Thank you for your comments on our article, “Morphometric analysis of cervical vertebrae in relation to mandibular growth.” Your interest in our research has given us the opportunity to provide more data and to further clarify some aspects of our research.
One strength of using Burlington Growth Study data was its longitudinal nature, which allowed repeated measurements of the same subjects over time. Because of this, we were able to accurately determine the mandibular growth peak using the difference between mandibular length at each time point (1-year intervals) and the preceding stage. As reported in our article, peak mandibular growth was found at CVM stages 1 to 4 with similar frequency. The null hypothesis that peak growth occurs with equal probability across these stages could not be rejected (1-sample chi-square test, P = 0.782). This is the first reason that we concluded that CVM stages could not accurately identify the mandibular growth peak.
In addition to this analysis, we entered mandibular length as a response variable in a mixed model analysis. Modeling mandibular length as a function of time and cervical stage is equivalent to testing for the effect of age and cervical stage on “mandibular growth rate” because this may be simplistically defined as a change in length over time. In a supplementary analysis not reported in our article, all first-order interactions between CVM stage, sex, and chronologic age were entered in the mixed model. The result of this model is summarized in the Table . As expected, the rate of mandibular growth was strongly influenced by chronologic age, sex, and the interaction of age and sex. However, neither the main effect of CVM nor its first-order interactions with sex and chronologic age were statistically significant. This represents additional evidence against the validity of the CVM method.
| Covariate ∗ | F ratio | P value |
|---|---|---|
| CVM | 0.51 | 0.767 |
| Sex | 4.20 | 0.052 |
| CVM × sex | 1.38 | 0.248 |
| Chronologic age | 26.59 | <0.001 |
| Chronologic age × sex | 2.72 | 0.025 |
| CVM × chronologic age | 0.45 | 0.939 |
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