View article

Background In studies of all-cause mortality, the fundamental epidemiological concepts of rate and risk are connected through a well-defined one-to-one relation. An important consequence of this relation is that regression models such as the proportional hazards model that are defined through the hazard (the rate) immediately dictate how the covariates relate to the survival function (the risk).

Methods This introductory paper reviews the concepts of rate and risk and their one-to-one relation in all-cause mortality studies and introduces the analogous concepts of rate and risk in the context of competing risks, the cause-specific hazard and the cause-specific cumulative incidence function.

Results The key feature of competing risks is that the one-to-one correspondence between cause-specific hazard and cumulative incidence, between rate and risk, is lost. This fact has two important …