{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T16:00:31Z","timestamp":1747152031366,"version":"3.40.5"},"reference-count":26,"publisher":"Wiley","issue":"28","license":[{"start":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T00:00:00Z","timestamp":1597276800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2020,12,10]]},"abstract":"<jats:p>Generalized additive models (GAMs) with bivariate smoothers are frequently used to map geographic disease risks in epidemiology studies. A challenge in identifying health disparities has been the lack of intuitive and computationally feasible methods to assess whether the pattern of spatial effects varies over time. In this research, we accommodate time\u2010stratified smoothers into the GAM framework to estimate time\u2010specific spatial risk patterns while borrowing information from confounding effects across time. A backfitting algorithm for model estimation is proposed along with a permutation testing framework for assessing temporal heterogeneity of geospatial risk patterns across two or more time points. Simulation studies show that our proposed permuted mean squared difference (PMSD) test performs well with respect to type I error and power in various settings when compared with existing methods. The proposed model and PMSD test are used geospatial risk patterns of patent ductus arteriosus (PDA) in the state of Massachusetts over 2003\u20102009. We show that there is variation over time in spatial patterns of PDA risk, adjusting for other known risk factors, suggesting the presence of potential time\u2010varying and space\u2010related risk factors other than the adjusted ones.<\/jats:p>","DOI":"10.1002\/sim.8718","type":"journal-article","created":{"date-parts":[[2020,8,14]],"date-time":"2020-08-14T01:14:01Z","timestamp":1597367641000},"page":"4187-4200","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A stratified generalized additive model and permutation test for temporal heterogeneity of smoothed bivariate spatial effects"],"prefix":"10.1002","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8464-2817","authenticated-orcid":false,"given":"Yannan","family":"Tang","sequence":"first","affiliation":[{"name":"Department of Statistics University of California, Irvine  Irvine California USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Veronica M.","family":"Vieira","sequence":"additional","affiliation":[{"name":"Program in Public Health University of California, Irvine  Irvine California USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Scott M.","family":"Bartell","sequence":"additional","affiliation":[{"name":"Department of Statistics University of California, Irvine  Irvine California USA"},{"name":"Program in Public Health University of California, Irvine  Irvine California USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel L.","family":"Gillen","sequence":"additional","affiliation":[{"name":"Department of Statistics University of California, Irvine  Irvine California USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2020,8,13]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.envres.2015.12.010"},{"volume-title":"Generalized Additive Models","year":"1990","author":"Hastie T","key":"e_1_2_7_3_1"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781315370279"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1979.10481038"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1538-4632.1996.tb00936.x"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0086566"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00374"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00889887"},{"volume-title":"Interpolation of Spatial Data: Some Theory for Kriging","year":"2012","author":"Stein ML","key":"e_1_2_7_10_1"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-3121.1992.tb00605.x"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01275432"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00893321"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1993.10485354"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1080\/1361593022000029467"},{"key":"e_1_2_7_16_1","first-page":"43","volume-title":"An Introduction to Model\u2010Based Geostatistics","author":"Diggle PJ","year":"2003"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1201\/b17115"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-statistics-060116-054155"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2010.00749.x"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2016.1180986"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000000980"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2010.05.004"},{"key":"e_1_2_7_23_1","doi-asserted-by":"publisher","DOI":"10.1186\/1476-072X-5-26"},{"key":"e_1_2_7_24_1","doi-asserted-by":"crossref","unstructured":"BaiL BartellS BlissR VieiraV. 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