On the identifiability of copulas in bivariate competing risks models

TL;DR

This paper investigates the identifiability of copulas in bivariate competing risks models, demonstrating that many common copula families are identifiable even when one margin is unknown, addressing a longstanding crisis in the field.

Contribution

It shows that dependence structures modeled by copulas can be identified in competing risks models, even with incomplete margin information, which was previously considered impossible.

Findings

Many copula families are identifiable in competing risks models.

Identification is possible even when one margin is unknown.

Addresses the longstanding 'identifiability crisis' in the field.

Abstract

In competing risks models, the joint distribution of the event times is not identifiable even when the margins are fully known, which has been referred to as the "identifiability crisis in competing risks analysis" (Crowder, 1991). We model the dependence between the event times by an unknown copula and show that identification is actually possible within many frequently used families of copulas. The result is then extended to the case where one margin is unknown.