  A typical situation in competing risks analysis is that the researcher is
only interested in a subset of risks. This paper considers a depending
competing risks model with the distribution of one risk being a parametric or
semi-parametric model, while the model for the other risks being unknown.
Identifiability is shown for popular classes of parametric models and the
semiparametric proportional hazards model. The identifiability of the
parametric models does not require a covariate, while the semiparametric model
requires at least one. Estimation approaches are suggested which are shown to
be $\sqrt{n}$-consistent. Applicability and attractive finite sample
performance are demonstrated with the help of simulations and data examples.
