A Representation of Mortality Data by Competing Risks

SUMMARY Cohort mortality data is represented by a probabilistic combination of competing risks (diseases). Each risk is described by an age-at-death distribution and a net probability of occurrence. This representation is illustrated by a set of pathology data from a well-controlled laboratory animal experiment. human health and various environmental pollutants has focused mounting attention on the analysis of mortality data. Generally, the usual actuarial methods have not been concerned as much with individual diseases as with the construction of life tables and general mortality rates (Seal 1954, Grenander 1956, Kimball 1960). However, in the case of the well-controlled laboratory animal experiment or epidemiological study, the investigator is often concerned primarily with the effects which a certain treatment (exposure to pollutants) has upon the occurrence of a few specific terminal diseases (causes of death). He may, for example, use smog as his pollutant being primarily interested in the occurence of lung tumors. When comparing his data with that from a control group, it could happen that the observed incidence of lung tumors is lower in the treated group. This situation could occur if the treatment caused a generally lower age at death throughout the population. In this manner, sufficient opportunity is not allowed for the development of lung tumors, which have a tendency of occurring in older animals. In any case, it is easy to imagine some of the possible difficulties in the interpretation of this type of data and for further discussion the reader is referred to the paper by Kimball 1958. We shall assume that we have a complete set of cohort autopsy data giving both the age and cause of death for a population. The particular data used for illustration in this paper were obtained from a well-controlled laboratory experiment. Using these data we wish to describe both the incidence and age at death for each particular cause of death. Along this line