In this paper we investigate dependencies between associated diseases that a person has at the end of his live and the cause of death. We analyze public data about cause-specific mortality in conjunction with the problem of average risk estimation on empirical data. The use of the theory of Vapnik-Chervonenkis provides informative results about differences between distributions of associated diseases in group of people who died of cancer and group of people who died of another disease. This difference uncovers a relationship between some groups of associated diseases and risk of death of cancer.