{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T14:21:43Z","timestamp":1788272503718,"version":"build-2803163510"},"reference-count":19,"publisher":"PAGEPress Publications","issue":"2","license":[{"start":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T00:00:00Z","timestamp":1787184000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Geospat Health"],"abstract":"<jats:p>Bayesian spatial models for disease mapping, such as Besag-York-Molli\u00e9 (BYM) models, are widely used to model disease counts while accounting for spatial dependence. However, these models are not equipped to handle missing covariate values. Covariates are often partially observed, yet these models require separate imputation that ignores imputation uncertainty. We extend this Bayesian framework for disease mapping to accommodate missing covariates while modeling the disease counts. Missing covariate values are treated as unknown parameters that are estimated simultaneously with the other model\u2019s parameters within the same Bayesian model. Evaluation on the benchmark Scottish lip cancer dataset demonstrates that the proposed model is effective in recovering the parameters of interest, compared with the complete-data BYM2 model under low-to-moderate missingness in a covariate.<\/jats:p>","DOI":"10.4081\/gh.2026.1511","type":"journal-article","created":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:25:42Z","timestamp":1787228742000},"source":"Crossref","is-referenced-by-count":0,"title":["Bayesian hierarchical spatial models for disease mapping in the presence of missing covariates"],"prefix":"10.4081","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7371-7297","authenticated-orcid":false,"given":"Sami","family":"Ullah","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5817-0836","authenticated-orcid":false,"given":"Tianfa","family":"Xie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2549","published-online":{"date-parts":[[2026,8,20]]},"reference":[{"key":"38892","doi-asserted-by":"publisher","DOI":"10.1007\/BF00116466"},{"key":"38893","doi-asserted-by":"publisher","DOI":"10.1191\/0962280205sm388oa"},{"key":"38894","doi-asserted-by":"publisher","DOI":"10.1186\/s12889-025-22896-w"},{"key":"38895","doi-asserted-by":"publisher","DOI":"10.2807\/1560-7917.ES.2024.29.27.2300688"},{"key":"38896","doi-asserted-by":"publisher","DOI":"10.2307\/2532003"},{"key":"38897","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1989.10478783"},{"key":"38898","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2001.00197.x"},{"key":"38899","doi-asserted-by":"publisher","DOI":"10.1016\/j.idm.2025.05.003"},{"key":"38900","doi-asserted-by":"publisher","DOI":"10.1016\/j.sste.2011.03.001"},{"key":"38901","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1284-3_4"},{"key":"38902","doi-asserted-by":"publisher","DOI":"10.1590\/0102-311xen212923"},{"key":"38903","doi-asserted-by":"publisher","DOI":"10.1002\/asmb.2568"},{"key":"38904","doi-asserted-by":"publisher","DOI":"10.1177\/0962280210371561"},{"key":"38905","unstructured":"Morris M, 2019. spatial models in stan: intrinsic auto-regressive models for areal data. Stan case study. Accessed 1 January 2026. Available from: https:\/\/mc-stan.org\/learn-stan\/case-studies\/icar_stan.html"},{"key":"38906","doi-asserted-by":"publisher","DOI":"10.1016\/j.sste.2019.100301"},{"key":"38907","doi-asserted-by":"publisher","DOI":"10.1214\/16-STS576"},{"key":"38908","doi-asserted-by":"publisher","DOI":"10.1016\/j.spasta.2021.100540"},{"key":"38909","doi-asserted-by":"publisher","DOI":"10.1214\/20-BA1221"},{"key":"38910","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxl008"}],"container-title":["Geospatial Health"],"original-title":[],"link":[{"URL":"https:\/\/www.geospatialhealth.net\/gh\/article\/download\/1511\/1604","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.geospatialhealth.net\/gh\/article\/download\/1511\/1607","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.geospatialhealth.net\/gh\/article\/download\/1511\/1603","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T13:59:20Z","timestamp":1788271160000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.geospatialhealth.net\/gh\/article\/view\/1511"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,20]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,7,23]]}},"URL":"https:\/\/doi.org\/10.4081\/gh.2026.1511","relation":{},"ISSN":["1970-7096","1827-1987"],"issn-type":[{"value":"1970-7096","type":"electronic"},{"value":"1827-1987","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8,20]]}}}