Institute of Medical Statistics and Biometry Giulio A. Maccacaro, University of Milan, Milan, Italy.
Stat Med. 2009 Dec 10;28(28):3483-91. doi: 10.1002/sim.3641.
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.
正畸医生非常关注牙科托槽的粘结失败问题。临床经验表明，有些患者比其他患者更容易出现粘结失败。因此，可以预计在正畸托槽失败的统计分析中，通常假设观察结果之间是相互独立的，这一假设是不成立的。解决此问题的一种方法是应用脆弱性模型，该模型用随机效应项（即脆弱性）来模拟失败时间之间的关联。我们假设同一患者的托槽具有相同的脆弱性，即由于某些未知或未观察到的协变量，存在一个潜在的共同组效应。本研究旨在使用具有共享脆弱性项的 Cox 比例风险模型来研究与托槽失败相关的可能风险因素，并将结果与使用基本 Cox 比例风险模型获得的结果进行比较。在 8 年的时间里，从 54 名女性（平均年龄 +/- SD：13.3 +/- 4.8 岁）和 46 名男性（平均年龄 +/- SD：13.1 +/- 3.8 岁）的队列中获得了 1677 个托槽的生存数据。年龄、性别、垂直颅面形态和托槽的解剖位置作为协变量被纳入 Cox 模型。研究结果表明，托槽失败明显受到牙弓内牙齿位置的影响，上颌后区的失败风险最高。年龄、性别和垂直颅面形态不影响托槽失败。具有共享脆弱性项的 Cox 比例风险模型是一种用于模拟正畸托槽失败的有用方法。
