The competing risks illness-death model under cross-sectional sampling

The competing risks illness-death model describes the dynamics of healthy subjects who may move to an "illness" state before entering into one of several competing terminal states. A motivating example concerns patients in a hospital who may acquire infections during their stay, where the competing terminal states are discharged alive and death in the hospital. We consider a cross-sectional sampling of independent competing risks illness-death processes in which data are subject to length bias and censoring and develop estimators for functionals of the underlying distribution such as the joint probability of the terminal state and illness (infection) and cumulative incidence functions. We apply the methodology to infection data obtained in a cross-sectional study of patients hospitalized in intensive care units.