K-modes clustering","volume":"18","author":"Chaturvedi","year":"2001","journal-title":"Journal of Classification"},{"key":"2025031214361605300_bib7","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1093\/infdis\/jiac136","article-title":"Global prevalence of post-acute sequelae of COVID-19 (PASC) or long COVID: a meta-analysis and systematic review","volume":"226","author":"Chen","year":"2022","journal-title":"The Journal of Infectious Diseases"},{"key":"2025031214361605300_bib8","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support-vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"Machine Learning"},{"key":"2025031214361605300_bib9","doi-asserted-by":"crossref","first-page":"101019","DOI":"10.1016\/j.eclinm.2021.101019","article-title":"Characterizing long COVID in an international cohort: 7 months of symptoms and their impact","volume":"38","author":"Davis","year":"2021","journal-title":"eClinicalMedicine"},{"key":"2025031214361605300_bib10","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1038\/s41579-022-00846-2","article-title":"Long COVID: major findings, mechanisms and recommendations","volume":"21","author":"Davis","year":"2023","journal-title":"Nature Reviews Microbiology"},{"key":"2025031214361605300_bib11","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S1473-3099(20)30120-1","article-title":"An interactive web-based dashboard to track COVID-19 in real time","volume":"20","author":"Dong","year":"2020","journal-title":"Lancet Infect Disease"},{"key":"2025031214361605300_bib12","article-title":"A detailed study of patients with long-haul COVID: an analysis of private healthcare claims","volume-title":"Technical Report","author":"FAIR\u00a0Health","year":"2021"},{"key":"2025031214361605300_bib13","first-page":"238","article-title":"Discriminatory analysis. 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