Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models
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.
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Volume (Year): 55 (2001)
Issue (Month): 4 (December)
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- Satten, Glen A. & Datta, Somnath & Robins, James, 2001. "Estimating the marginal survival function in the presence of time dependent covariates," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 397-403, October.
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