  Most papers implicitly assume competing risks to be induced by residual
cohort heterogeneity, i.e. heterogeneity that is not captured by the recorded
covariates. Based on this observation we develop a generic statistical
description of competing risks that unifies the main schools of thought.
Assuming heterogeneity-induced competing risks is much weaker than assuming
risk independence. However, we show that it still imposes sufficient
constraints to solve the competing risk problem, and derive exact formulae for
decontaminated primary risk hazard rates and cause-specific survival functions.
The canonical description is in terms of a cohort's covariate-constrained
functional distribution of individual hazard rates of all risks. Assuming
proportional hazards at the level of individuals leads to a natural
parametrisation of this distribution, from which Cox regression, frailty and
random effects models, and latent class models can all be recovered in special
limits, and which also generates parametrised cumulative incidence functions
(the language of Fine and Gray).
  We demonstrate with synthetic data how the generic method can uncover and map
a cohort's substructure, if such substructure exists, and remove
heterogeneity-induced false protectivity and false exposure effects.
Application to real survival data from the ULSAM study, with prostate cancer as
the primary risk, is found to give plausible alternative explanations for
previous counter-intuitive inferences.
