# A Statistical Procedure for Exploring a Skeletal Age-Explicative Tool for Growing Patients
## 1 Introduction  
The assessment of skeletal age is one of the most important determinants of treatment outcomes in growing patients whenever the targets are skeletal structures, like in orthopedics, orthodontics, and pediatrics [1]. In such disciplines, the problem of skeletal age estimation plays a fundamental role [2]. Although the literature provides contradictory evidence about the actual possibility of affecting growth's driving factors, the debate is still open, and many clinicians prefer to start orthodontic treatment during an active growth phase to take advantage of it. A representative example is the intervention for skeletal class II malocclusions, whose treatment yields optimal results when carried out around the pubertal growth spurt, during which the peak of mandibular growth is also observed [3]. In many cases, the orthodontists must be able to determine whether the subject is in a slowor fast-growing phase and for how long the growth can be expected to last in order to plan the intervention [4; 5]. Therefore, many methods for skeletal age assessment have been developed and described. The simplest indicator of skeletal maturity is chronological age. Unfortunately, the literature shows that this simple indicator is also the worst. Indeed, puberty starts at very different ages in different individuals, even for subjects of the same sex [6; 7]; therefore, skeletal age does not always correspond to chronological age [8; 9]. On the other hand, the method considered to be the gold-standard is the evaluation of the level of bone maturation of the phalanges and wrist bones, using technique described by different authors [6; 10]. Because this requires an additional radiograph of the hand, which has no other clinical value for orthodontic diagnosis, authors have tried to identify less invasive methods. An example is the evaluation of the skeletal maturation stage of the second, third, and fourth cervical vertebrae on lateral cephalograms [11; 12]. The so-called \"ecervical vertebral maturation method\" showed an acceptable correlation with the hand-wrist maturation method [12]. Although useful in reducing the patient's radiation exposure [13], some authors questioned its precision in assessing the skeletal maturation stage. A simpler method for the assessment of bone maturation is based on radiographic analysis of the second phalanx of the middle finger [14; 15; 16; 17; 18] instead of the whole hand. Another technique for the estimation of skeletal age was proposed by [PERSON] et al. and is based on dental maturity (root and crown) assessed on orthopantomography (OPC) [19]. [PERSON] et al. proposed another method that was based on mandibular morphometric measurements, like condylar height and tangential ramus height (the height of the ramus measured a line passing from the top of the condyle and intersecting with a line tangential to the gonion of the mandible), which were reported to be correlated with chronological age [20]. Moreover, due to the correlation found between dental age and skeletal age, some authors suggested that dental age assessment could be a supplementary tool for estimating a patient's pubertal spurt in Class II malocclusion cases, which is considered the best period for the treatment [21], providing significant improvement also airway dimensions as well [22]. Despite all these attempts, the greatest precision is still offered by the evaluation of the hand-wrist radiograph or the evaluation of the sole second phalanx of the middle finger, but at the cost of additional radiographs [23]. The scientific question--and the clinical purpose--behind the present study was to investigate if the combination of multiple non-invasive predictors of skeletal age could provide a better estimate, comparable to the gold standard, but at a lower biological cost.