Evaluation of the predictive impact of cephalometric variables. Logistic regression and ROC curves

In the context of orthodontic treatment planning, the decisions to be made are often affected by the assumption of future growth patterns, especially the direction of mandibular rotation. Using longitudinally available lateral cephalograms from the Belfast Growth Study, it was examined whether, on the basis of the cephalometric variables at the ages of 7, 9 and 11, the direction of mandibular rotation can be predicted in the respective subsequent 4-year intervals. For statistical analysis of this problem, logistic regression models were applied to describe and quantify the influence of potential explanatory variables on the direction of mandibular rotation (dependent variable). In addition, graphical methods taken from the field of medical diagnostics were applied for prediction and for determination of predictive accuracy. The use of logistic regression models revealed no relations between the explanatory variables SN-MeGo and S-Go/N-Me and the subsequent mandibular growth pattern. Only the upper and lower parts of the gonial angle showed a minor predictive impact. A graphical evaluation of their prognostic impact by means of "receiver operating characteristics" (ROC) curves, complemented by determination of the areas under the curves, confirmed the relations discovered. Nevertheless the prognostic limits of the lateral cephalogram emerged clearly for all variables investigated.