Table 2 Examined variables of children’s three-dimensional occlusal features [19, 20]

λ Incisor relationship, classified as:

Class I: lower incisor edges occlude with or lie immediately below the cingulum plateau of upper incisors.

Class II: lower incisors edges lie posterior to the cingulum plateau of upper incisors.

Class III: lower incisors edges lie anterior to the cingulum plateau of upper incisors. The overjet is reduced or reversed.

λ Anterior crossbite, classified as:

Segments: Both 11, 21 and or more maxillary incisors occluded lingual to mandibular incisors.

Individual teeth: One maxillary incisors occluded lingual to mandibular incisors.

λ Overjet :

measured from the palatal surface of the mesial corner of the most protruded fully erupted maxillary incisor to the labial surface of the corresponding mandibular incisor. In this study, an overjet of greater than 3 mm was considered increased overjet.

λ Reverse overjet

Measured from the incisal edge of mandibular incisors to the labial surface of the most retruded fully erupted maxillary incisor, which is in anterior crossbite

λ Primary canine relationship, classified as:

Class I: tip of maxillary primary canine tooth is in the same vertical plane as the distal surface of mandibular primary canine

Class II: tip of maxillary primary canine tooth is mesial to the distal surface of mandibular primary canine

Class III: tip of maxillary primary canine tooth is distal to the distal surface of mandibular primary canine

λ Primary molar relationship, classified as:

Flush terminal: the distal surfaces of the upper and lower second primary molars are in the same vertical plane in centric occlusion

Distal step: the distal surfaces of the lower primary second molar is in a posterior relationship to the distal surface of the upper second molar in centric occlusion

Mesial step: the distal surfaces of the lower primary second molar is in an anterior relationship to the distal surface of the upper second molar in centric occlusion

λ First molar relationship, classified as:

Class I: mesiobuccal cusp of the upper first molar occludes with the mesiobuccal groove of the lower first molar. Discrepancies of up to half a cusp width either way were also included in this category.

Class II: mesiobuccal cusp of the lower first molar occludes distal to the Class I position.

Class III: mesiobuccal cusp of the lower first molar occludes mesial to the Class I position.

In addition, categories of permanent molars haven’t established occlusion and permanent molars unerupted are included.

λ Anterior overbite

Coverage of the mandibular incisor by the fully erupted maxillary incisor, classified as:

< 0, 0–1/2, >1/2, with reference to the clinical crown height of the mandibular incisors.

λ Posterior open bite

When there are no vertical contacts between upper and lower occlusal surfaces of posterior teeth, both unilaterally or bilaterally.

λ Crossbite, recorded on right and left sides, classified as:

No crossbite present

Crossbite: When one or more of mandibular canines and molars occluded buccally to the buccal cusps of opposing maxillary teeth molars

Lingual crossbite: When one or more of the mandibular primary canines or molars occluded lingually to the lingual cusps of the opposing maxillary teeth