{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T16:40:11Z","timestamp":1792600811399,"version":"4.5.0"},"reference-count":31,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"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":["Biometrical J"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>\n                    Physical activity plays an important role in the well\u2010being of patients with Chronic Obstructive Pulmonary Disease (COPD). The telEPOC program, developed at the Galdakao\u2010Usansolo University Hospital (Vizcaya, Spain), provided a telemonitoring data set resulting in a variable domain functional data set. In this sense, the aim is to study the impact of physical activity (measured as daily steps collected in a time interval delimited by the patient's participation in the experiment) on the rate of hospitalizations. To address this challenge, a novel basis expansion approach is proposed to fit a variable\u2010domain functional regression model, which assumes the functional nature of the covariate (daily steps) and incorporates the sample data into the model without alignment. This will enrich the interpretability of the model by incorporating the information provided by the domain through a two\u2010dimensional regression coefficient. In addition, a penalized estimation of the model is proposed in terms of a 2D P\u2010spline penalty, which allows considering different degree of smoothness for each dimension of the functional regression coefficient (anisotropic penalty). The performance of our methodology is also tested and compared with state\u2010of\u2010the\u2010art methods by means of a simulation study. Software for our method can be found in the\n                    <jats:bold>VDPO<\/jats:bold>\n                    R package available in CRAN.\n                  <\/jats:p>","DOI":"10.1002\/bimj.70164","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T12:59:39Z","timestamp":1787835579000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling Physical Activity Profiles in COPD Patients: A Basis Expansion Approach to Variable Domain Functional Regression Models"],"prefix":"10.1002","volume":"68","author":[{"given":"Pavel","family":"Hern\u00e1ndez\u2010Amaro","sequence":"first","affiliation":[{"name":"Universidad Carlos III de Madrid Madrid Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mar\u00eda","family":"Durb\u00e1n","sequence":"additional","affiliation":[{"name":"Universidad Carlos III de Madrid Madrid Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. Carmen","family":"Aguilera\u2010Morillo","sequence":"additional","affiliation":[{"name":"Universitat Polit\u00e8cnica de Val\u00e8ncia Valencia Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cristobal Esteban","family":"Gonzalez","sequence":"additional","affiliation":[{"name":"Osakidetza Basque Health Service Bilbao Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Inmaculada","family":"Arostegui","sequence":"additional","affiliation":[{"name":"University of the Basque Country UPV\/EHU Bilbao Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2013.04.007"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11749-012-0307-1"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1974.1100705"},{"key":"e_1_2_10_5_1","doi-asserted-by":"crossref","unstructured":"Breslow N. E. andD. G.Clayton.1993.Approximate Inference in Generalized Linear Mixed Models. Technical Report 421.","DOI":"10.1080\/01621459.1993.10594284"},{"issue":"447","key":"e_1_2_10_6_1","first-page":"794","article-title":"Variable Selection and Function Estimation in Additive Nonparametric Regression Using a Data\u2010Based Prior: Comment","volume":"94","author":"Brumback B. A.","year":"1999","journal-title":"Journal of the American Statistical Association"},{"key":"e_1_2_10_7_1","unstructured":"Burden A. R.Burden andJ.Faires.2016Numerical Analysis 10th ed. 8."},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(99)00036-X"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2003.08.008"},{"key":"e_1_2_10_10_1","volume-title":"A Practical Guide to Splines","author":"De Boor C.","year":"2001"},{"key":"e_1_2_10_11_1","doi-asserted-by":"crossref","unstructured":"Eilers P. H. C. andB. D.Marx.1996.Flexible Smoothing With B\u2010Splines and Penalties. Technical Report 2.","DOI":"10.1214\/ss\/1038425655"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/resp.12239"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12931-020-01395-z"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.2147\/COPD.S115350"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1136\/thx.2006.060145"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1378\/chest.11-2014"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxaa023"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.940044"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1198\/jcgs.2010.10007"},{"key":"e_1_2_10_20_1","unstructured":"Goldsmith J. F.Scheipl L.Huang et\u00a0al.2026.Refund: Regression With Functional Data R package version 0.1\u201040.https:\/\/CRAN.R-project.org\/package=refund."},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00342"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/jse.12252"},{"key":"e_1_2_10_23_1","unstructured":"Lee D.\u2010J.2010. \u201cSmoothing Mixed Models for Spatial and Spatio\u2010Temporal Data.\u201d PhD thesis Universidad Carlos III de Madrid."},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1177\/1471082X1001100104"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asac035"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0181921"},{"key":"e_1_2_10_27_1","unstructured":"R Core Team.2013.R: A Language and Environment for Statistical Computing."},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-98185-7"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/0470013192.bsa239"},{"key":"e_1_2_10_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-018-9818-2"},{"key":"e_1_2_10_31_1","doi-asserted-by":"crossref","unstructured":"Rodriguez\u2010Alvarez M. X. M.Oviedo de la Fuente M.Durban P. H. C.Eilers D.\u2010J.Lee andM.Stasinopoulos.2021.SOP: Generalised Additive P\u2010Spline Regression Models Estimation R package version 1.0\u20101.https:\/\/CRAN.R-project.org\/package=SOP.","DOI":"10.32614\/CRAN.package.SOP"},{"key":"e_1_2_10_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-016-9666-x"}],"container-title":["Biometrical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70164","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/bimj.70164","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70164","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T15:50:59Z","timestamp":1792597859000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/bimj.70164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,27]]},"references-count":31,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["10.1002\/bimj.70164"],"URL":"https:\/\/doi.org\/10.1002\/bimj.70164","archive":["Portico"],"relation":{},"ISSN":["0323-3847","1521-4036"],"issn-type":[{"value":"0323-3847","type":"print"},{"value":"1521-4036","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,27]]},"assertion":[{"value":"2024-11-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-19","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-27","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70164"}}