{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T12:07:36Z","timestamp":1782130056646,"version":"3.54.5"},"reference-count":24,"publisher":"Wiley","issue":"20-22","license":[{"start":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T00:00:00Z","timestamp":1758585600000},"content-version":"vor","delay-in-days":22,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Gaussian process (GP) regression is widely used for flexible and non\u2010parametric Bayesian modeling of data arising from underlying smooth functions. This paper introduces a solution to GP regression when the observations are subject to value\u2010based censoring. We derive exact and closed\u2010form expressions for the conditional posterior distributions of the underlying functions in both the single\u2010curve fitting case and in the case of a hierarchical model where multiple functions are modeled simultaneously. Our method can accommodate left, right, and interval censoring, and is directly applicable as an empirical Bayes method or integrated in a Markov\u2013Chain Monte Carlo sampler for full posterior inference. The method is validated through extensive simulations, where it substantially outperforms naive approaches that either exclude censored observations or treat them as fully observed values. We give an application to a real\u2010world dataset of longitudinal HIV\u20101 RNA measurements, where the observations are subject to left censoring due to a detection limit.<\/jats:p>","DOI":"10.1002\/sim.70277","type":"journal-article","created":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T11:47:32Z","timestamp":1758628052000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Gaussian Process Regression for Value\u2010Censored Functional and Longitudinal Data"],"prefix":"10.1002","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-0058-3804","authenticated-orcid":false,"given":"Adam","family":"Gorm Hoffmann","sequence":"first","affiliation":[{"name":"Section of Biostatistics, Department of Public Health University of Copenhagen  Copenhagen Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claus","family":"Thorn Ekstr\u00f8m","sequence":"additional","affiliation":[{"name":"Section of Biostatistics, Department of Public Health University of Copenhagen  Copenhagen Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin","family":"Zeymer Christoffersen","sequence":"additional","affiliation":[{"name":"Division of Robotics, Perception and Learning KTH Royal Institute of Technology  Stockholm Sweden"},{"name":"Department of Medical Epidemiology and Biostatistics Karolinska Institutet  Solna Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Kryger Jensen","sequence":"additional","affiliation":[{"name":"Section of Biostatistics, Department of Public Health University of Copenhagen  Copenhagen Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,9,23]]},"reference":[{"key":"e_1_2_9_2_1","volume-title":"Gaussian Processes for Machine Learning","author":"Williams C. 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R.Gabry J.\u010ce\u0161novar andA.Johnson \u201ccmdstanr: R Interface to \u2018CmdStan\u2019 \u201d(2023) https:\/\/mc\u2010stan.org\/cmdstanr\/ https:\/\/discourse.mc\u2010stan.org."},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.5550340403"},{"issue":"2","key":"e_1_2_9_17_1","first-page":"2","article-title":"TruncatedNormal: Truncated Multivariate Normal and Student Distributions","volume":"2","author":"Botev Z.","year":"2021","journal-title":"R Package Version"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1214\/10-BA505"},{"key":"e_1_2_9_19_1","doi-asserted-by":"crossref","unstructured":"A. G.Hoffmann C. T.Ekstr\u00f8m andA. K.Jensen \u201cComputationally Efficient Multi\u2010Level Gaussian Process Regression for Functional Data Observed Under Completely or Partially Regular Sampling Designs \u201d Manuscript Submitted for Publication(2024) arXiv Preprint arXiv:2406.13691 [Stat.ME].","DOI":"10.1007\/s11749-025-00996-4"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1097\/00126334-200411010-00004"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280215620229"},{"issue":"4","key":"e_1_2_9_22_1","first-page":"666","article-title":"Multivariate\u2010Nonlinear Mixed Models With Application to Censored Multi\u2010Outcome AIDS Studies","volume":"18","author":"Lin T.\u2010I.","year":"2017","journal-title":"Biostatistics"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12162"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01689-9"},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2022.2151454"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70277","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70277","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70277","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T01:04:15Z","timestamp":1775869455000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70277"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":24,"journal-issue":{"issue":"20-22","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1002\/sim.70277"],"URL":"https:\/\/doi.org\/10.1002\/sim.70277","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9]]},"assertion":[{"value":"2025-01-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-12","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-23","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70277"}}