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While copula\u2010based methods offer flexible dependence modeling, their parametric extensions face identifiability barriers. We address this problem through a novel fully identifiable parametric model that synergizes double\u2010Cox marginal structures with copula dependence, which is called the copula\u2010double\u2010Cox model. Using Weibull or generalized exponential (GenExp) distributions, the double\u2010Cox model links both scale and shape parameters to covariates via Cox\u2010type regressions. This structure accommodates non\u2010proportional hazards while containing the standard Cox model as a special case. We establish identifiability under dependent censoring and derive consistent estimators for baseline parameters, regression coefficients, and copula association. Simulations confirm robustness to association structure misspecification and over\u2010parameterization. Estimation accuracy is supported by asymptotic theory and standard error evaluation via the observed information matrix. Finally, we illustrate the proposed approach through a real\u2010world application to a dataset on monoclonal gammopathy of undetermined significance (MGUS), highlighting its practical relevance. The results show that our method provides an interpretable characterization of covariate effects on both failure time and censoring time through its double\u2010Cox structure. An open\u2010source R implementation of the copula\u2010double\u2010Cox model is provided on GitHub.<\/jats:p>","DOI":"10.1002\/sim.70647","type":"journal-article","created":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T20:42:56Z","timestamp":1782938576000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Identifiable Copula\u2010Double\u2010Cox Models: A Fully Parametric Framework for Dependent Right\u2010Censored Survival Data"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4565-270X","authenticated-orcid":false,"given":"Huazhen","family":"Yu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Nanjing University of Information Science and Technology  Nanjing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology Nanjing University of Aeronautics and Astronautics  Nanjing China"},{"name":"The State Key Laboratory of Blockchain and Data Security Zhejiang University  Hangzhou China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lixin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics Zhejiang Gongshang University  Hangzhou China"},{"name":"Center for Data Science Zhejiang University  Hangzhou China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,7,1]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1972.tb00899.x"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.72.1.20"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.1191\/0962280203sm335ra"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.5540330308"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2008.00986.x"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2009.00734.x"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecosta.2017.07.002"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7651"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asaa095"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2022.2161387"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2025.106296"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-024-09632-z"},{"key":"e_1_2_12_14_1","first-page":"467","volume-title":"Handbook of Statistics","author":"Basu A. 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