Validity of the Aalen–Johansen estimators of stage occupation probabilities and Nelson–Aalen estimators of integrated transition hazards for non-Markov models
✍ Scribed by Somnath Datta; Glen A. Satten
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 120 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
✦ Synopsis
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.