A Nested Copula Duration Model for Competing Risks with Multiple Spells

A copula graphic estimator for the competing risks duration model with multiple spells is presented. By adopting a nested copula structure the dependencies between risks and spells are modelled separately. This breaks up an implicit restriction of popular duration models such as multivariate mixed proportional hazards. It is shown that the dependence structure between spells is identifiable and can be estimated, in contrast to the dependence structure between competing risks. Thus, by allowing these two components to differ, the model is not identifiable. This is an important finding related to the general identifiability of competing risks models. Various features of the model are investigated by simulations and its practicality is illustrated by an application to unemployment duration data.