Survival analysis with clustered observations of orthodontic brackets.

Failures in the bonding of dental bracket are a big concern for orthodontists. Clinical experience suggests that some patients are more prone than others to experience failures. Therefore, it can be expected that in statistical analysis of orthodontic bracket failures, the usual assumption of independence between the observations is violated. An approach to overcome this problem is to apply the frailty model, in which the association between failure times is modelled with a random-effect term (i.e. frailty). We postulated that brackets of the same subject share the same frailty, that is, a latent common group effect, due to some unknown or unobserved covariates.The aim of this study was to investigate possible risk factors related to bracket failure using Cox proportional hazards model with a shared frailty term and to compare the results with those obtained using a basic Cox proportional hazards model.Survival data for 1677 brackets were obtained from a cohort of 54 females (mean age +/- SD: 13.3+/-4.8 yrs) and 46 males (mean age +/-SD: 13.1+/-3.8 yrs) over a eight-year period. Age, gender, vertical craniofacial morphology and anatomical location of brackets were entered into Cox models as covariates. The findings indicated that bracket failure was significantly affected by tooth position within the dental arch, with the highest failure risk in maxillary posterior region. Age, gender and vertical craniofacial morphology did not affect bracket failure. A Cox proportional hazards model with a shared frailty term represents a useful approach for modelling orthodontic bracket failures.