Coarsening at random in general sample spaces and random censoring in continuous time

Heitjan and Rubin proposed a concept, coarsening at random, generalizing Rubin's theory of missing at random. Their analysis was done in discrete sample spaces. We propose a generalization to general sample spaces. Among Heitjan and Rubin's applications was right-censoring in survival analysis. We discuss the application of the generalized theory to various censoring patterns in continuous time and connect to the modern theory of random censoring.