Agreement of the Newly Developed Moyers' Equations and Moyers' Tables

Abstract

Objective: This study aimed to develop the Moyers' prediction equation to be used with tooth widths predicting app on smartphone.

Materials and methods: Four equations were developed separately for sex and dental arches. Internal validation with Moyers' table was finished. External validation on 37 subjects with agreement test of both Moyers' prediction equations and Moyers' prediction tables was performed.

Statistical analysis: A general linear model procedure was used to create four prediction equations. Internal validation was evaluated using the coefficient of determination. External validation was performed using Bland and Altman (BA) test.

Results: Four equations were developed for OrthoAnalysis app on smartphone. The overall coefficient of determination of all equations and prediction table was 0.998 (p < 0.05) indicating good agreement of the two methods. The agreement test on the 37 subjects was that the BA test revealed the BA limits of agreement between the residuals of two predictions was -0.001 mm and ranged from -0.143 to 0.140 mm with almost all plots lying inside this difference interval.

Conclusions: In summary, four novel estimation equations were developed and showed very low difference to the well accepted original Moyers' prediction tables. Therefore, the equations used in the orthodontic app for predicting unerupted tooth width were verified and valid for clinical use.

Fig. 1

Correlation plot of the predictions from Moyers' table and the developed equations. Legend: Correlation plot of the predictions from Moyers' table (abscissa) and predictions from the newly developed equations (ordinate). Both abscissa and ordinate coordinate's distribution showed strong positive correlation.

Fig. 2

Residual plots between the two methods. All 148 residuals of the two methods were sorted from the least to the largest and plotted along the x-axis, using a cross symbol for Moyers' equation and a circle symbol for the Moyers' table. The y-axis showed the unit of difference from actual tooth width in mm. The plots of both predictions distributed very close to each other in almost every individual pair reflecting an agreement of these two prediction methods.

Fig. 3

Bland and Altman (BA) plot of the difference of residuals of both prediction methods. Legend: BA plot of the difference of residuals that is the difference between the prediction result and the real tooth width of both prediction methods. The averages of the residuals of two methods were plotted against the x-axis. The differences of the residuals of the two methods were plotted against the y-axis. The dotted line represented the 95% limit of agreement (LoA) showing the limit of the acceptability of the difference. The BA LoA between the residuals of these two prediction methods was only −0.001 mm and ranged from −0.143 to 0.140 mm with almost all plots lying inside the difference interval.