{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T04:13:12Z","timestamp":1789877592999,"version":"4.0.1"},"reference-count":16,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2013,9,9]],"date-time":"2013-09-09T00:00:00Z","timestamp":1378684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2013,9,9]],"date-time":"2013-09-09T00:00:00Z","timestamp":1378684800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2013,9,9]],"date-time":"2013-09-09T00:00:00Z","timestamp":1378684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2014,2,20]]},"abstract":"<jats:p>Age\u2010period\u2010cohort (APC) models are used to analyze temporal trends in disease or mortality rates, dealing with linear dependency among associated effects of age, period, and cohort. However, the nature of sparseness in such data has severely limited the use of APC models. To deal with these practical limitations and issues, we advocate cubic smoothing splines. We show that the methods of estimable functions proposed in the framework of generalized linear models can still be considered to solve the non\u2010identifiability problem when the model fitting is within the framework of generalized additive models with cubic smoothing splines. Through simulation studies, we evaluate the performance of the cubic smoothing splines in terms of the mean squared errors of estimable functions. Our results support the use of cubic smoothing splines for APC modeling with sparse but unaggregated data from a Lexis diagram. Copyright \u00a9 2013 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.5970","type":"journal-article","created":{"date-parts":[[2013,9,9]],"date-time":"2013-09-09T07:06:52Z","timestamp":1378710412000},"page":"595-606","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Age\u2010period\u2010cohort models using smoothing splines: a generalized additive model approach"],"prefix":"10.1002","volume":"33","author":[{"given":"Bei","family":"Jiang","sequence":"first","affiliation":[{"name":"Department of Mathematical and Statistical Sciences University of Alberta  Edmonton AB Canada T6G 2G1"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keumhee C.","family":"Carriere","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Statistical Sciences University of Alberta  Edmonton AB Canada T6G 2G1"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2013,9,9]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19980630)17:12<1305::AID-SIM853>3.0.CO;2-W"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531004"},{"key":"e_1_2_6_4_1","volume-title":"Sociological Methodology","author":"Fienberg SE","year":"1978"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780060405"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780060406"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.pu.12.050191.002233"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2533105"},{"key":"e_1_2_6_9_1","volume-title":"Age\u2010period\u2010cohort Models: Statistical Inference in the Lexis Diagram","author":"Carstensen B","year":"2004"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2764"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1093\/jncimonographs\/lgj016"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2253"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4473-3"},{"key":"e_1_2_6_14_1","doi-asserted-by":"crossref","first-page":"144","DOI":"10.24095\/hpcdp.29.4.01","article-title":"Explaining Alberta's Rising Mesothelioma Rates","volume":"29","author":"Cree M","year":"2009","journal-title":"Chronic Diseases in Canada"},{"key":"e_1_2_6_15_1","volume-title":"Generalized Additive Models","author":"Hastie TJ","year":"1990"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347115"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.2307\/2530926"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.5970","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.5970","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.5970","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T15:25:24Z","timestamp":1696519524000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.5970"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,9]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,2,20]]}},"alternative-id":["10.1002\/sim.5970"],"URL":"https:\/\/doi.org\/10.1002\/sim.5970","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,9]]}}}