Competing Risks and Conditional Probabilities

This paper is in response to an article by Kimball [1969] on evaluation of the partial crude probabilities in the theory of competing risks. Contrary to Kimball's conclusions, it is shown that the general model of competing risks under the proportionality assumption satisfies the criteria of internal consistency and reasonableness in describing survival and death processes, and that the conditional probability suggested as a substitute for the partial crude probability violates these criteria.