Nonparametric Estimation of Marginal Temporal Functionals in a Multi-State Model

Multi-state models are generalizations of traditional survival analysis and reliability studies. They are common in medical and engineering applications where a subject (say a patient or a machine) is moving through a succession of states (each representing a stage of disease progression or the condition of a machine) with time. In addition, several key questions in event history analysis and multi-variate survival analysis can be formulated in terms of a staged system making the use of multi-state models extremely broad. While the use of parametric and semiparametric models to various transitions are the most common approaches to study multi-state data, this overview paper deals entirely with nonparametric methods. In addition, we limit our exposition to estimation questions related to marginal models rather than conditional (e.g., regression) models. We review a number of methods from the recent past dealing with estimation of hazards, transition and state occupation probabilities, state entry, exit and waiting time distributions and also discuss some ongoing and future research problems on these topics. Various forms of censoring that occur in the collection of multi-state data are discussed including right and interval censoring.