Dependent competing risks: Bounds for net survival functions with fixed crude survival functions

Using the formulation of latent failure times, the problem of inference on survival time in the presence of competing risks is discussed. Even for the simplified problem where dose and other covariates are fixed, it is not well known that the distributions of the latent failure times are not identifiable from the usual competing risks data. Bounds for the joint survival function and marginal survival functions for the latent failure times are given, and an example illustrates the determination of empirical bounds that estimate the true bounds. In general, the bounds are wide and therefore not very useful. Some alternate approaches are briefly mentioned.