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Dropout is generally regarded as a non\u2010ignorable mechanism when the probability of the occurrence of missing values is related to both observed and unobserved data. This paper aims at extending the  linear mixed models to cope with the problem of non\u2010ignorable dropout for modeling continuous longitudinal data in the situation where outliers or heavy\u2010tailed noises may be present. We consider the selection modeling strategy with a logistic link function to describe the relationship between the probability of missing process and some possible factors, including responses and extra covariates. A Monte Carlo expectation conditional maximization algorithm is developed to simultaneously compute maximum likelihood (ML) estimates of the missingness indexing parameters within the logistic link function and mixed\u2010effects parameters of the full\u2010data\n                    <jats:italic>t<\/jats:italic>\n                    linear mixed\u2010effects (tLME) model that are of scientific interest. Additionally, the standard errors of the ML estimates can be calculated using the Monte Carlo version of the empirical information matrix. Two simulation studies are conducted to assess the capability of the tLME model in the presence of non\u2010ignorable dropout and outliers. The performance is compared to its normal counterpart on the basis of information criteria indices, the precision of estimation for fixed effects and missingness indexing parameters, and the predictive accuracy of missing responses. The proposed methodology is demonstrated through a real\u2010world example from an AIDS clinical trial, which provides practical implications when the non\u2010ignorable dropout is considered in the\u00a0analysis.\n                  <\/jats:p>","DOI":"10.1002\/bimj.70122","type":"journal-article","created":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T07:08:08Z","timestamp":1773990488000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extending\n                    <i>t<\/i>\n                    linear mixed models for longitudinal data with non\u2010ignorable dropout applied to AIDS studies"],"prefix":"10.1002","volume":"68","author":[{"given":"Yu\u2010Chen","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics National Chung Hsing University Taichung Taiwan"},{"name":"Department of Statistics National Cheng Kung University Tainan Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0344-7954","authenticated-orcid":false,"given":"Wan\u2010Lun","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics and Institute of Data Science National Cheng Kung University Tainan Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis M.","family":"Castro","sequence":"additional","affiliation":[{"name":"Department of Statistics Pontificia Universidad Cat\u00f3lica de Chile Santiago Chile"},{"name":"SENTINET: Surveillance, Epidemiology, and New Technologies for Infectious Emerging Threats"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3992-1128","authenticated-orcid":false,"given":"Tsung\u2010I","family":"Lin","sequence":"additional","affiliation":[{"name":"Institute of Statistics National Chung Hsing University Taichung Taiwan"},{"name":"Department of Public Health China Medical University Taichung Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,3,20]]},"reference":[{"key":"e_1_2_14_2_1","first-page":"267","volume-title":"2nd International Symposium on Information Theory","author":"Akaike H.","year":"1973"},{"key":"e_1_2_14_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/02664763.2016.1266309"},{"key":"e_1_2_14_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7994"},{"key":"e_1_2_14_5_1","doi-asserted-by":"publisher","DOI":"10.2147\/CLEP.S72247"},{"key":"e_1_2_14_6_1","unstructured":"CDC: Centers for Disease Control and Prevention. \u201cAbout HIV.\u201d Accessed September 22 2024.https:\/\/www.cdc.gov\/hiv\/about\/index.html."},{"key":"e_1_2_14_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201400064"},{"key":"e_1_2_14_8_1","doi-asserted-by":"publisher","DOI":"10.1177\/1471082X1001100401"},{"key":"e_1_2_14_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1977.tb01600.x"},{"key":"e_1_2_14_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2986113"},{"key":"e_1_2_14_11_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177009938"},{"key":"e_1_2_14_12_1","doi-asserted-by":"publisher","DOI":"10.2307\/2533322"},{"key":"e_1_2_14_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/1913710"},{"key":"e_1_2_14_14_1","doi-asserted-by":"publisher","DOI":"10.1097\/00042560-199602010-00007"},{"key":"e_1_2_14_15_1","doi-asserted-by":"publisher","DOI":"10.1198\/0003130042854"},{"key":"e_1_2_14_16_1","doi-asserted-by":"publisher","DOI":"10.2307\/1913937"},{"key":"e_1_2_14_17_1","first-page":"475","article-title":"The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models","volume":"5","author":"Heckman J. 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