In this talk we consider the estimation and inference problem of interval censored data. These types of data arise when patients are followed-up at different visits and the exact occurence of the event of interest is unknown. Instead, one only knows that the event has occurred between two time visits. These data also encompass left-censored observations (when the event has occurred before the first visit) and right-censored data (when the event has not yet occurred after the last follow-up time). We study the nonparametric and regression settings by specifying a piecewise constant function for the hazard rate. Treating the true event times of interest as unobserved data, the EM algorithm is implemented. In order to determine the number and locations of the cuts of the hazard function, a L0 penalized likelihood method is used, such that a large grid of cuts is initially implemented and the penalization technique forces two similar adjacent values to be equal. Statistical inference of the model parameters are derived from likelihood theory. The method is illustrated on a dental dataset where 322 patients with 400 avulsed and replanted permanent teeth were followed-up prospectively in the period from 1965 to 1988 at the university hospital in Copenhagen, Denmark. The following replantation procedure was used: the avulsed tooth was placed in saline as soon as the patient was received at the emergency ward. If the tooth was obviously contaminated, it was cleansed with gauze soaked in saline or rinsed with a flow of saline from a syringe. The tooth was replanted in its socket by digital pressure. The patients were then examined at regular visits to the dentist. In this study, we focused on a complication called ankylosis such that the variable of interest is the time from replantation of the tooth to ankylosis. 28% of the data were left censored, 35.75% were interval censored and 36.25% were right censored. A Cox model was implemented on this dataset and showed that the stage of root formation (mature or immature tooth) and the length of extra-alveolar storage time were significantly associated with the risk of experiencing ankylosis.
This is a joint work with Grégory Nuel (DR CNRS, LPSM, Paris 6) and Eva Lauridsen (Department of Pediatric Dentistry and Clinical Genetics, School of Dentistry, University of Copenhagen).