Abstract
目的
研究中国人群腭中缝(midpalatal suture，MPS)形态特点分期与Demirjian牙龄间的相关性，以探索牙龄对腭中缝骨化闭合程度的预测能力。
方法
本研究为回顾性研究，收集1 076例样本(女675例，男401例，年龄6.0~20.9岁)，观察锥形束CT(cone-beam CT，CBCT)水平位腭中缝区域，记录各样本的MPS分期, 同时观察并记录各样本的牙龄。采用Spearman相关系数检验与诊断试验，研究作为有序分类变量的MPS分期与牙龄间的相关关系。
结果
(1) 左下第二前磨牙：牙龄B~D期者绝大部分处于MPS 1~2期，占95.2%；牙龄E期者MPS 1~2期占85.3%，3期占14.7%；牙龄F期者MPS 3期、1~2期、4s1期分别占45.1%、46.1%和8.8%；牙龄G期者MPS 3期、4s1期、1~2期分别占49.8%、24.9%和18.9%；牙龄H期者大部分处于MPS 4~5期，占80.1%，另16.3%处于3期。(2)左下第二磨牙：牙龄B~D期者绝大部分处于MPS 1~2期，占89.7%；牙龄E期者MPS 1~2期占67.4%，3期占26.1%；牙龄F期者MPS 3期、1~2期、4s1期分别占55.3%、34.2%和10.5%；牙龄G期者MPS 3期、4s1期、1~2期分别占50.7%、24.3%和16.8%；牙龄H期者大部分处于MPS 4~5期，占83.8%；另14.2%处于3期。(3)以牙龄诊断MPS分期，效能较好的配对有：左下第二磨牙牙龄-MPS：H-4s2、H-5、D-1；左下第二前磨牙牙龄-MPS：H-4s2、H-5、G-3。其余配对的诊断效能一般。(4)MPS分期与左下第二磨牙牙龄的Spearman系数最高，为0.68，其次是第二前磨牙，为0.64。(5)若左下第二磨牙或第二前磨牙处于牙龄H期，则该个体很可能超过MPS 4s2期。
结论
除少数诊断效能较好的配对外，牙龄诊断MPS分期的效能总体一般。因此，以牙龄评估腭中缝骨化闭合程度时，应酌情加拍治疗前CBCT，以明确腭中缝骨化闭合状态。
Keywords: 腭中缝, 锥束计算机体层摄影术, Demirjian牙龄, 诊断效能
Abstract
Objective
To investigate the correlation between morphological stages of midpalatal suture (MPS) and Demirjian dental age.
Methods
In this retrospective study, 1 076 cone-beam CT (CBCT) images (female: 675, male: 401; age range: 6.0 to 21.0 years) were included. Horizontal view of each sample's CBCT images was observed, each sample's MPS stage was recorded, and dental age. MPS stage and dental age were ordered with categorical variables. Therefore, their correlation was investigated through Spearman correlation coefficient analysis and diagnostic test analysis.
Results
(1) For left lower second premolar: 95.2% of those in dental age stage B-D were in MPS 1-2, accounting for the largest proportion. 85.3% of those in dental age stage E were in MPS 1-2, still accounting for the largest proportion. Another 14.7% were in MPS 3.45.1% of those in dental age stage F were in MPS 3, 46.1% in MPS 1-2, and another 8.8% in MPS 4s1.49.8% of those in dental age stage G were in MPS 3.24.9% in MPS 4s1, and 18.9% in MPS 1-2.80.1% of those in dental age stage H were in MPS 4-5. Another 16.3% were in MPS 3. (2) For left lower second molar: 89.7% of those in dental age stage B-D were in MPS 1-2, accounting for the largest proportion. 67.4% of those in dental age stage E were in MPS 1-2, still accounting for the largest proportion. Another 26.1% were in MPS 3.55.3% of those in dental age stage F were in MPS 3, 34.2% in MPS 1-2, and another 10.5% in MPS 4s1.50.7% of those in dental age stage G were in MPS 3, 24.3% in MPS 4s1, and 16.8% in MPS 1-2.83.8% of those in dental age stage H were in MPS 4-5, another 14.2% were in MPS 3. (3) To diagnose MPS stage with dental age, diagnostic pairs with good performance included: Dental age of left lower second molar-MPS: H-4s2, H-5, D-1; Dental age of left lower second premolar-MPS: H-4s2, H-5, G-3. Other diagnostic pairs were of ordinary diagnostic efficiency. (4) For dental age-MPS Spearman correlation analysis, dental age of left lower second molar-MPS had the highest Spearman coefficient (0.68), dental age of left lower second premolar-MPS was the second high (0.64). (5) Dental age stage H of left lower second molar or left lower second premolar indicated that the individual was later than MPS 4s2.
Conclusion
Dental age's diagnostic efficiency for MPS stage is ordinary on the whole, except for some pairs with good performance. Therefore, pre-treatment CBCT examination should be considered as assistance for evaluating maturation and fusion status of midpalatal suture.
Keywords: Midpalatal suture, Cone-beam computed tomography, Demirjian dental age, Diagnostic efficiency
腭中缝(midpalatal suture，MPS)是腭部的解剖结构，在婴幼儿时期未闭合，随生长发育，逐渐成熟、骨化并闭合[1]。Melsen等[2]观察人头骨标本后发现，腭中缝骨化闭合的生理年龄存在个体差异，Persson等[3]认为腭中缝骨化闭合的起始时间与骨骼生长发育的相关性较强。
上颌快速扩展腭中缝是一种常用的正畸治疗方法[4]，依据力量大小与支抗来源，分为传统牙支持式、微种植体支持式与手术辅助式。目前，传统牙支抗式上颌快速扩展腭中缝是多数青少年患者的常规扩展腭中缝方法之一。传统牙支持式上颌快速扩展腭中缝的骨性疗效与腭中缝骨化闭合状态密切相关[5-6]，扩展腭中缝起始年龄越大，骨性改变(以腭中缝打开与上颌牙槽骨改建为主)的比例将越小，而牙性改变(以上磨牙颊倾为主)的比例将越大[7]，且治疗副作用也更加明显[8-10]。对于腭中缝部分或全部骨化闭合的患者，微种植体支持式与手术辅助式上颌快速扩展腭中缝提供了骨性扩展腭中缝的可能[10]，但这两种方法都包含较复杂的有创操作。
本课题组曾对1 076例中国人群样本的锥形束CT(cone-beam CT，CBCT)影像进行了水平位的观察，归纳出有节点意义的形态特征，将腭中缝连续的骨化闭合过程划分为5期，建立了适用于中国人群的腭中缝形态特点分期方法(MPS分期)，并验证了该方法的观察者内与观察者间一致性[11]。
Demirjian牙龄(简称牙龄)是一种常用的骨骼发育评估指标，由Demirjian等在1973—1976年建立，通过观察恒牙的发育程度，获知个体生长发育状态[12-13]，其包含四个独立的指标：左下尖牙、第一前磨牙、第二前磨牙与第二磨牙[14-16]。以每颗牙齿作为独立观察指标，可以避免掩盖信息，从而更有效地评估牙龄与其他生长发育指标间的可能关联[15]。牙龄与生理年龄的相关系数约为0.7[17]，相关性一般；与颈椎骨龄的相关性最高的牙齿为左下尖牙和第二磨牙，但仅能较准确判断颈椎骨龄高峰前期，而无法有效预测高峰期的起止。因此，牙龄仅适合作为骨骼生长发育状态的初步参考[16, 18]。
目前尚未见腭中缝生长发育与牙龄间关系的研究结果。本研究的目的是明确中国人群腭中缝形态特点分期与牙龄间的相关性，探索牙龄对腭中缝骨化闭合程度的预测能力。
1. 资料与方法
1.1. 研究对象
本研究经北京大学口腔医院伦理委员会审批通过(PKUSSIRB-20180739147)。收集2013年1月至2018年4月期间在北京大学口腔医院就诊，且根据诊断和(或)治疗需要在放射科拍摄CBCT的患者，选择能观察到腭中缝全长区域的CBCT。共纳入1 076例患者，包括女性675例, 男性401例，年龄范围6.0~20.9岁。纳入标准：Ⅰ类矢状骨型；无正畸或正颌治疗史；无系统性疾病或对颅面部骨骼发育有影响的综合征史；无颅面部骨骼外伤、上颌肿瘤或唇腭裂史。
1.2. CBCT检查及MPS分期和牙龄的记录
采用NEWTOM VGi(QR S.r.1.Corp, Verona, Italy)大视野CBCT，管电压110 kV，管电流2.81 mA，扫描视野15 cm×15 cm，轴向层厚0.3 mm，体素为各向同性，曝光时间3.6 s。检查时患者直立，头部处于自然头位，下颌以颏托固定，保持Frankfort平面与地面平行。拍摄时，患者咬合处于牙尖交错位，面部肌肉尽可能放松。CBCT下观察并记录各样本的MPS分期[11]与牙龄[14-15]。
1.3. 统计学分析
1.3.1. 频数分布统计
采用Microsoft Excel 2011软件(Mac版，Microsoft Corp.，Redmond，USA)进行MPS分期与牙龄的频数分布统计。
1.3.2. 相关系数检验
MPS分期与牙龄均为有序等级变量，若二者均符合正态分布且呈等距或等比的线性关系，则采用Pearson相关系数检验；若以上任一条件不满足，则应采用Spearman相关系数检验[19]。本研究采用SPSS 19.0软件(IBM Corp.，Armonk，New York，USA)进行二者间的Spearman相关系数检验。
1.3.3. 诊断试验分析
通过受试者工作特征(receiver operating characteristic，ROC)曲线以及诊断效能指标值，评估某诊断指标相对于金标准指标的诊断效能[20]。为探索牙龄对腭中缝骨化闭合程度的预测能力，本研究将MPS分期作为金标准指标，牙龄作为待评估指标，采用Python 3.6统计软件(Mac版，Continuum Analytics 5.3.0，Anaconda Inc. New York，USA)进行诊断试验分析。诊断效能指标包括：ROC曲线下面积(area under ROC curve，AUC)、灵敏度、特异度、阳性似然比(positive likelihood ratio，PLR)。
2. 结果
2.1. 腭中缝形态特点分期与牙龄的频数分布
MPS分期与牙龄的频数总体呈正向分布，且女性与男性的分布相似。选取代表性较强的左下第二前磨牙与第二磨牙进行描述，频数分布见表 1。
表 1.
腭中缝形态特点分期与牙龄频数分布表
Frequency distribution of MPS stage and dental age
| MPS stage | Dental age of left lower second premolar | Dental age of left lower second molar | |||||||||||||||
| B | C | D | E | F | G | H | Total | B | C | D | E | F | G | H | Total | ||
| MPS, midpalatal suture. | |||||||||||||||||
| 1 | 1 | 1 | 13 | 21 | 29 | 30 | 11 | 106 | 1 | 3 | 37 | 16 | 18 | 27 | 4 | 106 | |
| 2 | 0 | 0 | 5 | 8 | 18 | 17 | 13 | 61 | 0 | 0 | 11 | 15 | 8 | 18 | 9 | 61 | |
| 3 | 0 | 0 | 1 | 5 | 46 | 124 | 109 | 285 | 0 | 0 | 6 | 12 | 42 | 136 | 89 | 285 | |
| 4s1 | 0 | 0 | 0 | 0 | 6 | 62 | 195 | 263 | 0 | 0 | 0 | 2 | 8 | 65 | 188 | 263 | |
| 4s2 | 0 | 0 | 0 | 0 | 2 | 14 | 261 | 277 | 0 | 0 | 0 | 1 | 0 | 18 | 258 | 277 | |
| 5 | 0 | 0 | 0 | 0 | 1 | 2 | 81 | 84 | 0 | 0 | 0 | 0 | 0 | 4 | 80 | 84 | |
| Total | 1 | 1 | 19 | 34 | 102 | 249 | 670 | 1 076 | 1 | 3 | 54 | 46 | 76 | 268 | 628 | 1 076 | |
对于左下第二前磨牙，牙龄B~D期者绝大部分处于MPS 1~2期，占95.2%。牙龄E期者仍是MPS 1~2期占比最大，此时3期占比上升，二者分别占85.3%和14.7%。牙龄F期者MPS 3期与1~2期占比基本相等，其次是4s1期，三者分别占45.1%、46.1%和8.8%。牙龄G期者MPS 3期占比最大，其次是4s1期，再次是1~2期，三者分别占49.8%、24.9%和18.9%。牙龄H期者大部分处于MPS 4~5期，占80.1%，另16.3%处于3期。
对于左下第二磨牙，牙龄B~D期者多处于MPS 1~2期，占89.7%。牙龄E期者仍是MPS 1~2期占比最大，此时3期占比上升，二者分别占67.4%和26.1%。牙龄F期者MPS 3期占比最大，其次是1~2期，再次是4s1期，三者分别占55.3%、34.2%和10.5%。牙龄G期者仍是MPS 3期占比最大，但其次是4s1期，再次才是1~2期，三者分别占50.7%、24.3%和16.8%。牙龄H期者大部分处于MPS 4~5期，占83.8%，另14.2%处于3期。
2.2. Spearman相关系数检验与诊断试验分析
MPS分期与牙龄的Spearman相关系数检验结果见表 2，左下第二磨牙的Spearman系数最高(0.68)，其次是第二前磨牙(0.64)，男性略大于女性。各牙齿牙龄诊断效能最强的三组配对，按AUC值由大到小排序为：(1)左下尖牙牙龄-MPS：H-4s2、G-3、H-5；(2)左下第一前磨牙牙龄-MPS：H-4s2、H-5、G-3；(3)左下第二前磨牙牙龄-MPS：H-4s2、H-5、G-3；(4)左下第二磨牙牙龄-MPS：H-4s2、H-5、D-1。诊断试验分析结果见图 1与表 3。AUC值最大的是左下第二磨牙(0.67~0.73)，其次是第二前磨牙(0.64~0.72)。诊断效能最强的三组配对中，前两对的灵敏度大于特异度，而第三对的特异度大于灵敏度。
表 2.
腭中缝形态特点分期与牙龄的Spearman相关系数检验
Spearman correlation analysis between MPS stage and dental age
| Items | Left lower canine | Left lower first premolar | Left lower second premolar | Left lower second molar | |||||||
| Spearman | P value | Spearman | P value | Spearman | P value | Spearman | P value | ||||
| Female | 0.578 | < 0.001 | 0.557 | < 0.001 | 0.602 | < 0.001 | 0.667 | < 0.001 | |||
| Male | 0.668 | < 0.001 | 0.662 | < 0.001 | 0.676 | < 0.001 | 0.699 | < 0.001 | |||
| Total | 0.618 | < 0.001 | 0.605 | < 0.001 | 0.636 | < 0.001 | 0.683 | < 0.001 | |||
图 1.
腭中缝形态特点分期与牙龄诊断试验分析：ROC曲线
Diagnostic test analysis between MPS stage and dental age: ROC curve
A, left lower canine; B, left lower first premolar; C, left lower second premolar; D, left lower second molar. DA, dental age; MPS, midpalatal suture.
表 3.
腭中缝形态特点分期与牙龄诊断试验分析：诊断效能指标
Diagnostic test analysis between MPS stage and dental age: diagnostic efficiency indexes
| Index | Left lower canine | Left lower first premolar | Left lower second premolar | Left lower second molar | |||||||||||
| DA H-MPS 4s2 | DA G-MPS 3 | DA H-MPS 5 | DA H-MPS 4s2 | DA H-MPS 5 | DA G-MPS 3 | DA H-MPS 4s2 | DA H-MPS 5 | DA G-MPS 3 | DA H-MPS 4s2 | DA H-MPS 5 | DA D-MPS 1 | ||||
| DA, dental age; MPS, midpalatal suture; AUC, area under receiver operating characteristic curve; PLR, positive likelihood ratio. | |||||||||||||||
| AUC | 0.696 | 0.662 | 0.649 | 0.678 | 0.660 | 0.642 | 0.715 | 0.685 | 0.639 | 0.734 | 0.700 | 0.666 | |||
| PLR | 1.710 | 3.066 | 1.471 | 1.605 | 1.488 | 3.025 | 1.841 | 1.624 | 2.753 | 2.011 | 1.724 | 19.917 | |||
| Sensitivity | 0.946 | 0.481 | 0.929 | 0.946 | 0.976 | 0.425 | 0.942 | 0.964 | 0.435 | 0.931 | 0.952 | 0.349 | |||
| Specificity | 0.447 | 0.843 | 0.369 | 0.411 | 0.344 | 0.860 | 0.488 | 0.406 | 0.842 | 0.537 | 0.448 | 0.982 | |||
3. 讨论
牙龄与生理年龄的相关性一般，相关系数约为0.7[17]，与颈椎骨龄的相关性在不同人群中存在差异，仅适合作为骨骼生长发育的初步参考[21-22]。本研究结果显示，牙龄与MPS分期的Spearman相关系数以左下第二磨牙最高(0.68)，其次是左下第二前磨牙(0.64)，表明在牙龄预测MPS分期时，左下第二磨牙诊断效能最强，其次是左下第二前磨牙。诊断效能最强的配对为：(1)左下第二磨牙牙龄H期与D期，分别对应MPS 4s2~5期与1期；(2)左下第二前磨牙牙龄H期与G期，分别对应MPS 4s2~5期与3期。
AUC值一般介于0.5~1.0之间：AUC=1.0代表灵敏度与特异度均为1.0，这种完美的指标实际情况下基本不存在；AUC=0.5相当于随机猜测，不具有预测价值；0.5 < AUC < 0.7时诊断效能一般，0.7≤AUC < 0.9时效能较好，AUC≥0.9时效能优秀[20, 23]。因此，牙龄-MPS分期配对里，左下第二磨牙牙龄H期-MPS 4s2、左下第二磨牙牙龄H期-MPS 5、左下第二前磨牙牙龄H期-MPS 4s2的诊断效能较好，其余配对的效能均一般。因此，以牙龄评估腭中缝骨化闭合程度时，应酌情加拍治疗前CBCT。
除AUC值外，灵敏度与特异度也具有一定参考意义。左下第二磨牙诊断效能最强的三组配对中，前两对的灵敏度均大于特异度，第二前磨牙情况相似(表 3)。因此，若检查发现左下第二磨牙或第二前磨牙已完全萌出且牙根发育完成，则腭中缝骨化闭合很可能已过半。
此外，各牙齿牙龄H期者仍有14%~19%样本处于MPS 1~3期(表 1)，传统牙支持式上颌快速扩展腭中缝仍存在成功机会，可酌情加拍扩展腭中缝前的CBCT，以明确腭中缝骨化闭合状态。
以传统牙支持式上颌快速扩展腭中缝，矫治器的佩戴、固位与加力要求有稳定的支抗牙与高度足够的临床冠[17]。影响牙齿萌出的因素较多[24]，因此，需仔细评估牙齿生长状态。观察牙龄除有助于明确腭中缝骨化闭合程度外，也有助于明确支抗牙的发育情况。
综上，除少数诊断效能较好的配对(左下第二磨牙牙龄H期-MPS 4s2，左下第二磨牙牙龄H期-MPS 5，左下第二前磨牙牙龄H期-MPS 4s2)外，牙龄诊断腭中缝形态特点分期的效能总体一般，应酌情加拍治疗前CBCT，以明确腭中缝骨化闭合状态。MPS分期与左下第二磨牙牙龄的Spearman系数最高(0.68)，其次是第二前磨牙(0.64)，若左下第二磨牙或第二前磨牙处于H期，则该个体腭中缝很可能超过4s2期。今后尚需扩大样本量，探索中国人群腭中缝形态特点分期各期样本的传统牙支持式上颌快速扩展腭中缝的效应差异，以进一步评估该分期方法的临床参考意义。
Funding Statement
国家自然科学基金(81970979)和科技部科技基础资源调查专项课题(2018FY101005)
Supported by National Natural Science Foundation of China (81970979) and Special Foundation for National Science and Technology Basic Research Program of China, Ministry of Science and Technology of China (2018FY101005)
References
- 1.Bjork A. Sutural growth of the upper face studied by the implant method. Acta Odontol Scand. 1966;24(2):109–127. doi: 10.3109/00016356609026122. [DOI] [PubMed] [Google Scholar]
- 2.Melsen B. Palatal growth studied on human autopsy material. Am J Orthod. 1975;68(1):42–54. doi: 10.1016/0002-9416(75)90158-X. [DOI] [PubMed] [Google Scholar]
- 3.Persson M, Thilander B. Palatal suture closure in man from 15 to 35 years of age. Am J Orthod. 1977;72(1):42–52. doi: 10.1016/0002-9416(77)90123-3. [DOI] [PubMed] [Google Scholar]
- 4.Haas AJ. The treatment of maxillary deficiency by opening the midpalatal suture. Angle Orthod. 1965;35:200–217. doi: 10.1043/0003-3219(1965)035<0200:TTOMDB>2.0.CO;2. [DOI] [PubMed] [Google Scholar]
- 5.McNamara JA Jr, Baccetti T, Franchi L, et al. Rapid maxillary expansion followed by fixed appliances: a long-term evaluation of changes in arch dimensions. Angle Orthod. 2003;73(4):344–353. doi: 10.1043/0003-3219(2003)073<0344:RMEFBF>2.0.CO;2. [DOI] [PubMed] [Google Scholar]
- 6.Baccetti T, Franchi L, Cameron CG, et al. Treatment timing for rapid maxillary expansion. Angle Orthod. 2001;71(5):343–350. doi: 10.1043/0003-3219(2001)071<0343:TTFRME>2.0.CO;2. [DOI] [PubMed] [Google Scholar]
- 7.Rungcharassaeng K, Caruso JM, Kan JY, et al. Factors affecting buccal bone changes of maxillary posterior teeth after rapid maxillary expansion. Am J Orthod Dentofacial Orthop. 2007;132(4):428. doi: 10.1016/j.ajodo.2007.02.052. [DOI] [PubMed] [Google Scholar]
- 8.Barber AF, Sims MR. Rapid maxillary expansion and external root resorption in man: A scanning electron microscope study. Am J Orthod. 1981;79(6):630–652. doi: 10.1016/0002-9416(81)90356-0. [DOI] [PubMed] [Google Scholar]
- 9.Rinaldi MRL, Azeredo F, de Lima EM, et al. Cone-beam computed tomography evaluation of bone plate and root length after maxillary expansion using tooth-borne and tooth-tissue-borne banded expanders. Am J Orthod Dentofacial Orthop. 2018;154(4):504–516. doi: 10.1016/j.ajodo.2017.12.018. [DOI] [PubMed] [Google Scholar]
- 10.Garib DG, Henriques JF, Janson G, et al. Rapid maxillary expansion: Tooth tissue-borne versus tooth-borne expanders. A computed tomography evaluation of dentoskeletal effects. Angle Orthod. 2005;75(4):548–557. doi: 10.1043/0003-3219(2005)75[548:RMETVT]2.0.CO;2. [DOI] [PubMed] [Google Scholar]
- 11.高 璐, 谷 岩. 中国人群腭中缝生长发育形态特点分期与其相应生理年龄分布的初步研究. 中华口腔正畸学杂志. 2020;27(2):61–66. [Google Scholar]
- 12.Demirjian A, Goldstein H, Tanner JM. A new system of dental age assessment. Hum Biol. 1973;45(2):211–227. [PubMed] [Google Scholar]
- 13.Demirjian A, Goldstein H. New systems for dental maturity based on seven and four teeth. Ann Hum Biol. 1976;3(5):411–421. doi: 10.1080/03014467600001671. [DOI] [PubMed] [Google Scholar]
- 14.Macha M, Lamba B, Avula JSS, et al. Estimation of correlation between chronological age, skeletal age and dental age in children: a cross-sectional study. J Clin Diagn Res. 2017;11(9):ZC01–ZC04. doi: 10.7860/JCDR/2017/25175.10537. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 15.李 萌, 李 果, 王 虎. Demirjian牙龄推断法及其应用与更新. 国际口腔医学杂志. 2014;41(6):725–729. [Google Scholar]
- 16.Perinetti G, Contardo L, Gabrieli P, et al. Diagnostic performance of dental maturity for identification of skeletal maturation phase. Eur J Orthod. 2011;34(4):487–492. doi: 10.1093/ejo/cjr027. [DOI] [PubMed] [Google Scholar]
- 17.Proffit WR. Contemporary orthodontics. Philadelphia: Elsevier; 2018. [Google Scholar]
- 18.Różyło-Kalinowska I, Kolasa-Rączka A, Kalinowski P. Relationship between dental age according to Demirjian and cervical vertebrae maturity in Polish children. Eur J Orthod. 2010;33(1):75–83. doi: 10.1093/ejo/cjq031. [DOI] [PubMed] [Google Scholar]
- 19.Ladewig VM, Capelozza-Filho L, Almeida-Pedrin RR, et al. Tomographic evaluation of the maturation stage of the midpalatal suture in post-adolescents. Am J Orthod Dentofacial Orthop. 2018;153(6):818–824. doi: 10.1016/j.ajodo.2017.09.019. [DOI] [PubMed] [Google Scholar]
- 20.Hajian-Tilaki K. Receiver operating characteristic (ROC) curve analysis for medical diagnostic test evaluation. Caspian J Intern Med. 2013;4(2):627–635. [PMC free article] [PubMed] [Google Scholar]
- 21.Korbmacher H, Schilling A, Puschel K, et al. Age-dependent three-dimensional micro-computed tomography analysis of the human midpalatal suture. J Orofac Orthop. 2007;68(5):364–376. doi: 10.1007/s00056-007-0729-7. [DOI] [PubMed] [Google Scholar]
- 22.Knaup B, Yildizhan F, Wehrbein H. Age-related changes in the midpalatal suture. J Orofac Orthop. 2004;65(6):467–474. doi: 10.1007/s00056-004-0415-y. [DOI] [PubMed] [Google Scholar]
- 23.黄 悦勤. 临床流行病学. 北京: 人民卫生出版社; 2014. [Google Scholar]
- 24.葛 立宏. 儿童口腔医学. 北京: 北京大学医学出版; 2013. [Google Scholar]