Survival analysis with clustered observations of orthodontic brakets

Objectives: Failure of brackets after bonding is still a big concern for orthodontists. It can be expected that these failures are influenced from a number of factors, including age, gender, position within the mouth and due the well-known difference of occlusal forces between short-face and long-face subjects, also from vertical craniofacial morphology. So far, the effects of these factors on bonding failures have been poorly investigated, also because of methodological difficulties. The aim of this study was to determine the effects of age, gender, location within the mouth, and vertical craniofacial morphology on failures of orthodontic brackets. Methods: Data were collected from a group of patients treated with fixed orthodontic appliances over a ten-year period in a dental practice in Naples (Italy), using a retrospective cohort design. We collected clinical records from 100 patients (46 males and 54 females; age range 7-40 years), who underwent orthodontic treatment by means of 1677 brackets. For each patient, the following information was obtained: age at the start of treatment, gender, vertical craniofacial morphology (short-, normal-, and long-faces) and mouth location of each bracket (maxillary or mandibular teeth, anterior or posterior segment of dental arch). The outcome variable was bracket failure. In the setting of correlated survival observations, we estimated the survival of orthodontic brackets, assuming dependence among multiple observations within the same subject. Our hypothesis was that the brackets in the mouth of the same subject share the same frailty that is a latent common group effect, due to some unknown or unobserved common covariates. We used Cox proportional hazards model with a shared frailty to account for correlation between brackets belonging to the same subject. Across subjects, the frailties were assumed to be gamma-distributed latent random effects that affect the hazard multiplicatively. Results: The risk of the brackets failure was not significantly related to age, gender, and vertical craniofacial morphology, whereas it is positively associated with the location of brackets with hazard ratio of 1.90 (95% CI: 1.47-2.46) for posterior maxilla, 1.61 (95% CI: 1.25-2.09), for posterior mandible and 0.93 (95% CI: 0.72-1.21) for anterior mandible, as compared to anterior maxilla. Conclusions: The failure of orthodontic brackets is affected by the location of the brackets within the mouth, with the highest failure risk at the maxillary posterior regions. Age, gender and vertical craniofacial morphology do not affect the survival of brackets. The Cox proportional hazards model with a shared frailty represents an interesting approach for investigations of clustered observations in orthodontic research.