Bivariate Cox model and copulas

TL;DR

This paper proposes a novel class of Cox models that incorporate covariate effects into the dependence structure of bivariate data via copulas, enabling explicit modeling of covariate influence on dependence.

Contribution

It introduces a new Cox model framework that modifies copulas to capture covariate effects on dependence, maintaining stability of well-known copula classes.

Findings

Model effectively captures covariate influence on dependence

Stable under various copula classes, including archimedean and extreme value

Provides explicit parametric forms for covariate effects

Abstract

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.