{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T21:21:00Z","timestamp":1789852860654,"version":"4.0.1"},"reference-count":31,"publisher":"Wiley","issue":"30","license":[{"start":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T00:00:00Z","timestamp":1697414400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2023,12,30]]},"abstract":"<jats:p>The accelerated failure time (AFT) model offers an important and useful alternative to the conventional Cox proportional hazards model, particularly when the proportional hazards assumption for a Cox model is violated. Since an AFT model is basically a log\u2010linear model, meaningful interpretations of covariate effects on failure times can be made directly. However, estimation of a semiparametric AFT model imposes computational challenges even when it only has time\u2010fixed covariates, and the situation becomes much more complicated when time\u2010varying covariates are included. In this paper, we propose a penalised likelihood approach to estimate the semiparametric AFT model with right\u2010censored failure time, where both time\u2010fixed and time\u2010varying covariates are permitted. We adopt the Gaussian basis functions to construct a smooth approximation to the nonparametric baseline hazard. This model fitting method requires a constrained optimisation approach. A comprehensive simulation study is conducted to demonstrate the performance of the proposed method. An application of our method to a motor neuron disease data set is provided.<\/jats:p>","DOI":"10.1002\/sim.9926","type":"journal-article","created":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T23:56:26Z","timestamp":1697500586000},"page":"5577-5595","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On semiparametric accelerated failure time models with time\u2010varying covariates: A maximum penalised likelihood estimation"],"prefix":"10.1002","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8193-538X","authenticated-orcid":false,"given":"Ding","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematical and Physical Sciences Macquarie University  Sydney 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