Comparison of individualized facial growth prediction models based on the partial least squares and artificial intelligence.

OBJECTIVES: To compare facial growth prediction models based on the partial least squares and artificial intelligence (AI). MATERIALS AND METHODS: Serial longitudinal lateral cephalograms from 410 patients who had not undergone orthodontic treatment but had taken serial cephalograms were collected from January 2002 to December 2022. On every image, 46 skeletal and 32 soft-tissue landmarks were identified manually. Growth prediction models were constructed using multivariate partial least squares regression (PLS) and a deep learning method based on the TabNet deep neural network incorporating 161 predictor, and 156 response, variables. The prediction accuracy between the two methods was compared. RESULTS: On average, AI showed less prediction error by 2.11 mm than PLS. Among the 78 landmarks, AI was more accurate in 63 landmarks, whereas PLS was more accurate in nine landmarks, including cranial base landmarks. The remaining six landmarks showed no statistical difference between the two methods. Overall, soft-tissue landmarks, landmarks in the mandible, and growth in the vertical direction showed greater prediction errors than hard-tissue landmarks, landmarks in the maxilla, and growth changes in the horizontal direction, respectively. CONCLUSIONS: PLS and AI methods seemed to be valuable tools for predicting growth. PLS accurately predicted landmarks with low variability in the cranial base. In general, however, AI outperformed, particularly for those landmarks in the maxilla and mandible. Applying AI for growth prediction might be more advantageous when uncertainty is considerable.

Evaluation of an individualized facial growth prediction model based on the multivariate partial least squares method.

OBJECTIVES: To develop a facial growth prediction model incorporating individual skeletal and soft tissue characteristics. MATERIALS AND METHODS: Serial longitudinal lateral cephalograms were collected from 303 children (166 girls and 137 boys), who had never undergone orthodontic treatment. A growth prediction model was devised by applying the multivariate partial least squares (PLS) algorithm, with 161 predictor variables. Response variables comprised 78 lateral cephalogram landmarks. Multiple linear regression analysis was performed to investigate factors influencing growth prediction errors. RESULTS: Using the leave-one-out cross-validation method, a PLS model with 30 components was developed. Younger age at prediction resulted in greater prediction error (0.03 mm/y). Further, prediction error increased in proportion to the growth prediction interval (0.24 mm/y). Girls, subjects with Class II malocclusion, growth in the vertical direction, skeletal landmarks, and landmarks on the maxilla were associated with more accurate prediction results than boys, subjects with Class I or III malocclusion, growth in the anteroposterior direction, soft tissue landmarks, and landmarks on the mandible, respectively. CONCLUSIONS: The prediction error of the prediction model was proportional to the remaining growth potential. PLS growth prediction seems to be a versatile approach that can incorporate large numbers of predictor variables to predict numerous landmarks for an individual subject.

Time series analysis.

INTRODUCTION: This article describes a simple method of applying a time series analysis to sample data sets using a free and open statistical software program, Language R. METHODS: Records of new patients who visited 2 different university-affiliated orthodontic departments in 2 different countries were collected. Time series analysis was performed by applying Language R software. The data sets and codes were provided for tutorial and illustrative purposes. RESULTS: Using time series decomposition, the trend component and the seasonal variation were separated and visualized graphically. CONCLUSIONS: Time series analysis may be helpful to clinicians by providing a simple tool to evaluate patient characteristics and manage the practice.

Assessment of reliability in orthodontic literature.

OBJECTIVES: To map the statistical methods applied to assess reliability in orthodontic publications and to identify possible trends over time. MATERIALS AND METHODS: Original research articles published in 2009 and 2019 in a subset of orthodontic journals were downloaded. Publication characteristics, including publication year, number of authors, single vs multicenter study, geographic origin of the study, statistician involvement, study category, subject category, types of reliability assessment, and statistical methods applied to assess reliability, were recorded. Descriptive statistics, Chi-square tests, and logistic regression analyses were performed to investigate associations between reliability analysis and study characteristics. RESULTS: A total of 768 original research articles were analyzed. The most prevalent study category was observational (69%) with a statistician involved in 16% of studies. Overall, reliability was assessed in 47% of studies, and the most frequent methods applied to assess reliability were intraclass correlation coefficients or kappa statistics (60.4%). The odds of applying appropriate methods were greater in 2019 than in 2009 (odds ratio [OR]: 2.43; 95% confidence interval [CI]: 1.75, 3.37; P < .001). Involvement of a statistician resulted in greater odds of applying appropriate methods compared to no statistician involvement (OR: 1.88; 95% CI: 1.23, 2.87; P < .01). CONCLUSIONS: Over the past decade (2009 vs 2019), reliability assessment became more common in the orthodontic literature, and studies applying correct statistical methods to assess reliability significantly increased. This trend was more apparent in studies that involved a statistician, which may highlight the role of the statistician.

Evaluation of an automated superimposition method based on multiple landmarks for growing patients.

OBJECTIVES: To determine if an automated superimposition method using six landmarks (Sella, Nasion, Porion, Orbitale, Basion, and Pterygoid) would be more suitable than the traditional Sella-Nasion (SN) method to evaluate growth changes. MATERIALS AND METHODS: Serial lateral cephalograms at an average interval of 2.7 years were taken on 268 growing children who had not undergone orthodontic treatment. The T1 and T2 lateral images were manually traced. Three different superimposition methods: Björk's structural method, conventional SN, and the multiple landmark (ML) superimposition methods were applied. Bjork's structural method was used as the gold standard. Comparisons among the superimposition methods were carried out by measuring the linear distances between Anterior Nasal Spine, point A, point B, and Pogonion using each superimposition method. Multiple linear regression analysis was performed to identify factors that could affect the accuracy of the superimpositions. RESULTS: The ML superimposition method demonstrated smaller differences from Björk's method than the conventional SN method did. Greater differences among the cephalometric landmarks tested resulted when: the designated point was farther from the cranial base, the T1 age was older, and the more time elapsed between T1 and T2. CONCLUSIONS: From the results of this study in growing patients, the ML superimposition method seems to be more similar to Björk's structural method than the SN superimposition method. A major advantage of the ML method is likely to be that it can be applied automatically and may be just as reliable as manual superimposition methods.

Evaluation of automated cephalometric analysis based on the latest deep learning method.

OBJECTIVES: To compare an automated cephalometric analysis based on the latest deep learning method of automatically identifying cephalometric landmarks (AI) with previously published AI according to the test style of the worldwide AI challenges at the International Symposium on Biomedical Imaging conferences held by the Institute of Electrical and Electronics Engineers (IEEE ISBI). MATERIALS AND METHODS: This latest AI was developed by using a total of 1983 cephalograms as training data. In the training procedures, a modification of a contemporary deep learning method, YOLO version 3 algorithm, was applied. Test data consisted of 200 cephalograms. To follow the same test style of the AI challenges at IEEE ISBI, a human examiner manually identified the IEEE ISBI-designated 19 cephalometric landmarks, both in training and test data sets, which were used as references for comparison. Then, the latest AI and another human examiner independently detected the same landmarks in the test data set. The test results were compared by the measures that appeared at IEEE ISBI: the success detection rate (SDR) and the success classification rates (SCR). RESULTS: SDR of the latest AI in the 2-mm range was 75.5% and SCR was 81.5%. These were greater than any other previous AIs. Compared to the human examiners, AI showed a superior success classification rate in some cephalometric analysis measures. CONCLUSIONS: This latest AI seems to have superior performance compared to previous AI methods. It also seems to demonstrate cephalometric analysis comparable to human examiners.

How much deep learning is enough for automatic identification to be reliable?

OBJECTIVES: To determine the optimal quantity of learning data needed to develop artificial intelligence (AI) that can automatically identify cephalometric landmarks. MATERIALS AND METHODS: A total of 2400 cephalograms were collected, and 80 landmarks were manually identified by a human examiner. Of these, 2200 images were chosen as the learning data to train AI. The remaining 200 images were used as the test data. A total of 24 combinations of the quantity of learning data (50, 100, 200, 400, 800, 1600, and 2000) were selected by the random sampling method without replacement, and the number of detecting targets per image (19, 40, and 80) were used in the AI training procedures. The training procedures were repeated four times. A total of 96 different AIs were produced. The accuracy of each AI was evaluated in terms of radial error. RESULTS: The accuracy of AI increased linearly with the increasing number of learning data sets on a logarithmic scale. It decreased with increasing numbers of detection targets. To estimate the optimal quantity of learning data, a prediction model was built. At least 2300 sets of learning data appeared to be necessary to develop AI as accurate as human examiners. CONCLUSIONS: A considerably large quantity of learning data was necessary to develop accurate AI. The present study might provide a basis to determine how much learning data would be necessary in developing AI.

Automated identification of cephalometric landmarks: Part 2-Might it be better than human?

OBJECTIVES: To compare detection patterns of 80 cephalometric landmarks identified by an automated identification system (AI) based on a recently proposed deep-learning method, the You-Only-Look-Once version 3 (YOLOv3), with those identified by human examiners. MATERIALS AND METHODS: The YOLOv3 algorithm was implemented with custom modifications and trained on 1028 cephalograms. A total of 80 landmarks comprising two vertical reference points and 46 hard tissue and 32 soft tissue landmarks were identified. On the 283 test images, the same 80 landmarks were identified by AI and human examiners twice. Statistical analyses were conducted to detect whether any significant differences between AI and human examiners existed. Influence of image factors on those differences was also investigated. RESULTS: Upon repeated trials, AI always detected identical positions on each landmark, while the human intraexaminer variability of repeated manual detections demonstrated a detection error of 0.97 ± 1.03 mm. The mean detection error between AI and human was 1.46 ± 2.97 mm. The mean difference between human examiners was 1.50 ± 1.48 mm. In general, comparisons in the detection errors between AI and human examiners were less than 0.9 mm, which did not seem to be clinically significant. CONCLUSIONS: AI showed as accurate an identification of cephalometric landmarks as did human examiners. AI might be a viable option for repeatedly identifying multiple cephalometric landmarks.

Automated identification of cephalometric landmarks: Part 1-Comparisons between the latest deep-learning methods YOLOV3 and SSD.

OBJECTIVE: To compare the accuracy and computational efficiency of two of the latest deep-learning algorithms for automatic identification of cephalometric landmarks. MATERIALS AND METHODS: A total of 1028 cephalometric radiographic images were selected as learning data that trained You-Only-Look-Once version 3 (YOLOv3) and Single Shot Multibox Detector (SSD) methods. The number of target labeling was 80 landmarks. After the deep-learning process, the algorithms were tested using a new test data set composed of 283 images. Accuracy was determined by measuring the point-to-point error and success detection rate and was visualized by drawing scattergrams. The computational time of both algorithms was also recorded. RESULTS: The YOLOv3 algorithm outperformed SSD in accuracy for 38 of 80 landmarks. The other 42 of 80 landmarks did not show a statistically significant difference between YOLOv3 and SSD. Error plots of YOLOv3 showed not only a smaller error range but also a more isotropic tendency. The mean computational time spent per image was 0.05 seconds and 2.89 seconds for YOLOv3 and SSD, respectively. YOLOv3 showed approximately 5% higher accuracy compared with the top benchmarks in the literature. CONCLUSIONS: Between the two latest deep-learning methods applied, YOLOv3 seemed to be more promising as a fully automated cephalometric landmark identification system for use in clinical practice.

Predicting soft tissue changes after orthognathic surgery: The sparse partial least squares method.

OBJECTIVES: To develop a prediction algorithm for soft tissue changes after orthognathic surgery that would result in accurate predictions (1) regardless of types or complexity of operations and (2) with a minimum number of input variables. MATERIALS AND METHODS: The subjects consisted of 318 patients who had undergone the surgical correction of Class II or Class III malocclusions. Two multivariate methods-the partial least squares (PLS) and the sparse partial least squares (SPLS) methods-were used to construct prediction equations. While the PLS prediction model included 232 input variables, the SPLS method included a reduced number of variables generated by a handicapping algorithm via the sparsity control. The accuracy between the PLS and SPLS models was compared. RESULTS: There were no significant differences in prediction accuracy depending on surgical movements, the sex of the subjects, or additional surgeries. The predictive performance with a reduced set of 34 input variables chosen using the SPLS method was statistically indistinguishable from the full set of variables with the original PLS prediction model. CONCLUSIONS: The prediction method proposed in the present study was accurate for a wide range of orthognathic surgeries. A reduced set of input variables could be selected through the SPLS method while simultaneously maintaining a prediction level that was as accurate as that of the original PLS prediction model.

A sparse principal component analysis of Class III malocclusions.

OBJECTIVES: To identify the most characteristic variables out of a large number of anatomic landmark variables on three-dimensional computed tomography (CT) images. A modified principal component analysis (PCA) was used to identify which anatomic structures would demonstrate the major variabilities that would most characterize the patient. MATERIALS AND METHODS: Data were collected from 217 patients with severe skeletal Class III malocclusions who had undergone orthognathic surgery. The input variables were composed of a total of 740 variables consisting of three-dimensional Cartesian coordinates and their Euclidean distances of 104 soft tissue and 81 hard tissue landmarks identified on the CT images. A statistical method, a modified PCA based on the penalized matrix decomposition, was performed to extract the principal components. RESULTS: The first 10 (8 soft tissue, 2 hard tissue) principal components from the 740 input variables explained 63% of the total variance. The most conspicuous principal components indicated that groups of soft tissue variables on the nose, lips, and eyes explained more variability than skeletal variables did. In other words, these soft tissue components were most representative of the differences among the Class III patients. CONCLUSIONS: On three-dimensional images, soft tissues had more variability than the skeletal anatomic structures. In the assessment of three-dimensional facial variability, a limited number of anatomic landmarks being used today did not seem sufficient. Nevertheless, this modified PCA may be used to analyze orthodontic three-dimensional images in the future, but it may not fully express the variability of the patients.

How to test validity in orthodontic research: a mixed dentition analysis example.

INTRODUCTION: The data used to test the validity of a prediction method should be different from the data used to generate the prediction model. In this study, we explored whether an independent data set is mandatory for testing the validity of a new prediction method and how validity can be tested without independent new data. METHODS: Several validation methods were compared in an example using the data from a mixed dentition analysis with a regression model. The validation errors of real mixed dentition analysis data and simulation data were analyzed for increasingly large data sets. RESULTS: The validation results of both the real and the simulation studies demonstrated that the leave-1-out cross-validation method had the smallest errors. The largest errors occurred in the traditional simple validation method. The differences between the validation methods diminished as the sample size increased. CONCLUSIONS: The leave-1-out cross-validation method seems to be an optimal validation method for improving the prediction accuracy in a data set with limited sample sizes.

Testing a better method of predicting postsurgery soft tissue response in Class II patients: A prospective study and validity assessment.

OBJECTIVE: (1) To perform a prospective study using a new set of data to test the validity of a new soft tissue prediction method developed for Class II surgery patients and (2) to propose a better validation method that can be applied to a validation study. MATERIALS AND METHODS: Subjects were composed of two subgroups: training subjects and validation subjects. Eighty Class II surgery patients provided the training data set that was used to build the prediction algorithm. The validation data set of 34 new patients was used for evaluating the prospective performance of the prediction algorithm. The validation was conducted using four validation methods: (1) simple validation and (2) fivefold, (3) 10-fold, and (4) leave-one-out cross-validation (LOO). RESULTS: The characteristics between the training and validation subjects did not differ. The multivariate partial least squares regression returned more accurate prediction results than the conventional method did. During the prospective validation, all of the cross-validation methods (fivefold, 10-fold, and LOO) demonstrated fewer prediction errors and more stable results than the simple validation method did. No significant difference was noted among the three cross-validation methods themselves. CONCLUSION: After conducting a prospective study using a new data set, this new prediction method again performed well. In addition, a cross-validation technique may be considered a better option than simple validation when constructing a prediction algorithm.

A more accurate soft-tissue prediction model for Class III 2-jaw surgeries.

INTRODUCTION: The use of bimaxillary surgeries to treat Class III malocclusions makes the results of the surgeries more complicated to estimate accurately. Therefore, our objective was to develop an accurate soft-tissue prediction model that can be universally applied to Class III surgical-orthodontic patients regardless of the type of surgical correction: maxillary or mandibular surgery with or without genioplasty. METHODS: The subjects of this study consisted of 204 mandibular setback patients who had undergone the combined surgical-orthodontic correction of severe skeletal Class III malocclusions. Among them, 133 patients had maxillary surgeries, and 81 patients received genioplasties. The prediction model included 226 independent and 64 dependent variables. Two prediction methods, the conventional ordinary least squares method and the partial least squares (PLS) method, were compared. When evaluating the prediction methods, the actual surgical outcome was the gold standard. After fitting the equations, test errors were calculated in absolute values and root mean square values through the leave-1-out cross-validation method. RESULTS: The validation result demonstrated that the multivariate PLS prediction model with 30 orthogonal components showed the best prediction quality among others. With the PLS method, the pattern of prediction errors between 1-jaw and 2-jaw surgeries did not show a significantly difference. CONCLUSIONS: The multivariate PLS prediction model based on about 30 latent variables might provide an improved algorithm in predicting surgical outcomes after 1-jaw and 2-jaw surgical corrections for Class III patients.

A better statistical method of predicting postsurgery soft tissue response in Class II patients.

OBJECTIVE: To propose a better statistical method of predicting postsurgery soft tissue response in Class II patients. MATERIALS AND METHODS: The subjects comprise 80 patients who had undergone surgical correction of severe Class II malocclusions. Using 228 predictor and 64 soft tissue response variables, we applied two multivariate methods of forming prediction equations, the conventional ordinary least squares (OLS) method and the partial least squares (PLS) method. After fitting the equation, the bias and a mean absolute prediction error were calculated. To evaluate the predictive performance of the prediction equations, a leave-one-out cross-validation method was used. RESULTS: The multivariate PLS method provided a significantly more accurate prediction than the conventional OLS method. CONCLUSION: The multivariate PLS method was more satisfactory than the OLS method in accurately predicting the soft tissue profile change after surgical correction of severe Class II malocclusions.

Survival analysis of a miniplate and tube device designed to provide skeletal anchorage.

INTRODUCTION: The aim of this prospective cohort study was to compute the clinical survival and complication rates of a miniplate with a tube device (C-tube) used for orthodontic treatment. METHODS: From August 2003 to May 2012, 217 patients were recruited. They received 341 C-tube miniplates. Some C-tube miniplates were removed because orthodontic treatment ended. Others remained beyond the study period and were recorded as censored data. Survival was classified as a C-tube miniplate that functioned in the mouth regardless of any complications. Success was defined as survival without complications. From the data, the effects of these clinical variables on the survival of the C-tube miniplates were evaluated: sex, age, jaw, placement sites, oral hygiene, tube clearance, inflammation, miniplate shape, number of screws, and length of the fixation screws. Survival analyses using the Kaplan-Meier method and the Cox proportional hazard model were applied. RESULTS: Of the 341 miniplates, 14 failed, and 32 had complications. Two-year survival and success rates were 0.91 and 0.80, respectively. In terms of the simple ratio statistic, this was equivalent to a success rate of 96%. The status of oral hygiene maintenance and the operators' experience had significant associations with the complication rates (P <0.001). CONCLUSIONS: The C-tube miniplate has an advantage in versatility in terms of force application. When placing a miniplate, the most important factor is maintaining good tissue health by means of good oral hygiene. Even with good hygiene, the doctor's experience in performing the flap surgery was the second most important factor for success.

How to report reliability in orthodontic research: Part 2.

Proper statistical analysis is an absolutely essential tool for both clinicians and researchers attempting to implement evidence-based decisions. When analyzing reliability, statistical graphic representation is the best method. Other previously published error studies of 2-dimensional measurements, such as cephalometric landmarks, have inappropriately applied 1-dimensional approaches, such as linear or angular measurements. The aim of this article is to illustrate a graphic presentation method that can be applied to 2-dimensional data sets. We propose that this technique can show errors in both the x-axis and the y-axis simultaneously and should be used when reporting the reliability of a 2-dimensional data set. Our prediction error analysis of soft-tissue changes after orthognathic surgery will be presented as an example. By using different colors in each ellipse, this method can also identify any between-group differences.

How to report reliability in orthodontic research: Part 1.

In reporting reliability, duplicate measurements are often needed to determine if measurements are sufficiently in agreement among the observers (interobserver agreement) and/or within the same observer (intraobserver agreement). Some reports are often analyzed inappropriately using paired t tests and/or correlation coefficients. The aim of this article is to highlight the statistical problems of reliability testing using paired t tests and correlation coefficients and to encourage good reliability reporting within orthodontic research. With regard to the complex issue of reliability, a simple and singular statistical approach is not available. However, some methods are better than others. A graphic technique based on the Bland-Altman plot that can be simultaneously applied for both intra- and interobserver reliability will also be discussed.

Do Class III patients have a different growth spurt than the general population?

INTRODUCTION: Understanding the timing and length of the growth spurt of Class III prognathic patients is fundamental to the strategy of interceptive orthopedic orthodontics as well as to the timing of orthognathic surgery. Consequently, this study was undertaken to determine whether there are any significant differences in the stature growth pattern of Class III subjects compared with non-Class III subjects and the general population. METHODS: Twelve-year longitudinal stature growth data were collected for 402 randomly selected adolescents in the general population, 55 Class III mandibular prognathic patients, and 37 non-Class III patients. The growth data were analyzed by using the traditional linear interpolation method and nonlinear growth functions. The 6 stature growth parameters were measured: age at takeoff, stature at takeoff, velocity at takeoff, age at peak height velocity, stature at peak height velocity, and velocity at peak height velocity. Comparisons in the stature growth parameters and 15 cephalometric variables among the general population, Class III subjects, and non-Class III subjects were made with multivariate analysis. RESULTS: Patients with Class III prognathism did not have different growth parameters compared with Class II subjects or the general population. CONCLUSIONS: This study does not allow meaningful conclusions with regard to the relationship of mandibular size and stature growth pattern. The application of nonlinear growth curves vs the traditional linear interpolation method was also discussed.

A more accurate method of predicting soft tissue changes after mandibular setback surgery.

PURPOSE: To propose a more accurate method to predict the soft tissue changes after orthognathic surgery. PATIENTS AND METHODS: The subjects included 69 patients who had undergone surgical correction of Class III mandibular prognathism by mandibular setback. Two multivariate methods of forming prediction equations were examined using 134 predictor and 36 soft tissue response variables: the ordinary least-squares (OLS) and the partial least-squares (PLS) methods. After fitting the equation, the bias and a mean absolute prediction error were calculated. To evaluate the predictive performance of the prediction equations, a 10-fold cross-validation method was used. RESULTS: The multivariate PLS method showed significantly better predictive performance than the conventional OLS method. The bias pattern was more favorable and the absolute prediction accuracy was significantly better with the PLS method than with the OLS method. CONCLUSIONS: The multivariate PLS method was more satisfactory than the conventional OLS method in accurately predicting the soft tissue profile change after Class III mandibular setback surgery.