{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T06:49:54Z","timestamp":1792133394965,"version":"4.4.0"},"reference-count":35,"publisher":"Wiley","issue":"23-24","license":[{"start":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T00:00:00Z","timestamp":1791936000000},"content-version":"vor","delay-in-days":13,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"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":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Estimating health indicators for specific population subgroups is a recurring challenge in epidemiology and public health. When survey data are used, small area estimation (SAE) methods can improve precision by borrowing strength across domains. In many applications, however, outcomes are self\u2010reported and affected by coarsening mechanisms, such as rounding and digit preference, that reduce data resolution and may bias inference. This paper addresses both issues by developing a Bayesian unit\u2010level SAE framework for semi\u2010continuous, coarsened responses. Motivated by the 2019 Italian European Health Interview Survey, we estimate smoking indicators for domains defined by the cross\u2010classification of Italian regions and age groups, capturing both smoking prevalence and intensity. The model adopts a two\u2010part structure: a logistic component for smoking prevalence and a flexible mixture of lognormal distributions for average cigarette consumption, coupled with an explicit model for coarsening and top\u2010coding. Although the parameters governing the heaping mechanism are estimated from the data, its structural specification relies on assumptions about plausible rounding regimes and therefore requires substantive expert judgment. Simulation studies show that ignoring coarsening can yield biased and unstable domain estimates with poor interval coverage, whereas the proposed model improves accuracy and achieves near\u2010nominal coverage. The empirical application provides a detailed picture of smoking patterns across region\u2013age domains, helping to characterize the dynamics of the phenomenon and inform targeted public health policies.<\/jats:p>","DOI":"10.1002\/sim.70780","type":"journal-article","created":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T04:44:07Z","timestamp":1792039447000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coarsened Data in Small Area Estimation: A Bayesian Two\u2010Part Model for Mapping Smoking Behavior"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2164-5815","authenticated-orcid":false,"given":"Aldo","family":"Gardini","sequence":"first","affiliation":[{"name":"Department of Statistical Sciences University of Bologna  Bologna Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4152-9712","authenticated-orcid":false,"given":"Lorenzo","family":"Mori","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences University of Bologna  Bologna Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,14]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3809"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0023443"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.2105\/AJPH.2020.305611"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41591-020-01210-8"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10476202"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348396"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2532251"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/81.4.701"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxm001"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3281"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1080\/02664763.2015.1077372"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.5419"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-023-01405-4"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1214\/15-AOAS809"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssc.12205"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1093\/jssam\/smv032"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118735855"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201200271"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201300233"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssa.12872"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.healthplace.2011.12.010"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.annepidem.2018.03.015"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sste.2022.100525"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.18332\/tid\/162379"},{"key":"e_1_2_11_26_1","first-page":"66","article-title":"European Health Interview Survey (EHIS) 2\u2010Background and Study Methodology","volume":"4","author":"Hintzpeter B.","year":"2019","journal-title":"Journal of Health Monitoring"},{"key":"e_1_2_11_27_1","unstructured":"Eurostat \u201cDaily Smokers of Cigarettes by Sex Age and Level \u201dEurostat."},{"key":"e_1_2_11_28_1","unstructured":"American Lung Association \u201cOverall Smoking Trends \u201dAmerican Lung Association."},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.1093\/jssam\/smad020"},{"key":"e_1_2_11_30_1","volume-title":"Handbook of Mixture Analysis","author":"Celeux G.","year":"2018"},{"key":"e_1_2_11_31_1","unstructured":"Stan Development Team \u201cRStan: The R Interface to Stan \u201dStan Development Team."},{"key":"e_1_2_11_32_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2005.031010.x"},{"key":"e_1_2_11_33_1","doi-asserted-by":"publisher","DOI":"10.3390\/e19100555"},{"key":"e_1_2_11_34_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610920701826088"},{"key":"e_1_2_11_35_1","doi-asserted-by":"publisher","DOI":"10.2307\/3316146"},{"key":"e_1_2_11_36_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214507000001094"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70780","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70780","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70780","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T06:32:54Z","timestamp":1792132374000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70780"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":35,"journal-issue":{"issue":"23-24","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["10.1002\/sim.70780"],"URL":"https:\/\/doi.org\/10.1002\/sim.70780","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"2026-02-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-05","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70780"}}