{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T17:59:36Z","timestamp":1780941576957,"version":"3.54.1"},"reference-count":24,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003968","name":"Iran National Science Foundation","doi-asserted-by":"publisher","award":["4015320"],"award-info":[{"award-number":["4015320"]}],"id":[{"id":"10.13039\/501100003968","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>While shrinkage and preliminary test estimation have long been studied in linear and static Cox models, their theoretical integration within models featuring time-dependent covariates has remained unresolved due to the evolving risk set and nonhomogeneous information accumulation inherent in such data. In this study, we develop a unified framework for shrinkage estimation in the time-dependent Cox proportional hazards model, by extending the classical Stein-type theory to a dynamic semiparametric survival setting. Our theoretical analyses reveal that the positive-rule Stein estimator preserves unbiasedness under valid restrictions while adaptively attenuating variance inflation when the restriction is approximately correct, striking a principled balance between efficiency and robustness. A comprehensive Monte Carlo simulation study and an empirical application to the Mayo Clinic primary biliary cirrhosis dataset substantiate the theoretical advantages, demonstrating that the superior estimation strategy achieves substantial efficiency gains relative to both unrestricted and penalized estimators such as adaptive LASSO.<\/jats:p>","DOI":"10.1371\/journal.pone.0345123","type":"journal-article","created":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T17:28:02Z","timestamp":1780939682000},"page":"e0345123","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Integrating preliminary test and Stein-type techniques to improve estimation in the time-dependent Cox model"],"prefix":"10.1371","volume":"21","author":[{"given":"Rohollah","family":"Ramezani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4647-8002","authenticated-orcid":true,"given":"Mohammad Reza","family":"Rabiei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Arashi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,6,8]]},"reference":[{"issue":"2","key":"pone.0345123.ref001","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","article-title":"Regression Models and Life-Tables","volume":"34","author":"DR Cox","year":"1972","journal-title":"Journal of the Royal Statistical Society Series B: Statistical Methodology"},{"issue":"4","key":"pone.0345123.ref002","doi-asserted-by":"crossref","DOI":"10.1214\/aos\/1176345976","article-title":"Cox\u2019s Regression Model for Counting Processes: A Large Sample Study","volume":"10","author":"PK Andersen","year":"1982","journal-title":"Ann Statist"},{"key":"pone.0345123.ref003","doi-asserted-by":"crossref","DOI":"10.1002\/9781118150672","volume-title":"Counting processes and survival analysis","author":"RT Fleming","year":"2005"},{"key":"pone.0345123.ref004","volume-title":"Statistical models based on counting processes","author":"PK Andersen","year":"1995"},{"key":"pone.0345123.ref005","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1525\/9780520313880-018","article-title":"Inadmissibility of the usual estimator for the mean of a multivariate normal distribution","volume-title":"Contribution to the Theory of Statistics","author":"C Stein","year":"1956"},{"key":"pone.0345123.ref006","first-page":"443","article-title":"Estimation with Quadratic Loss","volume-title":"Springer Series in Statistics","author":"W James","year":"1992"},{"issue":"3","key":"pone.0345123.ref007","doi-asserted-by":"crossref","first-page":"254","DOI":"10.3390\/e27030254","article-title":"Efficient Post-Shrinkage Estimation Strategies in High-Dimensional Cox\u2019s Proportional Hazards Models","volume":"27","author":"SE Ahmed","year":"2025","journal-title":"Entropy (Basel)"},{"issue":"1","key":"pone.0345123.ref008","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1515\/ijb-2018-0109","article-title":"Shrinkage estimation applied to a semi-nonparametric regression model","volume":"17","author":"H Zareamoghaddam","year":"2020","journal-title":"Int J Biostat"},{"key":"pone.0345123.ref009","volume-title":"Advances in shrinkage and penalized estimation strategies: Honoring the contributions of Professor A K Md. 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