## 2 Materials and Methods  
This study was approved by the institutional review board of Korea National Institute for Bioethics Policy (P01-202209-01-035). Due to the retrospective nature of the study, informed consent from the patients was waived. Patients who received orthodontic treatment between March 2014 and April 2020 at the Department of Orthodontics of the Good Will Dental Hospital and those who met the inclusion criteria were included in the study. The analysis included patients who (1) received orthodontic treatment using one or more orthodontic micro-implant screws, (2) underwent cone-beam computed tomography (CBCT) for orthodontic diagnosis, (3) had micro-implants installed in the buccal interdental area of premolars or molars, and (4) had intraoral radiographs taken after application of micro-implants. The exclusion criteria were as follows: (1) presence of chronic disease and ongoing medication, (2) craniofacial syndromes, and (3) micro-implants placed in areas other than the buccal alveolar bone, such as the palate, retromolar area, and the anterior region. A total of 404 micro-implants (DualTop, Jeil Medical Co., Seoul, Republic of Korea) with a diameter of 1.6 mm and a length of 6 mm were evaluated in 164 orthodontic patients (127 female patients, 37 male patients; mean age, 23.6 \(\pm\) 5.8 years) (Table 1). The micro-implants were self-tapping implants with tapered shapes. The mean number of the micro-implants was 2.5 \(\pm\) 1.2 per patient. The orthodontic micro-implants were placed directly by self-drilling with a hand driver under local anesthesia. All patients were treated using the same right-handed operator ([PERSON]) with a clinical experience of more than 15 years. The insertion torque was not recorded. Micro-implants were implanted into the maxillary or mandibular buccal alveolar bone between the first and second premolars, first and second molars, or the second premolar and the first molar on the attached gingival area close to the mucogingival junction. In some patients, orthodontic forces ranging from 50 g to 200 g were applied immediately after the implantation, which was defined as immediate loading. In other patients, orthodontic forces were applied within 2-8 weeks following implantation, which was regarded as delayed loading. Micro-implants that showed inflammation and mobility were regarded as failed micro-implants and were removed. In cases of failed micro-implants, they were replanted in the same position after 2-3 months. Cortical bone thickness and alveolar bone density were measured using diagnostic CBCT to investigate their effects on micro-implant survival as well as to control for the effects of varying bone thickness and density when assessing the risk of micro-implant failure in patients with varying facial types. CBCT images were obtained using a PaX-Zenith3D machine with the following operational settings: tube voltage, 85 kV; tube current, 6 mA; scan time, 24 s; voxel size, 0.20 mm; field of view, 19 cm \(\times\) 20 cm. The images were saved as Digital Imaging and Communications in Medicine files, which were then used to reconstruct three-dimensional (3D) images as multiplanar reformatted (MPR) images using InVivoDental software (version 6.0, Anatomage, San Jose, CA, USA). CBCT images were reoriented using the occlusal plane as the reference plane; this connects the mesiobuccal cusps of the first molars and the right central incisor tip. The site of implantation was located by measuring the distance from the crown tip to the point where the micro-implant enters the alveolar bone intraorally, and the nearest area was located on MPR views of the CBCT images. Cortical and cancellous bone densities were determined on the axial view via measurement in Hounsfield units (HU) on the line bisecting the inter-radicular space; this was achieved by creating a 1.0 mm\({}^{2}\) rectangle shape in the cancellous bone and a 2.0 mm\({}^{2}\) rectangle shape in the cortical bone around the area of the micro-implant's placement (Figure 1).