A Bayesian analysis of amalgam restorations in the Royal Air Force using the counting process approach with nested frailty effects.

Survival analysis methods are increasingly used in dental research to measure risk of tooth eruption and caries as well as life spans of amalgam restorations. Analyses have been extended to account for lack of independence in the data, which arises from the clustering of observations within units such as tooth-surfaces, teeth and subjects. There are various analytical strategies and modelling approaches now available to us in dealing with clustered dental data. In this article, the modelling strategy of Cox's proportional hazards regression is formulated using the counting process approach, which can easily be extended to include time-variant covariates as well as nested random frailty effects. A semi-parametric Bayesian method is presented for the analysis of the proposed model. The methodology is applied to an analysis of nested clustered data on life-span of amalgam restorations in the UK Royal Air Force. These data have previously been analysed using a non-Bayesian approach. The Gibbs sampler, a Markov chain Monte Carlo method, is used to generate samples from the marginal posterior distribution of the parameters of this Bayesian model.