In multistage models, individuals (or experimental units) move through a succession of "stages" corresponding to distinct states. The resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied. Traditional survival analysis is the simplest example of a multistage model, where individuals begin in an initial stage (say, alive) and may move irreversibly to a second stage (death). In this paper, we consider general multistage models with a directed tree structure in which individuals traverse through stages in a possibly non-Markovian manner. We construct nonparametric estimators of various marginal quantities related to the model such as the stage occupation probabilities and the marginal cumulative transition hazards. Empirical calculations of these quantities are not possible due to the lack of complete data. We consider more severe forms of censoring than the commonly used right censoring such as the current status and interval censoring schemes. Asymptotic validity of our estimators is justified through approximate unbiasedness arguments. Finite sample behavior of our estimators is studied by simulation. We show that our estimators based on these limited data compares well with those based on complete data. A real data example is also provided as an illustration of our method where we could compare our results with the empirical answers.
Nonparametric Marginal Estimation in a Multistage Model Using Current Status Data