Marginal Estimation of Stage Occupation Probabilities in a Multistage Model with Current Status Data
by
Somnath Datta
Department of Bioinformatics and Biostatistics, University of Louisville
Coauthors: Rajeshwari Sundaram

Multistage models are used to describe individuals (or experimental units) moving through a succession of “stages” corresponding to distinct states (for example, healthy, diseased, diseased with complications, dead). 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 (progressive models) in which individuals traverse through stages in a possibly non-Markovian manner. We construct nonparametric estimators of 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 current status information which represents a more severe form of censoring than the commonly used right censoring. Asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators. Finite sample behavior of our estimators is studied by simulation, in which we show that our estimators based on these limited data compares well with those based on complete data. We also apply our method to a real life data set arising from a cardiovascular diseases study in Taiwan. We also discuss how covariates, if available, could be incorporated into this marginal estimation approach by modeling the inspection time distribution semiparametrically.

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Date received: September 30, 2005