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A na\u00efve approach is to treat the last observed time as the exact event time, which may induce biased estimators of the model parameters. In this paper, we first develop a Cox model with time\u2010dependent covariates for the event time and a proportional hazards model with frailty for the gap time. We then construct the upper limits using the latent gap times to resolve the issue of interval\u2010censored event time data with unknown upper limits. A data\u2010augmentation technique and a Monte Carlo EM (MCEM) algorithm are developed to facilitate computation. Theoretical properties of the computational algorithm are also investigated. Additionally, new model comparison criteria are developed to assess the fit of the gap time data as well as the fit of the event time data conditional on the gap time data. Our proposed method compares favorably with competing methods in both simulation study and real data analysis.<\/jats:p>","DOI":"10.1002\/sim.9732","type":"journal-article","created":{"date-parts":[[2023,4,4]],"date-time":"2023-04-04T23:54:26Z","timestamp":1680652466000},"page":"2455-2474","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modeling and maximum likelihood based inference of\u00a0interval\u2010censored data with unknown upper limits and\u00a0time\u2010dependent covariates"],"prefix":"10.1002","volume":"42","author":[{"given":"Jing","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Computer Science and Statistics University of Rhode Island Kingston 02881 Rhode Island USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lijiang","family":"Geng","sequence":"additional","affiliation":[{"name":"Department of Statistics University of Connecticut Storrs 06269 Connecticut USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angela","family":"Starkweather","sequence":"additional","affiliation":[{"name":"School of Nursing University of Connecticut Storrs 06269 Connecticut USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1935-2447","authenticated-orcid":false,"given":"Ming\u2010Hui","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Statistics University of Connecticut Storrs 06269 Connecticut USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2023,4,4]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2530698"},{"volume-title":"The Statistical Analysis of Interval\u2010Censored Failure Time Data","year":"2007","author":"Sun J","key":"e_1_2_11_3_1"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1097\/AJP.0000000000000347"},{"key":"e_1_2_11_5_1","doi-asserted-by":"crossref","unstructured":"DemirizA.Used car pricing and beyond: a survival analysis framework. 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