This paper introduces a new class of Cox models for dependent bivariate data. The impact of the covariate on the dependence of the variables is captured through the modification of their copula. Various classes of well-known copulas are stable under the model (Archimedean type and extreme value copulas), meaning that the role of the covariate acts in a simple and explicit way on the copula in the class; specific parametric classes are considered.
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