Estimating survival of dental fillings on the basis of interval-censored data and multi-state models

We aim to compare the life expectancy of a filling in a primary tooth between two types of treatments. We define the probabilities that a dental filling survives without complication until the permanent tooth erupts from beneath (exfoliation). We relate the time to exfoliation of the tooth to the age of the child and the time to failure of the filling to the duration since the treatment. We followed up fillings at repeated examinations where information is collected regarding the filling and the tooth. Several fillings can be placed in the same mouth, possibly by the same dentist. To deal with all these particularities, we propose to use a parametric four-state model with three random effects to take into account the hierarchical cluster structure. For inference, right and interval censoring as well as left truncation have to be dealt with. With the proposed approach, we can conclude that the estimated probability that a filling survives without complication until exfoliation is larger for one treatment than for the other, for all ages of the child at the time of treatment.