{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T23:23:40Z","timestamp":1791329020079,"version":"4.3.1"},"reference-count":30,"publisher":"Wiley","issue":"30","license":[{"start":{"date-parts":[[2008,9,3]],"date-time":"2008-09-03T00:00:00Z","timestamp":1220400000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2008,12,30]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We are interested in longitudinal data of a continuous response that show profiles with an initial sharp change and approaching asymptotes for each patient, and many patients drop out with a reason related to the response. In this paper, we focus on a model that assumes a dropout process is missing at random (MAR). In this dropout process, we can obtain consistent maximum likelihood estimators as long as both the mean and covariance structures are correctly specified. However, parsimonious covariance structures for the profiles approaching asymptotes are unclear. An autoregressive linear mixed effects model can express the profile with random individual asymptotes. We show that this model provides a new parsimonious covariance structure. The covariance structure at steady state is compound symmetry and the other elements of the covariance depend on the measurement points. In simulation studies, the estimate of the asymptote is unbiased in MAR dropouts, but biased in non\u2010ignorable dropouts. We also applied this model to actual schizophrenia trial data. Copyright \u00a9 2008 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.3417","type":"journal-article","created":{"date-parts":[[2008,9,3]],"date-time":"2008-09-03T09:58:39Z","timestamp":1220435919000},"page":"6351-6366","source":"Crossref","is-referenced-by-count":18,"title":["An autoregressive linear mixed effects model for the analysis of longitudinal data which include dropouts and show profiles approaching asymptotes"],"prefix":"10.1002","volume":"27","author":[{"given":"Takashi","family":"Funatogawa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ikuko","family":"Funatogawa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Masahiro","family":"Takeuchi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2008,9,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1176\/ajp.151.6.825"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198524847.001.0001","volume-title":"Analysis of Longitudinal Data","author":"Diggle PJ","year":"2002"},{"key":"e_1_2_1_4_2","volume-title":"Statistical Analysis with Missing Data","author":"Little RJA","year":"1987"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2531905"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1995.10476615"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2529876"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/2531694"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780140307"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19990915\/30)18:17\/18<2465::AID-SIM269>3.0.CO;2-2"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2670"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/1.4.465"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9876.00241"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780040407"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780070110"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(82)90095-1"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.950"},{"key":"e_1_2_1_18_2","first-page":"115","volume-title":"Statistical Models for Longitudinal Studies of Health","author":"Rosner B","year":"1992"},{"key":"e_1_2_1_19_2","volume-title":"Models for Repeated Measurements","author":"Lindsey JK","year":"1993"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.2307\/2291750"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.2307\/2531727"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1002\/0471725315"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.2307\/2531777"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/86.1.1"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/89.4.841"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780070905"},{"key":"e_1_2_1_27_2","first-page":"267","volume-title":"Second International Symposium on Information Theory","author":"Akaike H","year":"1973"},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0116"},{"key":"e_1_2_1_29_2","volume-title":"Models for Repeated Measurements","author":"Lindsey JK","year":"1993"},{"key":"e_1_2_1_30_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476806"},{"key":"e_1_2_1_31_2","doi-asserted-by":"publisher","DOI":"10.2307\/2347788"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.3417","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.3417","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T16:18:19Z","timestamp":1709223499000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.3417"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,3]]},"references-count":30,"journal-issue":{"issue":"30","published-print":{"date-parts":[[2008,12,30]]}},"alternative-id":["10.1002\/sim.3417"],"URL":"https:\/\/doi.org\/10.1002\/sim.3417","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9,3]]}}}