Canine-related variables

• 1.

  Crowding in the maxillary anterior region.

• 2.

  The maxillary deciduous canine was assigned to 1 of 3 categories: missing tooth, where the deciduous canine had been extracted; present without root resorption; or present with root resorption.

• 3.

  Canine development was assigned to 1 of 4 categories based on root development: complete development, 75% of the root developed, 50% of the root developed, and 25% of the root developed.

• 4.

  Canine apex: open, closed, or dilacerated.

• 5.

  Detection of abnormalities, such as canine root resorption, mesiodens, peg-shaped lateral incisor, agenesis of permanent teeth, and impaction of other permanent teeth.

• 6.

  Canine rotation: mesiovestibular, distovestibular, mesiopalatal, or distopalatal.

• 7.

  Canine position in relation to adjacent teeth was determined from the CBCT images as palatal, buccal, or in the line of the arch.

• 8.

  Type of canine impaction was assigned to 1 of 3 categories: no impaction; vertical impaction, if the impacted canine was vertically inclined and covered with soft or bony tissue; and horizontal impaction, if the impacted canine was horizontally inclined and covered with soft or bony tissue.

• 9.

  The roots of the first premolar were categorized as single root, separated roots, or fused roots.

• 10.

  Anterior apical area was recorded as optimal, small, or severe.

• 11.

  Contact relationship between the canine and adjacent teeth was assigned to 1 of 2 categories based on the categories suggested by Ericson et al : contact, if the distance between the crown of the maxillary permanent canine and adjacent incisors is less than 1 mm; and no contact, if the distance between the crown of the maxillary permanent canine and adjacent incisors is more than 1 mm.

Linear measurements in millimeters

• 1.

  Canine cusp tip to the midline was measured in the axial view ( Fig 1 , A ).

  

  Cross-sectional CBCT images illustrating the reference lines of linear measurements: A, canine cusp tip and canine apex to the midline measured in the axial view; B, width of the canine and lateral incisor crown buccolingually measured in the sagittal view; C, length of the lateral incisor measured in the sagittal view.

• 2.

  Canine cusp tip to the occlusal plane was measured in the sagittal view. The occlusal plane was defined as the line from the mesiobuccal cusp of the maxillary first molar to the incisal edge of the maxillary central incisor in the sagittal view ( Fig 2 , A ).

  

  Cross-sectional CBCT images illustrating the reference lines of linear and angular measurements: A, canine cusp tip to the occlusal plane measured in the sagittal view; B, canine angulation to the occlusal plane measured in the sagittal view; C, lateral incisor inclination to the maxillary plane measured in the sagittal view.

• 3.

  Canine apex to the midline was measured in the axial view ( Fig 1 , A ).

• 4.

  Width of the canine crown buccolingually and mesiodistally was defined as the distance from the mesial contour to the distal contour of the maxillary canine ( Fig 1 , B ).

• 5.

  Width of the lateral incisor was measured buccolingually and mesiodistally at the cementoenamel junction ( Fig 1 , B ).

• 6.

  Length of the lateral incisor from the incisal edge to the apex was measured in the sagittal view ( Fig 1 , C ).

• 7.

  The mesiodistal space available for the canine between the lateral incisor and the first premolar at the occlusal level and at the apical thirds was measured in the axial view.

Angular measurements in degrees

• 1.

  Canine angulation to the midline, where the angle is formed by the long axis of the impacted canine and the midline of the maxilla in the coronal view ( Fig 3 ).

  

  Coronal view of CBCT image illustrating the reference lines of the angular measurements: A , canine angulation to the midline; B , canine angulation to the lateral incisor.

• 2.

  Canine angulation to the lateral incisor, where an angle is formed by the long axis of the impacted canine and the long axis of the lateral incisor in the coronal view ( Fig 3 ).

• 3.

  Canine angulation to the occlusal plane, where the angle in the sagittal view is formed by the long axis of the impacted canine and the occlusal plane ( Fig 2 , B ).

• 4.

  Lateral incisor inclination to the maxillary plane, where the angle in the sagittal view is formed by the long axis of the lateral incisor and the maxillary plane ( Fig 2 , C ).

Statistical analysis

Analyses were performed on data from subjects with unilateral impaction. The aim of this study was to predict whether a canine would be impacted, not whether a patient had an impacted canine. Therefore, in the statistical analysis, independent instead of dependent tests were used; Fisher exact tests and Mann-Whitney U tests were used to compare scores and measurements between impacted and nonimpacted canines from patients with unilateral impaction. The area under the receiver operating curve (AUC) was reported for each score and measurement to quantify the discriminative ability (0.5 = random prediction, 1 = perfect discrimination). The reliability of the measurements was assessed using the records of 12 randomly selected patients and having the same investigator (A.A.) repeat the linear and angular measurements. The systematic error was evaluated with the intraclass correlation coefficient (ICC).

From these results, 6 variables were considered for a multivariable model, based on the AUC, clinical considerations, and the correlations among the variables. A backward selection procedure, with 0.157 as the critical level for the P value, was applied to obtain a more parsimonious prediction model. This critical value corresponds to the use of the Akaike information criterion (AIC) for model selection. With the AIC, we required the increase in the model’s chi-square value to be larger than 2 times the degrees of freedom. A bootstrap resampling procedure was used to verify whether the variables retained in the final multivariable model are truly independent predictors or, rather, are noise variables. In the applied modeling approach, the same data were used to develop and validate the model. Furthermore, there was a clear risk of overfitting, originating from consideration of many predictors compared with the number of impactions and from the application of an automated model selection procedure. The resulting prediction model and its related AUC were therefore overoptimistic, in the sense that the future performance in new patients was overestimated. Therefore, a leave-1-out cross-validation was applied. Also, an optimism-corrected estimate of the performance (AUC) was obtained by a bootstrap resampling procedure. All analyses were performed with SAS software (version 9.2 for Windows; SAS, Cary, NC).