Fast Change Detection on Proportional Two-population Hazard Rates

We consider the problem of detecting an abrupt change on the structural relationship between two mortality rates. In this paper, we are particularly interested in a form of relationship between two population mortality based on the so-called proportional hazard rate framework. In order to set up an optimal detection procedure, we broadly follow the framework introduced in Lorden (1971), adapted to the case of sequentially observed Poisson process. In this case, we show that the cumulative sums algorithm is still optimal in the case of inhomogeneous Poisson process but for criterion that replaces the expected delay by the number of events until detection. To do so, an interesting connection is made between the initial problem and the classical ruin theory. Finally, a numerical analysis is provided based on Monte Carlo simulations but also on real datasets of insured and national populations.