Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. (English) Zbl 0998.62072
Summary: 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 [O.O. Aalen and S. Johansen Scand. J. Stat., Theory Appl. 5, 141-150 (1978; Zbl 0383.62058)] 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.
MSC:
| 62M09 | Non-Markovian processes: estimation |
| 62G05 | Nonparametric estimation |
| 62N02 | Estimation in survival analysis and censored data |
Citations:
Zbl 0383.62058References:
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