Net probabilities in the theory of competing risks

The problem of the hypothetical elimination of a cause of death is considered. It is demonstrated that models proposed by Kannisto (1947), Dorn (1950), Kimball (1958), Chiang (1961), and Schwartz & Lazar (1964) do not provide alternatives for the general model for independent risks suggested by D'Alembert in 1761 (cf. Todhunter, 1949), and that the model of Chiang may be regarded as in principle the best possible approximation to D'Alembert's model. The results given by all of the models converge towards those of the general model for independent risks when the subdivision of the period of observation is increased, and the lengths of the subintervals tend towards zero.