Studies in the History of Probability and Statistics. XXXV: Multiple decrements or competing risks

Given two states A and B such that individuals in state A have mutually exclusive probabilities, possibly dependent on the time spent in state A, of leaving that state because of (i) death, or (ii) passage to state B, what is the probability of an individual passing to state B and dying there within a given period? This problem has been of great interest and importance to actuaries for over 100 years and the solutions of their professional contemporaries have appeared in their textbooks. Twenty-five years ago statisticians felicitously named the technique the theory of competing risks (Neyman, 1950) and developed the formulae ab initio in the framework of Markov processes. Consideration of the problem started with Daniel Bernoulli's smallpox mathematics and continued with pension fund financing involving the payment of annuities to invalid lives. Most of the currently accepted techniques were developed during the nineteenth century. This article reviews the history both of actuarial and statistical contributions to the literature