Modeling multiple risks in the presence of double censoring

Self-consistent (SC) iterative algorithms will be proposed to non-parametrically estimate the cause-specific cumulative incidence functions in a multiple decrement, doubly censored context. Double censoring is defined to include both left and right censored observations, in addition to exact observations. The algorithms are a generalization of the classical univariate algorithms of Efron and Turnbull. Unlike any previous competing risk models proposed in the literature to date, the proposed algorithms will be fully non-parametric while also explicitly allowing for the possibility of masked modes of failure, whereby failure is known only to occur due to a subset from the set of all possible causes. In short, the method is useful in any actuarial application that encounters censored and/or masked risks. The paper concludes by showing how the method can be applied to employee benefits modeling.