A single risk approach to the semiparametric competing risks model with parametric Archimedean risk dependence

Abstract

This paper considers a dependent competing risks model with the distribution of one risk being a semiparametric proportional hazards model, whereas the model for the other risks and the degree of risk dependence of an Archimedean copula are unknown. Identifiability is shown when there is at least one covariate with at least two values. Estimation is done by means of a $\sqrt{n}$-consistent semiparametric two-step procedure. Applicability and attractive finite sample performance are demonstrated with the help of simulations. An application to unemployment duration confirms the importance of estimating rather than assuming risk dependence.