On the linearization of eruption series of the permanent teeth

In order to confirm the linearization of permanent eruption, Masuyama's linearization method was applied to the data of Kitamura's study. At first, we considered the eruption age t alpha i of permanent teeth T alpha, where alpha corresponds a tooth of every description, and examined the linear regression of Y alpha i = log10 t alpha i on m(y) alpha (the mean of Y alpha i with respect to i), but the result was not good. For the correlation coefficient r between two variables in linear regression, the percentage of subjects with r > or = 0.970 was only 10.3% in males and 28.8% in females in Kitamura's study. Next we took notice of the eruption age u beta i of each tooth, which is the beta-th in order of eruption. The fitness of the linear regression of Z beta i = log10 u beta i on mz beta (the mean of Z beta i) was very good. The percentage of subjects with r > or = 0.970 increased to 80.0% in males and 86.0% in females. Then we used m(y) (beta) (rearranged m(y) alpha in order of increasing size) instead of mz beta as an independent variable in the linear regression. The degree of the linearization was slightly inferior to that using mz beta. In every linearization, a quasi-fixed point with coordinates (C, C) existed on the linearized dentition plot, where the value of C was almost equal in each way, i.e., C = 10.23 (years) for males and C = 8.91 (years) for females in Kitamura's data. This linearized dentition plot will be useful in detecting certain growth disturbances. The existence of a quasi-fixed point may be useful in forecasting the age of the eruption of subsequent teeth, once the first eruption is observed.