Journal
STATISTICS & PROBABILITY LETTERS
Volume 55, Issue 4, Pages 403-411Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/S0167-7152(01)00155-9
Keywords
multistage model; nonparametric estimation; product integral; product limit estimator; survival analysis
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We consider estimation of integrated transition hazard and stage occupation probabilities using right censored i.i.d. data that come from a general multistage model which is not Markov. We show that the Nelson-Aalen estimator for the integrated transition hazard of a Markov process consistently estimates a population quantity even when the underlying process is not Markov. Further, the Aalen-Johansen estimators of the stage occupation probabilities constructed from these integrated hazards via product integration are valid (i.e., consistent) for a general multistage model that is not Markov. These observations appear to have been unnoticed in the literature, where validity of the Aalen-Johansen estimators is only claimed for Markov models. (C) 2001 Elsevier Science B.V. All rights reserved.
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