Nonparametric Competing Risks Models: Identification and Strong Consistency

In this chapter, it is shown, in the general case, that a multiple causes death model is equivalent to a competing independent risks model. Uniqueness of the representation and identification conditions are discussed. Martingales arguments generalizing results of Stute and Wang (Annals of Statistics, 21(3), 1591–1607 (1993)) are used to show the almost sure convergence of simple functionals of the predictable hazard measures and of the distributions of the latent or “fictitious” independent risks. These results entails the almost sure uniform convergence on the real line of the distributions of these independent risks.