Maxillofacial Morphology as a Predictive Factor for Caries Risk in Orthodontic Patients: A Cross-Sectional Study

This cross-sectional study aimed to explore the correlation between maxillofacial morphology and caries risk, assessed using salivary tests, in orthodontic patients. Despite enhancing the oral health-related quality of life, orthodontic treatment may adversely affect oral hygiene and increase caries risk. This study included 1071 patients all of whom underwent orthodontic examinations and salivary tests before starting orthodontic treatment at a hospital. Salivary tests were performed to assess the secretion rate, pH, buffering capacity, and counts of cariogenic bacteria. The maxillofacial morphology was evaluated using cephalometric X-rays and dental models. Statistical analyses revealed significant correlations among salivary characteristics, bacterial scores, and maxillofacial morphology. Notably, the facial angle and Y-axis values were associated with salivary secretion (p < 0.001), pH (p < 0.001), buffering capacity (p < 0.05), and cariogenic bacterial scores (p < 0.01), respectably. In conclusion, assessing the maxillofacial morphology before orthodontic treatment may aid in predicting the risk of bacterial oral diseases, offering valuable insights into personalized preventive measures. These findings underscore the potential for comprehensive evaluations to enhance caries risk assessment in orthodontic patients.

A study comparing oral hygiene in men and women reported that although men could have poorer oral hygiene compared to women, they showed better saliva test results and lower streptococcus mutans (S. mutans) counts [11].
Orthodontic treatment could improve the oral health-related quality of life of patients, including aspects of mastication, occlusion, and esthetics [12,13].However, using orthodontic appliances during orthodontic treatment, oral hygiene could deteriorate, resulting in changes in bacterial flora and an increased risk of bacterial diseases, such as white spot lesions, caries, and periodontitis [14][15][16][17][18]. Dental caries is irreversible once it causes substantial loss of tooth structure.Therefore, early detection and prevention of caries are crucial [19].Based on this background, an accurate assessment of caries risk in individual patients before undergoing orthodontic treatment is essential [20].Social factors, such as area of residence, occupation, and level of education, also influence caries risk.Of particular importance, however, are individual-level factors, such as the content and frequency of meals, oral hygiene, fluoride use, and saliva function [21].Evaluating the quantity and quality of patient saliva before starting orthodontic treatment is highly valuable for assessing the risk of caries during orthodontic treatment [22,23].Saliva-based caries risk assessment has gained attention as a non-invasive and convenient method for evaluating the patients' oral condition; many dental clinics perform caries risk assessments using saliva.However, reports addressing the impact of maxillofacial morphology on salivary characteristics are scarce, although malocclusion has been reported to increase the risk of caries [24,25].Furthermore, the correlation between maxillofacial morphology and caries risk remains unclear.
Therefore, this study aimed to investigate the correlation between the results of salivary tests and maxillofacial morphology.Moreover, this study sought to verify the feasibility of predicting caries risk in patients using salivary characteristics and counts of cariogenic bacteria.

Study Design and Ethical Statement
This cross-sectional study was approved by the appropriate Ethics Review Board (E-1039).The study participants were retrospectively selected using clinical records that met all the necessary items for the study.Since patients under 18 years of age were included, consent was obtained from their legal guardians.

Study Population
A total of 1071 patients (401 male and 670 female patients, age range: 4-71 years, mean age: 14.8 ± 9.8 years) who visited the orthodontic department of one hospital for initial examinations, salivary tests (caries risk assessment), and plaque control record (PCR) between April 2015 and March 2023 were included.All patients agreed to participate in the study.The salivary test included assessments of stimulated saliva secretion, pH, buffering capacity, and counts of S. mutans and Lactobacillus species.Maxillofacial morphology and occlusal status were evaluated using lateral cephalometric radiographs and dental models.

Saliva Collection and Oral Examination
The patients were instructed to avoid vigorous exercise, eating, smoking, and tooth brushing at least 2 h before the saliva test and avoid using antiseptic mouthwash within 6 h before saliva testing.The patients were asked to chew tasteless paraffin gum for 1 min while seated on a dental chair.After removing the gum, for the caries risk test (CRT) (Ivoclar Vivadent, Tokyo, Japan) or Dentocult (OralCare, Tokyo, Japan), the test surface of the strip mutans was rubbed on the patient's tongue surface for 5 back-and-forth motions.The strip was then placed inside the cap of a test tube containing bacitracin tablets inserted 15 min earlier.Subsequently, the same paraffin gum was chewed for 5 min, and the stimulated saliva was collected in a conical tube.If a sufficient amount of saliva could not be collected, the patient was asked to chew the gum for additional few minutes.The collected saliva and bacteria were immediately tested.PCR was recorded by the dental hygienist at the time of initial examination.

Saliva Testing
The saliva secretion rate (mL/min) was calculated based on the total amount of collected saliva.The saliva pH was measured using a Checkbuf pH meter (Horiba, Kyoto, Japan).The buffering capacity of saliva was evaluated using the CAT21Buf risk test (Morita Co., Osaka, Japan) [26].S. mutans and Lactobacillus counts were measured using CRT caries risk test or Dentocult, cultured at 37 • C for 48 h, and evaluated on a 4-point scale for each test, calculating the bacterial score (for CRT caries risk test: score 1, 2: <10 5 colony forming unit [CFU], score 3, 4: >10 5 CFU; for Dentocult: score 1: <10 5 CFU, score 2: <10 6 CFU, score 3: 10 6 -10 7 CFU, score 4: >10 7 CFU).The CRT caries risk test was used for patients presenting between April 2015 and March 2020, and the Dentocult was used for patients presenting between April 2020 and March 2023.

Maxillofacial Morphological Analysis
Lateral cephalometric radiographs were traced, and the traced data were analyzed using analysis software (COA5 version 1.8.1;JM Ortho, Tokyo, Japan).The anatomical landmarks, points, and angles used in this study are shown in Table 1.Linear measurements of overjet (OJ) and overbite (OB) were performed using dental models and calipers.All measurements were performed by the orthodontists at a hospital.

Anatomical Indicators Definition
Landmarks and points S (sella) Center of sella turcica N (nasion) The most anterior point of the frontonasal suture Or (orbitale) The lowest point on the average left and right inferior borders of the bony orbit Po (porion) The highest point on the superior surface of the soft tissue of the external auditory meatus A-Point The most posterior point on the anterior contour of the upper alveolar process B-Point The most posterior point on the anterior contour of the lower alveolar process Me (menton) The lowest point on the mandibular symphysis Pog (Pogonion) The most anterior point of the midline cross-sectional image of the mandibular miter Gn (gnathion) The midpoint of the nasolabial groove Ar (articulare) The intersection of the posterior margin of the mandibular branch and subnasal margin of the occipital bone U1 The tip of the maxillary central incisor L1 The tip of the mandibular central incisor Mo The central point of the cuspid fit of the upper and lower first molars Angles Facial angle ( • ) The angle between the Frankfurt (FH; Or-Po) plane and N-Pog plane Angle of convexity ( • ) The angle between the straight-line NA and A-Pog plane Y-axis ( • ) The angle between the S-Gn and FH plane Gonial angle ( • ) The angle between the ramus plane (a tangent line between the Ar and posterior margin of the mandibular branch) and mandibular plane SN/MP ( • ) The angle between the SN plane and the mandibular plane Ramus plane to SN ( • ) The angle between the ramus plane and SN plane ANB ( • ) The angle formed by point A, nasion, and point B Occlusal plane to SN ( • ) The angle between the line connecting Mo and midpoints of U1 and L1 and the SN plane FMA ( • ) The angle the between mandibular inferior margin plane and the FH plane Interincisal angle ( • ) The angle between the long axis of the U1 and the long axis of the L1

Statistical Analysis
Multiple regression analysis was used to evaluate the correlation between maxillofacial morphology and the results of the caries risk assessment tests and PCR.The p value < 0.05 was set as the significant value for partial regression coefficients.The confidence interval of the population mean was calculated using a 95% confidence level.BellCurve for Excel (Social Survey Research Information Co., Ltd., Tokyo, Japan) was used to evaluate correlations and calculate confidence intervals.After performing the test, we calculated the test power using G*Power 3.1 software (Heinrich Heine University, Düsseldorf, Germany) to check the degree of statistical power.

Statistical Analysis Results of Each Parameter
Table 2 shows the average values, standard deviations, and confidence intervals of the anatomical landmarks, points, angles, OJ, and OB used in the correlation analysis.Table 3 shows the average value, standard deviation, and statistical power of the five items investigated in the caries risk test and PCR.The statistical power for saliva flow rate, salivary pH, and S. mutans score was high; however, the statistical power for salivary buffering capacity, Lactobacillus score, and PCR was below 0.8.
the saliva-flow rate also increased, whereas pH and buffering capacity decreased.Similarly, the salivary flow rate showed a positive correlation with the Y-axis; however, salivary pH showed a negative correlation with the Y-axis.The angle of convexity, gonial angle, SN/MP, ramus plane to the SN, ANB, interincisal angle, FMA, and OJ showed no correlation with the amount of salivary secretion or other characteristics.the saliva-flow rate also increased, whereas pH and buffering capacity decreased.Similarly, the salivary flow rate showed a positive correlation with the Y-axis; however, salivary pH showed a negative correlation with the Y-axis.The angle of convexity, gonial angle, SN/MP, ramus plane to the SN, ANB, interincisal angle, FMA, and OJ showed no correlation with the amount of salivary secretion or other characteristics.

Correlation between PCR and Maxillofacial Morphology
PCR showed a negative correlation with the facial angle (ρ = −0.0512,p = 0.0304 *) (Figure 6a).No other angles were correlated with PCR.

Correlation between PCR and Maxillofacial Morphology
PCR showed a negative correlation with the facial angle (ρ = −0.0512,p = 0.0304 *) (Figure 6a).No other angles were correlated with PCR.

Discussion
This study investigated the correlations among salivary tests, cariogenic bacteria, and maxillofacial morphology.The results of this study revealed a close association between the facial angle and salivary characteristics, including the S. mutans score.Particularly, the saliva-flow rate showed a positive correlation with the facial angle and the Y-axis.This may be due to an increase in the individual's gum chewing efficiency with an increase in their facial angle and Y-axis, thereby increasing stimulated saliva secretion.Moreover, salivary pH and salivary buffering capacity showed a negative correlation with the facial angle and Y-axis.Therefore, the results of this study suggest that salivary protein

Correlation between PCR and Maxillofacial Morphology
PCR showed a negative correlation with the facial angle (ρ = −0.0512,p = 0.0304 *) (Figure 6a).No other angles were correlated with PCR.

Discussion
This study investigated the correlations among salivary tests, cariogenic bacteria, and maxillofacial morphology.The results of this study revealed a close association between the facial angle and salivary characteristics, including the S. mutans score.Particularly, the saliva-flow rate showed a positive correlation with the facial angle and the Y-axis.This may be due to an increase in the individual's gum chewing efficiency with an increase in their facial angle and Y-axis, thereby increasing stimulated saliva secretion.Moreover, salivary pH and salivary buffering capacity showed a negative correlation with the facial angle and Y-axis.Therefore, the results of this study suggest that salivary protein

Discussion
This study investigated the correlations among salivary tests, cariogenic bacteria, and maxillofacial morphology.The results of this study revealed a close association between the facial angle and salivary characteristics, including the S. mutans score.Particularly, the saliva-flow rate showed a positive correlation with the facial angle and the Y-axis.This may be due to an increase in the individual's gum chewing efficiency with an increase in their facial angle and Y-axis, thereby increasing stimulated saliva secretion.Moreover, salivary pH and salivary buffering capacity showed a negative correlation with the facial angle and Y-axis.Therefore, the results of this study suggest that salivary protein concentrations may differ according to specific maxillofacial morphology.However, further studies are needed to determine how the facial angle and Y-axis values are related to caries risk.Additionally, Preethi et al. reported that the flow rate, pH, and buffering capacity were slightly decreased in the saliva of children affected by caries [27].Since this study focused on the correlation between caries risk testing and maxillofacial morphology, the inclusion of a patient's oral status, such as the presence of caries, as an investigation item may be further explored.
No correlation was found between the saliva-flow rate, salivary properties, and angle of convexity.Moreover, no correlation was observed between the anteroposterior position of the maxilla and salivary properties in this study.
S. mutans score positively correlated with the facial angle, whereas the Lactobacillus score showed a positive correlation with the Y-axis.S. mutans has a strong ability to form biofilms and is a typical caries-causing bacterium [28,29].The facial angle and saliva-flow rate are positively correlated and known to inhibit the growth of S. mutans.Therefore, other factors may be responsible for this result.The risk of dental caries is higher with the intake of carbohydrate-rich diets, particularly with frequent consumption [30,31].These factors may have contributed to our results.In contrast, Lactobacillus species in the oral cavity cause a decline in oral pH by fermenting sugars and promoting biofilm formation and are strongly associated with the development of dentin caries [32].Thus, in patients with a large Y-axis, the results indicated an increased risk of dental caries.Both the facial angle and Y-axis showed positive correlations with the saliva-flow rate and cariogenic bacterial scores.Therefore, how these two factors could affect total caries risk assessment remains unclear.The interincisal angle negatively correlated with both S. mutans and Lactobacillus scores.A small angle of inclination of the upper and lower anterior teeth axis is considered to suggest difficulty in cutting food with the front teeth during meals, resulting in a prolonged mealtime and, consequently, a decline in oral pH and subsequent bacterial growth in the oral cavity.
The PCR values showed a negative correlation with the facial angle, indicating that patients with a skeletal tendency toward mandibular protrusion have a higher level of oral hygiene than patients with a skeletal tendency toward maxillary protrusion.At this stage, it is not possible to determine the cause of this result.As previously reported, oral hygiene is poor when there is crowding; hence, a small facial angle may indicate that the alveolar bone itself is small, and crowding is observed [33].Therefore, it is desirable to evaluate the amount of crowding in the future.
A limitation of this study is that it only investigated the correlation between caries risk assessment results and maxillofacial morphology.Other examination items such as age, sex, eating habits, contents of meals, presence of carious teeth, underlying diseases, and social factors would have provided more detailed insights.Moreover, the inclusion of all patients with available data is a limitation because the optimal sample size of the study population is unclear.
Future studies should investigate the relationship between maxillofacial morphology and caries prevalence in patients undergoing orthodontic treatment.Combining the results with those of the CRT could enable the assessment of each item in the caries risk evaluation test, identifying maxillofacial morphologies at a heightened risk of caries.Further research should be conducted to develop a more accurate screening test for assessing caries risk before orthodontic treatment.

Conclusions
The saliva-flow rate showed a strong positive correlation with the facial angle and the Y-axis.Salivary pH negatively correlated with the facial angle and Y-axis.Salivary buffering capacity negatively correlated with the facial angle.Both cariogenic bacterial scores negatively correlated with the interincisal angle.S. mutans score positively correlated with the facial angle, and the Lactobacillus score positively correlated with the Y-axis.The evaluation of specific maxillofacial morphologies showed a correlation with the assessment of salivary characteristics and cariogenic bacterial counts.

Figure 1 .
Figure 1.Correlations between the saliva flow rate and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *, p < 0.001 ***, respectively.

Figure 2 .
Figure 2. Correlations between salivary pH and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *, p < 0.001 ***, respectively.

Figure 1 .
Figure 1.Correlations between the saliva flow rate and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *, p < 0.001 ***, respectively.

Figure 1 .
Figure 1.Correlations between the saliva flow rate and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *, p < 0.001 ***, respectively.

Figure 2 .
Figure 2. Correlations between salivary pH and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *, p < 0.001 ***, respectively.

Figure 2 .
Figure 2. Correlations between salivary pH and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *, p < 0.001 ***, respectively.

Figure 3 .
Figure 3. Correlations between the salivary buffering capacity and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *.

Figure 4 .
Figure 4. Correlations between S. mutans score and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.01 **, and p < 0.001 ***, respectively.

Figure 3 .
Figure 3. Correlations between the salivary buffering capacity and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *.

Figure 3 .
Figure 3. Correlations between the salivary buffering capacity and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *.

Figure 4 .
Figure 4. Correlations between S. mutans score and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.01 **, and p < 0.001 ***, respectively.

Figure 4 .
Figure 4. Correlations between S. mutans score and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.01 **, and p < 0.001 ***, respectively.

Figure 5 .
Figure 5. Correlations between Lactobacillus score and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.01 **.

Figure 6 .
Figure 6.Correlations between PCR and maxillofacial morphology.Multiple regression analysis was used to determine the correlation between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *.

Figure 5 .
Figure 5. Correlations between Lactobacillus score and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.01 **.

Figure 5 .
Figure 5. Correlations between Lactobacillus score and maxillofacial morphology.Multiple regression analysis was used to determine the correlations between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.01 **.

Figure 6 .
Figure 6.Correlations between PCR and maxillofacial morphology.Multiple regression analysis was used to determine the correlation between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *.

Figure 6 .
Figure 6.Correlations between PCR and maxillofacial morphology.Multiple regression analysis was used to determine the correlation between (a) the facial angle, (b) angle of convexity, (c) Y-axis, (d) gonial angle, (e) SN/MP, (f) ramus plane to SN, (g) ANB, (h) occlusal plane to SN, (i) interincisal angle, (j) FMA, (k) OJ, and (l) OB.Each subject is indicated by a dot, and linear regression is indicated by a straight line.Single correlations are indicated by ρ and significant differences by p < 0.05 *.

Table 2 .
The confidence intervals for each parameter.

Table 3 .
The statistical powers of each parameter.