Identifiable Copula-Double-Cox Models: A Fully Parametric Framework for Dependent Right-Censored Survival Data

Dependent censoring, common in medical studies with informative dropout, invalidates standard Cox regression by violating the independent censoring assumption. While copula-based 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-Cox marginal structures with copula dependence, which is called the copula-double-Cox model. Using Weibull or generalized exponential (GenExp) distributions, the double-Cox model links both scale and shape parameters to covariates via Cox-type regressions. This structure accommodates non-proportional 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-parameterization. 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-world 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-Cox structure. An open-source R implementation of the copula-double-Cox model is provided on GitHub.