Decrement rates and a numerical method under competing risks

Abstract

Modeling the interactions of competing risks that affect the occurrence of various decrements such as death or disease is an essential issue in survival analysis and actuarial science. Popular assumptions for the construction of decrement models are uniform distributions of decrements in a multiple decrement table (mUDD) and associated single decrement tables (sUDD), respectively. Even though there are many theoretical generalizations to relaxing mUDD assumption, it is not clear how to obtain theoretical and numerical methods for modeling relationships of competing risks under a general assumption in associated single decrement tables beyond the sUDD. We fill this gap in the literature by discussing the conversion between probabilities of decrement and absolute rates under a general form of a distribution of fractional ages. In particular, we show that extracting absolute rates from the probabilities under the general competing risk assumption boils down to solving a system of non-linear equations and propose a novel numerical algorithm for its solution. Extensive numerical experiments relying on the algorithm verify that the algorithm delivers reliable results in terms of efficiency and accuracy.