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.

Multilevel survival analysis of amalgam restorations amongst RAF personnel.

OBJECTIVE: To introduce the concepts of multilevel survival analysis through an investigation into the longevity of amalgam restorations. BASIC RESEARCH DESIGN: The multilevel Cox proportional hazard model is illustrated using amalgam restoration data comprising three levels: repeated restorations at level-1, teeth at level-2, and subjects at level-3. The outcome was duration of amalgam restoration survival. Single-level and multilevel Cox methods are contrasted. PARTICIPANTS: The data were from a survey of amalgam restorations (reported elsewhere), involving 200 RAF personnel aged between 16 and 37 years at enlistment between 1947 and 1979, having served continuously for a minimum of 16 years prior to 1994. RESULTS: Differences existed between single-level and multilevel methods; the latter being the method of choice. Initial caries experience was a good predictor of longevity. Molar teeth fared worse than pre-molars and MOD & B, MOD & L, and MOD & BL restorations experienced considerably greater risk of failure than did MOD, MO, DO and MO/DO ext types, which in turn fared worse than occlusal restorations. Root-treated and pinned teeth also experienced an elevated risk of premature failure. There was a moderate but significant increase in restoration failure amongst subjects who were seen by more dentists throughout their service. CONCLUSIONS: The application of multilevel modelling to survival analysis provides an appropriate and powerful solution to the problem of lack of independence amongst dental restorations. It is beneficial that studies undertake a multilevel analysis in preference to ignoring hierarchy or omitting swathes of information in order to perform a single-level analysis.