## 4 Discussion  
According to the regression analysis, the error decreased as the length of the surgical guide increased, which suggested an advantage in using a surgical guide for insertion. With the regression formula we used, the error will diverge at the guide length of zero. However, the angular error and the error at the bottom of the hole will likely converge to a similar accuracy as the freehand insertion, because the driver will be supported by the operator's hand, even if a surgical guide is very thin. A length of 6.0 mm seemed to be preferable to avoid a collision against the tooth roots. Previous studies have reported that the interradicular distance was 2.4-6.5 mm in the maxillary palatal region and 2.4-3.3 mm in the buccal region [15; 16]. As the diameter of  
Figure 5: (**A**) A boxplot of the error at the opening of the hole. The black dot represents each sample. (**B**) A regression curve of the error. Figure 6: (**A**) A boxplot of the angular error. The black dot represents each sample. (**B**) A regression curve of the angular error. miniscrews is usually about 1.5 mm, an error at the bottom of the hole of more than 0.5 mm might be critical. With freehand drilling of 3.0 mm and 4.5 mm in length, errors of more than 0.5 mm were observed, which might cause collision against the tooth roots in a patient. Thus, when a miniscrew is inserted into a narrow interradicular space, a 6.0 mm or longer screw guide is preferable. As far as acceptable levels of accuracy are concerned, smaller surgical guides are better for handling in an intra-oral environment. Although the surgical guide of 3.0 mm had the worst accuracy regarding the position of the bottom of the hole, its maximum error was 1.0 mm in this study. Thus, when a miniscrew is inserted in a relatively wider space, such as between the palatal root of the upper first molar and the second premolar, a surgical guide of 3.0 mm might be long enough. In addition, a shorter guide is suitable for areas where the soft tissue is thick because if the guide is too long, it consumes the available cutter length of the drill bit, and the hole depth might become too shallow to penetrate the cortical bone. The length of the guide had no clinically significant effect on the positional error at the opening of the hole. The length of the guide did not have a statistically significant impact on the error, and the \(p\)-value was 0.0709 (\(p>0.05\)), which might have been because the sample size was too small for detecting the effect of the guide length. However, the difference in mean error was only 0.08 mm between the guides with lengths of 3.0 mm and 6.0 mm, which seemed to be negligible in clinical practice. Thus, there is no point in increasing the number of samples to detect the statistically significant effect of the guide length. The result of the regression analysis indicated that the fitting of the surgical guide was accurate. The constant \(\beta\) represents an absolute error which is not affected by the length of the guide, and it was 0.00 for the error at the opening of the hole, which meant there would be no error if the guide was long enough. On the other hand, the constant \(\beta\) was 0.84 for the angular error, which meant there was an error of 0.84 degrees, regardless of the length. This angular error was equivalent to 0.09 mm at the depth of 6.0 mm, which was a consistent value with the \(\beta\) of error at the bottom of the hole. With the self-tapping method, the surgical guides can be thinner and less bulky to handle than using the self-drilling method. Usually, the head of a miniscrew has a larger diameter than its body. Therefore, the guide hole must be larger than the diameter of the head, so that the surgical guide can be removed after the insertion. Furthermore, since the head is held by the screwdriver, the part where the diameter becomes largest is the driver (Figure 7) in the system. A surgical guide for the self-drilling method must cover the part with the largest diameter to maximize accuracy.