{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T21:21:34Z","timestamp":1777929694966,"version":"3.51.4"},"reference-count":56,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2016,8,8]],"date-time":"2016-08-08T00:00:00Z","timestamp":1470614400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2018,5]]},"abstract":"<jats:p>Many medical (and ecological) processes involve the change of shape, whereby one trajectory changes into another trajectory at a specific time point. There has been little investigation into the study design needed to investigate these models. We consider the class of fixed effect change-point models with an underlying shape comprised two joined linear segments, also known as broken-stick models. We extend this model to include two sub-groups with different trajectories at the change-point, a change and no change class, and also include a missingness model to account for individuals with incomplete follow-up. Through a simulation study, we consider the relationship of sample size to the estimates of the underlying shape, the existence of a change-point, and the classification-error of sub-group labels. We use a Bayesian framework to account for the missing labels, and the analysis of each simulation is performed using standard Markov chain Monte Carlo techniques. Our simulation study is inspired by cognitive decline as measured by the Mini-Mental State Examination, where our extended model is appropriate due to the commonly observed mixture of individuals within studies who do or do not exhibit accelerated decline. We find that even for studies of modest size ( n\u2009=\u2009500, with 50 individuals observed past the change-point) in the fixed effect setting, a change-point can be detected and reliably estimated across a range of observation-errors.<\/jats:p>","DOI":"10.1177\/0962280216662298","type":"journal-article","created":{"date-parts":[[2016,8,9]],"date-time":"2016-08-09T20:09:15Z","timestamp":1470773355000},"page":"1476-1497","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up"],"prefix":"10.1177","volume":"27","author":[{"given":"Simon R","family":"White","sequence":"first","affiliation":[{"name":"MRC Biostatistics Unit, Cambridge, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Graciela","family":"Muniz-Terrera","sequence":"additional","affiliation":[{"name":"School of Clinical Sciences, University of Edinburgh, Edinburgh, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fiona E","family":"Matthews","sequence":"additional","affiliation":[{"name":"MRC Biostatistics Unit, Cambridge, UK"},{"name":"Institute of Health and Society, Faculty of Medicine, Newcastle University, Newcastle, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,8,8]]},"reference":[{"key":"bibr1-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1975.10479875"},{"key":"bibr2-0962280216662298","doi-asserted-by":"publisher","DOI":"10.2307\/1268385"},{"key":"bibr3-0962280216662298","first-page":"105","volume-title":"Applied data analytic techniques for turning points research","author":"McArdle J","year":"2008"},{"key":"bibr4-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000001177"},{"key":"bibr5-0962280216662298","doi-asserted-by":"publisher","DOI":"10.2307\/2347570"},{"key":"bibr6-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(97)00115-2"},{"key":"bibr7-0962280216662298","first-page":"777","volume-title":"Advances in reliability \u2013 volume 20 of Handbook of Statistics","author":"Ebrahimi N","year":"2001"},{"key":"bibr8-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1175\/2009JCLI2597.1"},{"key":"bibr9-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1080\/02664760903563668"},{"key":"bibr10-0962280216662298","first-page":"617","volume-title":"Bayesian biostatistics","author":"Joseph L","year":"1996"},{"key":"bibr11-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2671"},{"key":"bibr12-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(20000229)19:4<617::AID-SIM360>3.0.CO;2-R"},{"key":"bibr13-0962280216662298","doi-asserted-by":"publisher","DOI":"10.1016\/j.annepidem.2007.10.006"},{"key":"bibr14-0962280216662298","first-page":"83","volume":"48","author":"Shaban SA","year":"1980","journal-title":"Int Stat Rev"},{"key":"bibr15-0962280216662298","doi-asserted-by":"crossref","DOI":"10.1214\/lnms\/1215463106","volume-title":"Change-point problems","author":"Carlstein E","year":"1994"},{"key":"bibr16-0962280216662298","unstructured":"Khodadadi A and Asgharian M. 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