Abstract
We develop nonparametric maximum likelihood estimation for the parameters of an irreversible Markov chain on states {0,1,2} from the observations with interval censored times of 0 → 1, 0 → 2 and 1 → 2 transitions. The distinguishing aspect of the data is that, in addition to all transition times being interval censored, the times of two events (0 → 1 and 1 → 2 transitions) can be censored into the same interval. This development was motivated by a common data structure in oral health research, here specifically illustrated by the data from a prospective cohort study on the longevity of dental veneers. Using the self-consistency algorithm we obtain the maximum likelihood estimators of the cumulative incidences of the times to events 1 and 2 and of the intensity of the 1 → 2 transition. This work generalizes previous results on the estimation in an "illness-death" model from interval censored observations.
| Original language | English |
|---|---|
| Journal | Biometrical journal. Biometrische Zeitschrift |
| Volume | 55 |
| Issue number | 6 |
| Pages (from-to) | 823-43 |
| Number of pages | 21 |
| DOIs | |
| Publication status | Published - Nov 2013 |
Keywords
- Dental data
- Interval censored "illness-death" model
- Nonparametric maximum likelihood estimation
- Randomized cohort study
- Self-consistency equations