On assessing independence of Competing Risks when failure times are discrete

The traditional approach to modelling for Competing Risks, via a multivariate distribution of latent failure times, is very natural for many applications but suffers from a well-documented problem of identifiability. However, the demonstrations of this problem in the literature apply to essentially continuous latent failure times where any atoms of probability in their distributions are not too intrusive. It is shown in this paper that for discrete failure times the classic results on the identifiability problem concerning the existence of equivalent independent risks are incomplete.