Dependent Decrement Theory

Currently, multiple decrement theory is based on the assumption that competing causes of decrement are stochastically independent, even though this assumption is usually not true in reality. This paper presents wellknown results in the theory of dependent competing risks that are fundamental in extending multiple decrement theory towards a dependent decrement theory. First, the state of the art is examined and the results that are based on the independence assumption are identified. Next, we use the well-developed theory of copula functions to model dependence, and we present a theorem that characterizes the mathematical relationship between the crude and net probabilities when the decrements are dependent. We also discuss the issue of identifiability and the related issue of measuring the effect of removing causes of decrement. Finally, we use an identifiability result to analyze the effect of removing heart/cerebrovascular diseases from the U.S. population when these diseases are correlated to other: causes of death.