• Dental data;
  • Interval censored “illness-death” model;
  • Nonparametric maximum likelihood estimation;
  • Randomized cohort study;
  • Self-consistency equations

We develop nonparametric maximum likelihood estimation for the parameters of an irreversible Markov chain on states inline image from the observations with interval censored times of 0 [RIGHTWARDS ARROW] 1, 0 [RIGHTWARDS ARROW] 2 and 1 [RIGHTWARDS ARROW] 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 [RIGHTWARDS ARROW] 1 and 1 [RIGHTWARDS ARROW] 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 [RIGHTWARDS ARROW] 2 transition. This work generalizes previous results on the estimation in an “illness-death” model from interval censored observations.