Characterizations of Competing Risks in Terms of Independent‐Risks Proxy Models

In competing risks a failure time T and a cause C , one of p possible, are observed. A traditional representation is via a vector ( T 1 , ..., T p ) of latent failure times such that T = min( T 1 , ..., T p ); C is defined by T = T C in the basic situation of failure from a single cause. There are several results in the literature to the effect that a joint distribution for ( T 1 , ..., T p ), in which the T j are independent, can always be constructed to yield any given bivariate distribution for ( C , T ). For this reason the prevailing wisdom is that independence cannot be assessed from competing risks data, not even with arbitrarily large sample sizes (e.g. Prentice et al. , 1978). A result was given by Crowder (1996) which shows that, under certain circumstances, independence can be assessed. The various results will be drawn together and a complete characterization can now be given in terms of independent‐risks proxy models.