A probabilistic approach to the construction of competing-risk life tables

"This paper aims to identify net and partial-crude probabilities in the competing-risk life table context, by using probabilistic approaches. Five types of lifelength random variables are defined to formulate these nonidentifiable probabilities. General expressions for net and partial-crude probabilities are first derived under independent risks assumptions. Two sets of explicit formulas for estimating the net and partial-crude probabilities are then derived in terms of the identifiable overall and crude probabilities by making the additional assumption of piecewise uniform distribution of the lifelength random variables. A study of the degree to which nonidentifiability can affect the net and partial-crude probabilities in a variety of situations is developed. An example from cross-sectional studies is employed to illustrate the methodology developed."