Semi-Markov models for partially censored data

Nonparametric likelihood methods are developed for the analysis of partially censored data arising from a multistate stochastic process. It is assumed that the underlying process follows a semi-Markov model in which state changes form an embedded Markov chain and sojourn times are independent with distributions depending only on adjoining states. The general likelihood function for a set of partially censored observations is determined and maximized nonparametrically. The resulting nonparametric maximum likelihood estimators of the model unknowns are found to have several attractive properties. Approximate distributional results are derived.