## 1 Introduction  
Temporary skeletal anchorage devices (TSADs) such as micro-implants are widely used for anchorage control in orthodontics [1, 2, 3, 4]. Traditional anchorage devices such as transpalatal arches have been shown to be insufficient in providing anchorage in vertical and anteroposterior dimensions in premolar extraction cases [5]. Extraoral appliances such as headgears may be used to reinforce anchorage; however, they rely on patient compliance, which can be a problem [6, 7].  
TSADs have increased the range of biologic tooth movement using orthodontic appliances, altering the principle of \"envelop of discrepancy\" suggested by [PERSON] and [PERSON] [8]. They can be used for various indications such as incisor retraction, molar intrusion, molar distalization, molar protraction, and the traction of impacted or unerupted teeth [9]. As a result, the need for orthognathic surgery decreased owing to advanced biomechanics for camouflage treatment in severe skeletal malocclusions, such as anterior openble [10, 11], and skeletal Class III malocclusions [12, 13]. Additionally, TSADs have provided skeletal anchorage for maxillary expansion [14] and maxillary protraction [15] for patients with skeletal discrepancies.  
As micro-implants are used temporarily during orthodontic treatment, their stability relies primarily on mechanical retention rather than osseointegration [16; 17]. Previous studies on the factors associated with the success of orthodontic micro-implants are often limited to the biomechanical properties of the local bone required for implantation, such as the cortical bone thickness and the alveolar bone density, and to technical factors related to the implantation procedure, including the use of predrilling, the proximity of the micro-implant to the adjacent roots, the height of the insertion point, and the angle of the placement [18; 19; 20; 21]. As the thickness and volume of the masseter muscle are significantly associated with different patterns of vertical facial growth [22; 23], the impact of the masticatory function on bone morphology and its effects on micro-implant success have been evaluated [16; 21; 24]. However, only a few studies have examined the influence of craniofacial patterns on micro-implant success [25; 26; 27].  
Despite the vast amount of research on factors affecting orthodontic micro-implant success, most of the studies have employed a univariate analysis, which does not consider the effects of other factors that may affect the outcome and lead to inaccurate results. Other studies have employed logistic regression analysis, which does not consider the time factor, which is critical for micro-implant survival. Survival analysis is a statistical method used in biomedical research, wherein the response variable, which is the time until the occurrence of an event of interest, and the survival differences among the groups of patients are tested [28]. The incidence of micro-implant failure is the event of interest in the study of orthodontic micro-implant success, and the probability of failure can be analyzed after adjusting for multiple patient-related factors known as covariates. These covariates can significantly affect the outcome. So far, only a few studies have performed survival analyses to evaluate the success of orthodontic micro-implants [29; 30].  
The purpose of this study was to investigate the effects of the patient-related factors such as anteroposterior and vertical skeletal patterns and alveolar bone density on the success rate of micro-implants.