title: Nonparametric estimation in an "illness-death" model when all transition times are interval censored.
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.
authors.affiliation: Stern School of Business, New York University, New York, NY, 10012, USA.
authors.forename: Halina
authors.initials: H
authors.lastname: Frydman
authors.forename: Thomas
authors.initials: T
authors.lastname: Gerds
authors.forename: Randi
authors.initials: R
authors.lastname: Grøn
authors.forename: Niels
authors.initials: N
authors.lastname: Keiding
mesh_terms: D000465:Algorithms; D015331:Cohort Studies; D003801:Dental Veneers / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains; D015233:Models, Statistical; D018709:Statistics, Nonparametric; D013997:Time Factors
keywords: Dental data; Interval censored “illness-death” model; Nonparametric maximum likelihood estimation; Randomized cohort study; Self-consistency equations