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SkeletaÂlnõÂ veÏk podle krcÏnõÂ paÂterÏe Skeletal age according to cervical spine
*MUDr. Agnieszka Predko, *Prof. MUDr. Milan KamõÂnek, DrSc., **Mgr. KaterÏina LangovaÂ, Ph.D., *Doc. Dr. Piotr Fudalej, PhD. *Ortodonticke oddeÏlenõ Kliniky zubnõÂho leÂkarÏstvõ LF UP Olomouc *Department of Orthodontics, Clinic of Dental Medicine, Medical Faculty of Palacky University Olomouc **UÂstav leÂkarÏske biofyziky, LF UP Olomouc **Institute of Biophysics in Medicine, Medical Faculty of Palacky University, Olomouc Abstrakt CõÂl: UÂkolem studie bylo oveÏrÏit spolehlivost a opakovatelnost urcÏenõ skeletaÂlnõÂho veÏku podle vyÂvoje krcÏnõ paÂterÏe (cervical vertebrae maturation - CVM) v modifikaci Baccettiho. CõÂlem bylo proveÏrÏit spolehlivost metody CVM u võÂce hodnotiteluÊ i shodu prÏi opakovaneÂm hodnocenõ stejnyÂch hodnotiteluÊ. MateriaÂl a metoda: Studie se zuÂcÏastnilo 11 ortodontistuÊ, kterÏÂõ hodnotili 50 bocÏnõÂch kefalometrickyÂch snõÂmkuÊ deÏtõ v obdobõ kolem pubertaÂlnõÂho ruÊstoveÂho spurtu. Byla u nich posuzovaÂna shoda v hodnocenõ sumaÂrneÏ pomocõ kappa podle Fleisse i shoda v hodnocenõ u vsÏech dvojic z 11 ortodontistuÊ. 11 ortodontistuÊ pak snõÂmky hodnotilo opakovaneÏ a bylo posuzovaÂno, jak se shoduje jejich 1. a 2.hodnocenõÂ. VyÂsledky: RuÊznõ hodnotõÂcõ se shodli na stejneÂm hodnocenõ jen pruÊmeÏrneÏ u 44 % snõÂmkuÊ. Z dvojic hodnotõÂcõÂch byla nejvysÏsÏÂõ shoda u jedne dvojice u 68 % snõÂmkuÊ, nejnizÏsÏÂõ u 16% snõÂmkuÊ. PrÏi opakovaneÂm hodnocenõ titõÂzÏ hodnotõÂcõ hodnotili stejneÏ jen pruÊmeÏrneÏ 57 % snõÂmkuÊ (od 44 % do 78 %). ZaÂveÏr: Metoda je maÂlo spolehliva a chyba metody je velka prÏi urcÏovaÂnõ faÂzõ skeletaÂlnõÂho veÏku kolem puberty. PrÏi podezrÏenõ na skeletaÂlnõ podklad anomaÂlie je doporucÏeno dalsÏÂõ vysÏetrÏenõ skeletaÂlnõÂho veÏku, naprÏ. pomocõ rtg snõÂmku ruky se zaÂpeÏstõÂm (Ortodoncie 2012, 21, cÏ. 4, s. 218-226). Abstract Aim: The objective of the study was to verify reliability and repeatability of skeletal age assessment according to the development of cervical spine, i.e. cervical vertebral maturation (CVM), according to Baccetti. We aimed to examine the reliability of the CVM method between orthodontists and the concordance in the repeated evaluation of the same orthodontists. Material and method: Eleven orthodontists took part in the study. They assessed 50 lateral cephalograms of children at the age around the pubertal growth spurt. Orthodontists repeated the evaluation after 3 weeks and the agreement between the 1st and 2nd evaluation was appraised. Interobserver agreement between 11 evaluators was assessed with the kappa statistics according to Fleiss and the agreement in all pairs of evaluators were assessed by means of the kappa statistics according to Cohen. Results: The complete agreement in evaluation between different orthodontists was only in 44 % of pictures. In pairs, the best agreement (interobserver agreement) was 68%, the worst 16%. In the repeated evaluation, the same evaluators gave the same assessment only in 57% of radiographs (between 44% and 78%). Conclusion: The method has a low reliability and the method error is high in determination of skeletal age around the puberty. When we suspect skeletal basis of an anomaly, we should recommend another examination for skeletal age, e.g. radiograph of the hand and wrist (Ortodoncie 2012, 21, No. 4, p. 218-226). KlõÂcÏova slova: skeletaÂlnõ veÏk, cervical vertebrae maturation, metoda CVM Key words: skeletal age, cervical vertebrae maturation, CVM method 218
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UÂvod Intenzita ruÊstu cÏelistõ v obdobõ dospõÂvaÂnõ hraje roli ve vyÂbeÏru zpuÊsobu leÂcÏby, ale i v urcÏenõ vhodneÂho veÏku pacienta pro zahaÂjenõ leÂcÏby. VeÏtsÏinou je optimaÂlnõ pro zahaÂjenõ ortodonticke leÂcÏby obdobõ pubertaÂlnõÂho ruÊstoveÂho zrychlenõÂ. PubertaÂlnõ zrychlenõ v ruÊstu cÏelistnõÂch kostõ a v prÏõÂruÊstcõÂch ve vyÂsÏce postavy se vyskytujõ soucÏasneÏ, nebo teÂmeÏrÏ soucÏasneÏ [1, 2, 3]. KalendaÂrÏnõ veÏk nebo zubnõ veÏk pacienta v tomto obdobõ nekoreluje prÏõÂlisÏ s jeho skeletaÂlnõÂm veÏkem. V ortodoncii se pouzÏõÂvajõ dveÏ hlavnõ metody urcÏenõ skeletaÂlnõÂho veÏku: hodnocenõ rtg snõÂmku ruky se zaÂpeÏstõÂm a hodnocenõ zmeÏn morfologie krcÏnõÂch obratluÊ na bocÏnõÂm kefalogramu. V ortodonticke praxi se prÏevaÂzÏneÏ vyuzÏõÂvajõ metody charakterizujõÂcõ vyÂvoj kostõ ruky ve vztahu ke krÏivce intenzity ruÊstu. Jsou to metody naprÏ. podle BjoÈrka [4, 5, 6, 7], Fishmana [8, 9], HaÈgga a Tarangera [10]. BjoÈrkova metoda na zaÂkladeÏ vyÂvoje kostõ ruky se zaÂpeÏstõÂm vznikla na zaÂkladeÏ longitudinaÂlnõ studie pacientuÊ sledovanyÂch v ruÊstove studii s titanovyÂmi implantaÂty. Lamparski v roce 1972 vydal atlas, kde popisuje zmeÏny tvaru krcÏnõÂch obratluÊ C2-C6 v obdobõ dospõÂvaÂnõÂ, zvlaÂsÏt' u dõÂvek a u chlapcuÊ, stejneÏ jako souvislost se skeletaÂlnõÂm veÏkem podle zmeÏn na rtg. snõÂmku ruky se zaÂpeÏstõÂm. PostupneÏ i dalsÏõ autorÏi publikovali sve modifikovane metody [11, 12, 13, 14, 15, 16, 17, 18]. Tyto studie uvaÂdeÏjõ mozÏnost vyuzÏitõ zmeÏn tvaru krcÏnõÂch obratluÊ viditelnyÂch na bocÏnõÂch kefalogramech pro urcÏenõ kostnõÂho veÏku a prÏedpoveÏd'pubertaÂlnõÂho ruÊstoveÂho spurtu, stejneÏ jako mozÏnost pouzÏitõ hodnocenõ vyÂvoje krcÏnõ paÂterÏe mõÂsto hodnocenõ rtg ruky se zaÂpeÏstõÂm, cÏõÂmzÏ se usÏetrÏõ jeden rtg snõÂmek. Baccettiho modifikace klasifikace kostnõÂho veÏku na zaÂkladeÏ posuzovaÂnõ zmeÏn tvaru trÏõ krcÏnõÂch obratluÊ C2, C3, C4 viditelnyÂch na kefalometrickeÂm snõÂmku ma 6 faÂzõ (obr. 1). Jeho modifikace ma naÂzev Cervical Vertebral Maturation (CVM). PrÏi faÂzi CS1 (Cervical Stage 1) jsou teÏla obratluÊ plochaÂ, majõ tvar lichobeÏzÏnõÂku, do maximaÂlnõÂho pubertaÂlnõÂho ruÊstoveÂho zrychlenõ je 2 a võÂce rokuÊ. PrÏi faÂzi CS2 se objevõ konkavita na spodnõ straneÏ obratle C2, nadaÂle jsou teÏla obratluÊ lichobeÏzÏnõÂkovaÂ. Do pocÏaÂtku pubertaÂlnõÂho spurtu je minimaÂlneÏ 1 rok. PrÏi faÂzi CS3 je konkavita na spodnõÂm povrchu C2 a C3. Tvar obratluÊ je lichobeÏzÏnõÂk nebo lezÏõÂcõ obdeÂlnõÂk. Podle Baccettiho je to zacÏaÂtek maximaÂlnõÂho pubertaÂlnõÂho spurtu. CS4 - je konkavita na spodnõÂm okraji obratluÊ C2, C3 a C4. Obratle C3 a C4 majõ tvar lezÏõÂcõÂho obdeÂlnõÂku. Podle Baccettiho je to konec maximaÂlnõÂho ruÊstoveÂho spurtu. CS5 - obratle C3 nebo C4 majõ tvar cÏtverce. MaximaÂlnõ ruÊst probeÏhl okolo jednoho roku prÏed tõÂmto stadiem. CS6 - obratle C3 nebo C4 majõ tvar stojõÂcõÂho obdeÂlnõÂku. UbeÏhly minimaÂlneÏ dva roky od zakoncÏenõ www.orthodont-cz.cz e-mail:
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Introduction The intensity of jaw growth in the adolescents plays an important role in the choice of the treatment method as well as in determining optimal treatment timing. Usually, the optimal period to start orthodontic treatment is during the adolescent growth spurt. Pubertal acceleration in jaw growth and in body growth correlates fully or almost fully [1, 2, 3]. Chronological or dental age of a patient in this period does not correlate well with his/her skeletal age. There are two major methods used for the determination of skeletal age: evaluation of radiographs of the hand and wrist, and evaluation of changes in morphology of cervical vertebrae assessed on lateral cephalograms. In orthodontic practice, the methods relating development of hand bones related and the curve of growth intensity are used. These include methods developed by BjoÈrk [4, 5, 6, 7], Fishman [8, 9], HaÈgg and Taranger [10]. BjoÈrk's method, based on the hand and wrist bones development, builds on the longitudinal study of patients monitored in a growth study with titanium implants. In 1972 Lamparski published the atlas in which he describes changes in the shape of cervical vertebrae C2-C6 in the adolescent period, separately for girls and boys, as well as the skeletal age related to radiographs of the hand and wrist. Other authors published their own modified methods [11, 12, 13, 14, 15, 16, 17, 18]. These studies reported the possible use of changes in the shape of cervical vertebrae that were visible on lateral cephalograms for the determination of skeletal age and for the prediction of pubertal growth spurt. If the use of cervical vertebrae instead of hand and wrist evaluation is possible, a patient can be spared one radiograph. Baccetti's modification of skeletal age classification, based on the three cervical vertebrae C2, C3, C4 visible on cephalogram, comprises 6 stages (Fig. 1). The modification is called Cervical Vertebrae Maturation (CVM) method. In stage CS1 (Cervical Stage 1) the bases of vertebrae are flat, the bodies are trapezoid, and the maximum pubertal growth is still 2 or more years ahead. In CS2 concavity in the inferior surface of the base of C2 appears; the bodies of vertebrae remain trapezoid. The pubertal growth spurt is still more than 1 year ahead. In stage CS3 the concavity is observed on the inferior surfaces of C2 and C3. The vertebrae have the shape of either trapezoid or rectangular horizontal. According to Baccetti this stage signals the beginning of the maximum pubertal growth spurt. At CS4 the concavity appears on the inferior surfaces of C2, C3 and C4. Vertebrae C3 and C4 have the shape 219
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Obr. 1. Cervical Vertebral Maturation (CVM ) podle Baccettiho Fig. 1. Cervical Vertebral Maturation (CVM ) according to Baccetti
ruÊstoveÂho skoku. MaximaÂlnõ pubertaÂlnõ ruÊst nastaÂva podle Baccettiho mezi faÂzemi CS3 a CS4 (Obr. 1). Baccetti a kol. doporucÏujõ metodu CVM (cervical vertebrae maturation) jako ukazatel pro vhodne zahaÂjenõ leÂcÏby funkcÏnõÂmi aparaÂty. UdaÂvajõÂ, zÏe uÂspeÏch ortodonticke leÂcÏby je zaÂvisly na tom, zda se skutecÏneÏ pouzÏil funkcÏnõ aparaÂt ve vhodne ruÊstove faÂzi [18]. PrÏi leÂcÏbeÏ anomaÂliõ druhe trÏõÂdy, prvnõÂho oddeÏlenõ doporucÏujõ synchronizaci s obdobõÂm intervalu CS3-CS4, kdy jsou podle nich nejveÏtsÏõ prÏõÂruÊstky na dolnõ cÏelisti, nebo teÏsneÏ po teÂto faÂzi [19]. VcÏasna leÂcÏba vad trÏetõ trÏõÂdy (ruptura sÏvu patroveÂho a faciaÂlnõ maska) je efektivnõ ve faÂzi CS1-CS2, obdobneÏ jako leÂcÏba zuÂzÏene hornõ cÏelisti s vyuzÏitõÂm ruptury patroveÂho sÏvu. Predko a kol. [20] publikovali vyÂsledky studie, ve ktere byly srovnaÂny metody hodnocenõ kostnõÂho veÏku na podkladeÏ hodnocenõ zmeÏn morfologie krcÏnõÂch obratluÊ CVM podle Baccettiho a hodnocenõ rtg snõÂmku ruky se zaÂpeÏstõÂm podle BojoÈrka. Ve studii bylo zjisÏteÏno, zÏe u deÏvcÏat je mozÏne z jedne metody prÏedpoveÏdeÏt faÂzi ve druhe metodeÏ pouze ve 45 %, u chlapcuÊ v 64 % pacientuÊ. Podle korelacÏnõ analyÂzy bylo take zjisÏteÏno, zÏe faÂzi MP3cap (maximaÂlnõ pubertaÂlnõ spurt podle BjoÈrka) odpovõÂdajõ vsÏechny faÂze od CS1 do CS6 podle metody CVM, nejvõÂce faÂze CS4, cozÏ by podle Baccettiho znamenalo konec maximaÂlnõÂho ruÊstu. U 76,2 % chlapcuÊ, kterÏõ meÏli faÂzi MP3cap, byly nalezeny faÂze CS4, CS5 a CS6, ktere by meÏly ukazovat konec ruÊstu. ZatõÂm nebylo publikovaÂno dostatek spolehlivyÂch vyÂzkumuÊ, ve kteryÂch se porovnaÂvajõ vyÂsledky hodnocenõ stejnyÂch snõÂmkuÊ neÏkolika leÂkarÏi. Proto bylo cõÂlem teÂto studie proveÏrÏit spolehlivost metody CVM u võÂce hodnotiteluÊ i shodu prÏi opakovaneÂm hodnocenõ stejnyÂch hodnotiteluÊ. MateriaÂl a metoda Bylo pouzÏito 50 skenuÊ kefalogramuÊ pacientuÊ ortodontickeÂho oddeÏlenõ Kliniky zubnõÂho leÂkarÏstvõ FN a LF v Olomouci. Pacienti byli ve veÏku 10 - 14 let u deÏvcÏat, 11,5 azÏ 15,5 u chlapcuÊ. Obratle C2, C3 a C4 byly viditelne na vsÏech snõÂmcõÂch. Skeny byly umõÂsteÏny na internetove straÂnce, na ktere byl teÂzÏ prÏesny popis metody 220
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of lying rectangle. According to Baccetti, CS4 means the end of the maximum growth spurt. At CS5, vertebrae C3 or C4 have the shape of a square. The maximum growth spurt was about a year before this stage. At CS6 vertebrae C3 or C4 have the shape of standing rectangle. The maximum growth spurt was finished at least two years ago. According to Baccetti the maximum pubertal growth spurt takes place between the stages CS3 and CS4 (Fig.1). Baccetti et al. recommend cervical vertebrae maturation (CVM) as the indicator for optimal timing of treatment with functional appliances. They state that the success of orthodontic treatment depends on whether the therapy was carried out in the appropriate growth stage [18]. They recommend CS3-CS4 period for the treatment of Class II anomalies, as there is the greatest growth gain in the mandible during these stages, or immediately after the period is finished [19]. The early treatment of Class III malocclusions (palatal suture expansion and facial mask) is most effective during CS1-CS2 period; also, the treatment of narrow maxilla by means of rapid maxillary expansion is most effective during CS1-CS2 period. Predko et al. [20] published results of their study in which they compared methods of evaluation of skeletal age based on the evaluation of changes in the morphology of cervical vertebras (CVM) according to Baccetti, and the evaluation of X-rays of the hand and wrist according to BjoÈrk. The authors found out that in girls it is possible to predict the stage in the latter method on the basis of the former one in 45% of cases, whilst in boys in 64%. The correlation analysis showed that to MP3cap stage (maximum pubertal growth spurt according to BjoÈrk) all stages from CS1 to CS6 according to CVM method correspond; the maximum correlation is found for CS4 which would mean - according to Baccetti - finished maximum growth. In 76.2% of boys in MP3cap stage, there were identified stages CS4, CS5 and CS6 that should indicate the growth end. So far, only a small number of reliable studies have been published in which the same radiographs were evaluated by different evaluators. Therefore, our study aims to verify the reliability of CVM method between orthodontists, and to comment on the agreement in repeated evaluations by the same judges. Material and method 50 scans of cephalograms of patients from Orthodontic Department of Clinic of Dental Medicine, Medical Faculty of Palacky University Olomouc were used. The patients were aged 10 - 14 years in girls, 11.5 to 15.5 in boys. Cervical vertebrae C2, C3 and C4 were visible in all pictures. Scans were placed in internet webwww.orthodont-cz.cz e-mail:
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a prÏõÂklady vsÏech 6 faÂzõ zraÂnõ obratluÊ podle metody CVM. O urcÏovaÂnõ skeletaÂlnõÂho veÏku podle CVM bylo pozÏaÂdaÂno 11 ortodontistuÊ (ve vyÂsledcõÂch oznacÏeni põÂsmeny A - K), z nichzÏ 6 udaÂvalo, zÏe tuto metodu pravidelneÏ pouzÏõÂvajõÂ. Byl urcÏen stupenÏ interindividuaÂlnõ variability v prvnõ seÂrii mezi vsÏemi 11 leÂkarÏi pomocõ kappa podle Fleisse. Koeficient kappa podle Fleisse se pouzÏõÂva pro vyjaÂdrÏenõ podõÂlu mõÂry skutecÏneÏ dosazÏene shody u võÂce hodnotiteluÊ. RovneÏzÏ byla vypocÏõÂtaÂna mõÂra shody v hodnocenõ u vsÏech dvojic z 11 ortodontistuÊ, to jest 55 paÂruÊ leÂkarÏuÊ. U jednotlivyÂch dvojic bylo pocÏõÂtaÂno procento shodnyÂch hodnocenõÂ. LeÂkarÏi pak byli pozÏaÂdaÂni o druhe hodnocenõ stejnyÂch snõÂmkuÊ, prÏicÏemzÏ v druhe seÂrii bylo pro neÏ zmeÏneÏno porÏadõ skenuÊ. Interval mezi prvnõÂm a druhyÂm hodnocenõÂm byl võÂce nezÏ 3 tyÂdny. Pro kazÏdeÂho leÂkarÏe bylo zjisÏteÏno procento stejnyÂch vyÂsledkuÊ v prveÂm a druheÂm hodnocenõÂ. Pro kazÏdeÂho leÂkarÏe pak byla take zjisÏteÏna intraindividuaÂlnõ variabilita pomocõ kappa podle Cohena. Koeficient kappa podle Cohena vyjadrÏuje mõÂru skutecÏneÏ dosazÏene shody u dvou hodnocenõÂ. Byl vypocÏõÂtaÂn korelacÏnõ koeficient podle Spearmana mezi prvyÂm a druhyÂm hodnocenõÂm i chyba metody pomocõ Dahlbergovy formule [21]. Chyba metody ukazuje velikost chybove variability dane metody. Dahlbergova formule je , kde d je rozdõÂl mezi prvnõÂm a druhyÂm hodnocenõÂm jednotlivyÂch snõÂmkuÊ a n udaÂva mnozÏstvõ dvojic opakovanyÂch hodnocenõÂ. VyÂsledky Shoda v hodnocenõ skeletaÂlnõÂho veÏku metodou CVM mezi 11 hodnotõÂcõÂmi (interobserver agreement) vyjaÂdrÏena pomocõ ukazatele kappa podle Fleisse byla 0,325, cozÏ ukazuje v jejich hodnocenõ pouze mõÂrnou shodu (tab. 1). Shoda v hodnocenõ pro 55 paÂruÊ leÂkarÏuÊ v procentech shodneÏ hodnocenyÂch snõÂmkuÊ je pruÊmeÏrneÏ 44 % Tab. 1. Interpretace spolehlivosti - mõÂry shody v hodnocenõ podle ukazatele kappy Tab. 1. Interpretation of the agreement assessed with the kappa statistics κ
Interpretation
Interpretace
<0
poor agreement
špatná shoda
0.01 – 0.20
slight agreement
slabá shoda
0.21 – 0.40
fair agreement
mírná shoda
0.41 – 0.60
moderate agreement
střední shoda
0.61 – 0.80
substantial agreement almost perfect agreement
podstatná shoda
0.81 – 1.00
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téměř úplná shoda
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site, where the precise description of 6 stages of cervical maturation method was described. The examples of stages were also presented. Eleven orthodontists were asked to assess the CVM skeletal age (they are designated by letters A - K). Six orthodontists stated they use the method regularly. The degree of interindividual variability (interobserver agreement) was established for all 11 dentists by means of kappa according to Fleiss. The kappa according to Fleiss is the measure of real agreement in more evaluators. The agreement in the evaluation of all pairs of orthodontists (55 pairs) was also assessed. The orthodontists were then asked to perform the evaluation of the same pictures again, after more than 3 weeks. The order of radiographs was changed for the second assessment. The percentage of identical results in the first and the second evaluation was registered for each orthodontist. For each orthodontist, an intraindividual variability was determined by kappa according to Cohen, which shows the measure of agreement between two evaluations. The correlation coefficient according to Spearman between the first and the second evaluation, and the method error according to Dahlberg's formula were calculated [21]: , where d is the difference between the first and the second evaluation, and n a number of pairs of repeated measurements. The method error shows the size of error variability. Results Mean interobserver agreement between 11 evaluators assessed by means of the kappa according to Fleiss was 0.325, which suggests only a mild agreement (table 1). Identical evaluation for 55 pairs of orthodontists is on average in 44 percent of scans (tab. 2). The highest agreement reached 68% (tab. 3), the lowest 16% (tab. 4). The agreement in repeated evaluation for individual orthodontists (intraobserver agreement) was given also in percent of identical evaluations, and was between 44% and 78%, the average of 57% (fig. 2, tab. 5). Repeatability of evaluation for each orthodontist (A K) for the first and the second evaluation was determined by kappa according to Cohen. Kappa values were between 0.300 and 0.597, which suggests mild to moderate agreement (tab. 5). The values of correlation coefficient between two evaluations by the same 221
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Tab. 2. MõÂra shody mezi paÂry hodnotiteluÊ v procentech stejneÏ hodnocenyÂch snõÂmkuÊ (prÏes 50 % - tucÏneÏ) Tab. 2. The percentage of identical evaluation between the pairs of evaluators (over 50% - in bold) A
B
C
D
A
---
48
16
48
B
----
36
58
C
----
----
----
34
30
24
22
32
20
40
20
D
----
----
----
----
34
52
32
62
40
52
62
E
----
----
----
----
----
46
36
48
38
42
48
F
----
----
----
----
----
----
44
68
38
40
66
G
----
----
----
----
----
----
----
40
32
42
38
H
----
----
----
----
----
----
----
----
38
54
64
I
----
----
----
----
----
----
----
----
----
30
56
J
----
----
----
----
----
----
----
----
----
----
42
---
E
F
G
54
54
36
46
64
34
H
I
J
K
50
54
38
66
58
38
46
58
Tab. 4. NejnizÏsÏõ shoda (pocÏet snõÂmkuÊ)pro paÂr hodnotiteluÊ (hodnotitele A a C). ShodneÏ hodnocene faÂze u obou hodnotiteluÊ oznacÏeny tucÏneÏ (8 snõÂmkuÊ, tj.16 %). Tab. 4. The lowest rate of agreement (a number of radiographs) for a pair of evaluators (evaluators A and C). The same stages given are in bold (8 radiographs. i.e.16%). C
A
1
2
3
1
5
3
1
2
1
1
3
2
5
1
4
1
1
7
H 1
F
2
3
4
5
6
8
8
2
1
1
3
3
4
1
3
5
1
2
10
7 2
20
14 2
1
5
6 Total 14
11 0
5
9
16
5
1
50 (100 %)
5
6
Total 9
10
2
1
1
12
2
1
12
1
8
4
2
1
1
2
2
14
6
7
6
3
50 (100 %)
Tab. 5. Shoda hodnocenõÂ pro ortodontisty A - K v prveÂm a druheÂm hodnocenõÂ Tab. 5. Agreement of evaluations for orthodontists A-K in the first and the second evaluation
Total
1
2
Total 11
4
2
5 6
Tab. 3. NejvysÏsÏõ shoda (pocÏet snõÂmkuÊ) pro paÂr hodnotiteluÊ (hodnotitele F a H). ShodneÏ hodnocene faÂze u obou hodnotiteluÊ oznacÏeny tucÏneÏ (34 snõÂmkuÊ, tj. 68 %). Tab. 3: The highest rate of agreement (a number of radiographs) for a pair of evaluators (evaluators F and H). The same stages are in bold letters (34 radiographs, i.e. 68%).
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A B C D E F G H I J K
Procento snímků se stejným hodnocením Per cent of the same results 74 56 44 50 48 78 62 68 52 48 50
kappa podle Cohena Cohen’s kappa ----* ----* 0.300 ----* 0.373 0.707 0.527 0.597 0.425 0.363 0.400
korelační koeficient correlation coefficient 0.679** 0.740** 0.654** 0.662** 0.710** 0.868** 0.706** 0.779** 0.688** 0.541** 0.807**
chyba metody podle Dahlberga Dahlberg’s method error 0.70 0.68 0.79 0.96 0.93 0.47 0.75 0.78 0.91 1.08 0.83
* kappa nenõ mozÏne vypocÏõÂtat, k tomu je trÏeba tabulka se symetrickyÂmi hodnotami z prveÂho a ze druheÂho hodnocenõÂ; ** signifikantnõ na uÂrovni p < 0,01 * kappa statistics can not be computed, they require a symmetric 2-way table in which the values of the first assessment match the values of the second assessment; ** significant at the level of p < 0.01
Tab. 6. MõÂra neshody prÏi druheÂm hodnocenõÂ ortodontistuÊ A - K Tab. 6. The degree of divergence between the first and the second evaluation by orthodontists A-K Odchylka při stanovení fází, cervical stages apart 1
Obr. 2. Shoda prÏi opakovaneÂm hodnocenõ pro jednotlive ortodontisty Fig. 2. Agreement in repeated evaluation for individual orthodontists
snõÂmkuÊ (tab. 2). NejvysÏsÏõ shoda byla 68 % (tab. 3) a nejnizÏsÏõ 16% (tab. 4). PrÏi opakovaneÂm hodnocenõ teÏchtyÂzÏ leÂkarÏuÊ (intraobserver agreement) procento shodnyÂch hodnocenõ cÏinilo od 44 % do 78 %, pruÊmeÏr byl 57 % (obr. 2, tab. 5) Byla take vyhodnocena opakovatelnost hodnocenõ kazÏdeÂho leÂkarÏe (A-K) v prveÂm a druheÂm hodnocenõ pomocõ kappa podle Cohena. Kappa se pohybovala od 0,300 do 0,597, cozÏ znamena mõÂrnou azÏ strÏednõ shodu 222
A
B
C
D
E
F
G
H
I
J
K
18% 36% 40% 30% 26% 18% 24% 18% 28% 30% 24%
průměr mean
26.55 %
2
4%
6%
12% 14% 20%
2%
10% 10% 14%
8%
24% 11.27 %
3
0%
0%
4%
2%
4%
2%
2%
0%
2%
10%
2%
2.55 %
4
4%
2%
0%
2%
2%
0%
2%
4%
4%
2%
0%
2%
5
0%
0%
0%
2%
0%
0%
0%
0%
0%
2%
0%
0.36 %
orthodontist were between 0.541 and 0.868. The method error according to Dahlberg was between 0.47 of a stage to 1.08 of a stage (tab. 5). The deviation of the second evaluation by one stage in individual dentists was between 18% and 40% of radiographs, the average of 26.55%, by two stages between 2% and 24% of radiographs (the average = 11.27%). There were also pictures in which the deviation for the second evaluation was higher (maximum www.orthodont-cz.cz e-mail:
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Obr. 3. Rtg snõÂmek cÏ. 40 byl v prvnõÂm meÏrÏenõÂ hodnocen jako stadium CS1, CS3, CS4, v druheÂm jako CS1, CS3, CS4, CS5, CS6. Fig. 3. Radiograph No. 40 was in the first measurement determined as stage CS1, CS3, CS4, in the second measurement as stage CS1, CS3, CS4, CS5, CS6.
Obr. 4. Rtg cÏ. 24. Jedna osoba oznacÏila v prveÂm i druheÂm oceneÏnõÂ jako faÂzi CS3 a ostatnõÂ jako CS4 (100 % intraobserver agrement). Fig. 4. Radiograph No. 24. One evaluator determined in both first and second measurement stage CS3, the rest of orthodontists determined CS4 (100% intraobserver agreement).
(tab. 5). KorelacÏnõ koeficient mezi dveÏma hodnocenõÂmi teÂhozÏ ortodontisty byl od 0,541 do 0,868. Ze dvou hodnocenõ byla vypocÏtena chyba metody podle Dahlberga. Chyba cÏinila od 0,47 faÂze do 1,08 faÂze (tab. 5). Odchylka prÏi druheÂm hodnocenõ o jednu faÂzi cÏinila pro jednotlive leÂkarÏe od 18 % do 40 % snõÂmkuÊ, pruÊmeÏrneÏ 26,55 %, o dveÏ faÂze od 2 % do 24 % snõÂmkuÊ (pruÊmeÏr 11,27 %). Byly teÂzÏ snõÂmky, u kteryÂch odchylky v druheÂm hodnocenõ byly veÏtsÏõ (maximaÂlneÏ 5, cÏili naprÏ. v prveÂm hodnocenõ faÂze 1 a ve druheÂm hodnocenõ faÂze 6 (tab. 6). PrÏõÂklad velke neshody je u snõÂmku 40 (obr. 3). PrÏõÂklad nejvysÏsÏõ shody byl u snõÂmku cÏ. 24 (obr. 4).
was 5, e.g. in the first evaluation of stage 1, and in the second evaluation of stage 6) (tab. 6). The example of great discrepancy is in the picture 40 (fig. 3). The example of good agreement is in the picture 24 (fig. 4).
Diskuse KazÏda diagnosticka metoda ma mõÂt dostatecÏnou mõÂru spolehlivosti a opakovatelnosti, ma vyjadrÏovat co nejveÏrneÏji funkci pro kterou je urcÏena, tj. ma byÂt pravdiva (trueness) a prÏesna (accuracy). Pro metodu CVM k urcÏovaÂnõ skeletaÂlnõÂho veÏku podle vyÂvoje krcÏnõÂch obratluÊ najdeme v literaturÏe v tomto smyslu velmi rozdõÂlna hodnocenõÂ. Optimisticke vyÂsledky ve sve studii dosaÂhli Ballrick a kol. [23]. 13 rezidentuÊ hodnotilo 15 kefalogramuÊ pawww.orthodont-cz.cz e-mail:
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Discussion Each diagnostic method should be as reliable and repeatable as possible. It means that it should reflect as precisely as possible the function for which it is used. It should have enough precision and accuracy. One can find very different evaluations in literature in the aspect how the method CVM indicates the skeletal age. Optimistic results report Ballrick et al. [23]: thirteen residents evaluated 15 cephalograms of adolescent (pubertal age) patients twice within the interval of two weeks. The agreement in the repeated evaluation was 0.82 weighted kappa. Franchi et al. [15] achieved a high degree of agreement when two evaluators assessed 24 patients and for each patient there were 6 consecutive cephalograms available. The agreement was 98.6%. A relatively high degree of agreement was reported also by Baccetti [18]. Gandini et al. [24] compared skeletal 223
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cientuÊ v pubertaÂlnõÂm veÏku v odstupu 2 tyÂdnuÊ. Shoda prÏi opakovaneÂm hodnocenõ byla 0,82 vaÂzÏene kappa. Franchi a kol. [15] dosaÂhli vysokou shodu, ktera byla pro 2 hodnotõÂcõ 98,6 %. Hodnotili 24 pacientuÊ a pro kazÏdeÂho bylo dostupnyÂch 6 konsekutivnõÂch kefalogramuÊ. Vysokou shodu ukaÂzal rovneÏzÏ Bacetti [18]. Gandini a kol. [24] porovnaÂvali skeletaÂlnõ veÏk podle CVM a rtg.ruky se zaÂpeÏstõÂm podle BjoÈrka u 30 pacientuÊ. Po 6 meÏsõÂcõÂch opakovali hodnocenõ a zõÂskali identicke vyÂsledky, tedy dosaÂhli 100% shody. Je vsÏak trÏeba vzõÂt v uÂvahu, zÏe pacienti byli ve veÏku od 7 do 18, tedy je mozÏneÂ, zÏe pacienti v krajnõÂch veÏkovyÂch obdobõÂch byli skeletaÂlneÏ jednoznacÏneÏji kvalifikovatelnõÂ. V nasÏõ skupineÏ byly deÏti ve veÏku kolem puberty (10 azÏ 15,5 let). Flores-Mir a kol. [25] ocenÏovali opakovatelnost cÏi spolehlivost hodnocenõ (intraexaminer reliability) pro 10 naÂkresuÊ kefalogramuÊ stejnyÂch pacientuÊ trÏikraÂt a dosaÂhli hodnoty 0,889 (od 0,723 do 0,968; p<0,001). Je trÏeba vzõÂt v uÂvahu malou hodnocenou skupinu. San Roman a kol. [16] posuzovali opakovatelnost metody na zaÂkladeÏ pruÊkresuÊ 50 snõÂmkuÊ hodnocenyÂch v odstupu 3 tyÂdnuÊ. VeÏk pacientuÊ byl od 5 do 18 let. Opakovatelnost hodnotili PearsonovyÂm koeficientem s hodnotami od 0,96 do 0,99 (p<0,001). VyÂsledky byly jisteÏ ovlivneÏny sÏirokyÂm rozpeÏtõÂm veÏku i pouzÏitõÂm pruÊkresuÊ na folii. PodobneÏ to bylo v praÂci Hassela a Farmana [12], kde byly opakovaneÏ hodnoceny pruÊkresy rentgenovyÂch snõÂmkuÊ pacientuÊ ve veÏku 8 - 18 let a potvrzena vysoka korelace jak mezi hodnotõÂcõÂmi tak i prÏi opakovaneÂm hodnocenõÂ. Naopak Gabriel a kol. [22] uvedli ve sveÂm vyÂzkumu malou shodu v opakovaneÂm hodnocenõ metodou CVM. Shoda u opakovaneÂho hodnocenõ (intraobserver agreement) se pohybovala v rozmezõ od 43,3 % do 80 %, pruÊmeÏr byl 62,3 %. V nasÏõ studii byly vyÂsledky obdobneÂ, tj. nejvysÏsÏõ dosazÏena shoda u hodnotõÂcõÂho leÂkarÏe byla 78 %, nejnizÏsÏõ 44 %, pruÊmeÏr 57 %. Shoda stejneÂho hodnocenõ mezi ruÊznyÂmi hodnotõÂcõÂmi (interobserver agreement) byla nõÂzkaÂ, pod 50% - byla 44 %. PrÏi hodnocenõ velkeÂho pocÏtu pacientuÊ je veÏtsÏõ pravdeÏpodobnost ruÊznorodosti v morfologii tvaru krcÏnõÂch obratluÊ. V nasÏõ skupineÏ je to naprÏ. obr. 3, kde dolnõ hrana obratle C2 je plochaÂ, ale tvar obratle se blõÂzÏõ cÏtverci. Tu je mozÏne vysveÏtlit obtõÂzÏe pro jednoznacÏneÏjsÏõ kvalifikaci jednotlivyÂch faÂzõÂ, protozÏe hodnotitele pravdeÏpodobneÏ nebyli schopni rozhodnout, ktere kriterium je duÊlezÏiteÏjsÏõÂ, zda profil obratle nebo konkavita dolnõ hrany. Nestman a kol. [26] upozornÏujõ take na probleÂm s urcÏenõÂm tvaru obratle, je-li to lichobeÏzÏnõÂk, cÏtverec nebo obdeÂlnõÂk, cozÏ podle nich povede k nõÂzke opakovatelnosti hodnocenõÂ. 224
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age according to CVM and radiograph of the hand and wrist according to BjoÈrk in 30 patients. They repeated the evaluation after 6 months and got identical results, i.e. they reached 100% agreement. However, one should not forget that their patients were between 7 and 18 years old, and therefore, the patients in the extreme age groups were easy to classify in terms of skeletal age. In our group there were children in their pubertal period (between the age of 10 and 15.5). Flores-Mil et al. [25] evaluated intraexaminer reliability for 10 tracings of cephalograms of the same patients three times and obtained the value 0.889 (between 0.723 and 0.968; p<0.001). However, the sample of patients whose radiographs were evaluated was rather small. San Roman et al. [16] examined the repeatability of the technique using tracings of 50 radiographs evaluated within the interval of three weeks. The patients were between 5 and 18 years old. The repeatability was assessed by Pearson coefficient and the values were between 0.96 and 0.99 (p<0.001). The results were certainly affected by the extensive age differences and due to the use of tracings. Hassel and Farman [12] evaluated tracings of radiographs of patients between the age of 8 and 18, and they proved a high correlation both between the evaluators and in the repeated evaluation. On the contrary, Gabriel et al. [22] found only a moderate agreement/correlation in their study on repeated evaluations of the CVM. The intraobserver agreement was between 43.3% and 80%, the mean value was 62.3%. Our research showed similar results, i.e. the intraobserver agreement oscillated between 78% and 44%, the mean value was 57%. The interobserver agreement was rather low, only 44%. When evaluating a great number of patients there is higher probability of a greater variety in the morphology of cervical vertebrae. This can be observed in e.g. figure 3, where the bottom edge of C2 is flat, however the overall shape of the vertebra is close to that of a square. This may be the reason why the classification of individual stages is not unambiguous - we think that the evaluators were not able to decide which criterion is more important - the vertebra profile or concavity of the lower edge. Nestman et al. [26] point out to the problem of identification of the shape of vertebrae, i.e whether it is trapezoid, square or rectangle. This also results in lower agreement in evaluation. In the CVM method we evaluated stages that changed smoothly from one to another; if an error by one stage were acceptable, the repeatability of the method would increase considerably. However, if we accept according to Baccetti - that the beginning of pubertal www.orthodont-cz.cz e-mail:
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V metodeÏ CVM hodnotõÂme faÂze, ktere prÏechaÂzejõ plynule jedna ve druhou, bylo by mozÏne tolerovat chybu o jednu faÂzi, opakovatelnost hodnocenõ by vyÂrazneÏ vzrostla. Pokud vsÏak prÏijmeme podle Bacettiho za pocÏaÂtek pubertaÂlnõÂho spurtu faÂzi CS3 a za konec CS4, tolerance chyby o jednu faÂzi by naÂm dala klinicky zcela jinou informaci (vhodna doba pro vyuzÏitõ pubertaÂlnõÂho ruÊstoveÂho spurtu u skeletaÂlnõÂch II. trÏõÂd, rozhodnutõ o leÂcÏbeÏ skeletaÂlnõÂch III. trÏõÂd a skeletaÂlnõÂho otevrÏeneÂho skusu). Podle nasÏich vyÂsledkuÊ je urcÏovaÂnõ skeletaÂlnõÂho veÏku metodou CVM maÂlo spolehliveÂ, aby bylo mozÏne na tomto urcÏenõ zalozÏit rozhodnutõ o plaÂnu leÂcÏby. Shoda v hodnocenõ ruÊznyÂch hodnotiteluÊ stejneÏ jako shoda v opakovaneÂm hodnocenõ hodnotiteluÊ je nõÂzkaÂ. Chyba metody (podle Dahlbergova vzorce) je vysokaÂ. Chyba metody je v nasÏõ studii teÂmeÏrÏ velikosti jedne faÂze (0,47 azÏ 1,08 faÂze). NicmeÂneÏ u leÂcÏby distookluze nenõ prÏesne urcÏenõ skeletaÂlnõÂho veÏku obvykle nutneÂ. Podle Tullochove [27] a O'Briena [28] prÏi leÂcÏbeÏ vad II. skeletaÂlnõ trÏõÂdy obvykle zacÏõÂnaÂme leÂcÏbu prÏi vyÂmeÏneÏ smõÂsÏeneÂho chrupu za staÂly a velikost prÏõÂruÊstku dolnõ cÏelisti u konkreÂtnõÂho pacienta je obtõÂzÏne prÏedpovõÂdat. Pokud vsÏak o zpuÊsobu i cÏasu leÂcÏby ma rozhodnout skeletaÂlnõ veÏk (skeletaÂlnõ vady III.trÏõÂdy a skeletaÂlnõ otevrÏeny skus), bude vhodne doplnit urcÏenõ skeletaÂlnõÂho veÏku rtg. snõÂmkem ruky se zaÂpeÏstõÂm, kde faÂze spojovaÂnõ epifyÂz a diafyÂz cÏlaÂnkuÊ prstuÊ DP3u, PP3u, MP3u naÂs informujõ o ukoncÏenõ maximaÂlnõÂho ruÊstoveÂho spurtu a zpomalovaÂnõ ruÊstu postavy i cÏelistõ [2]. ZaÂveÏry 1. Chyba metody CVM je velka prÏi urcÏovaÂnõ faÂzõ skeletaÂlnõÂho veÏku kolem puberty. 2. UrcÏovaÂnõ skeletaÂlnõÂho veÏku metodou CVM je maÂlo spolehliveÂ, aby bylo mozÏne na tomto urcÏenõ zalozÏit rozhodnutõ o plaÂnu leÂcÏby. 3. Pokud o zpuÊsobu a cÏasu leÂcÏby ma rozhodovat skeletaÂlnõ veÏk (skeletaÂlnõ vady III.trÏõÂdy, skeletaÂlnõ otevrÏeny skus) je potrÏebne doplnÏujõÂcõ rtg ruky se zaÂpeÏstõÂm.
rocÏnõÂk 21 cÏ. 4. 2012
growth spurt is CS3, and its end at CS4, the tolerance by one stage would bring clinically very different information (the time appropriate to use growth spurt in skeletal Class II, the decision on the treatment of skeletal class III, and the treatment of skeletal open bite). Our results demonstrated that the classification of skeletal age with the CVM method is not reliable enough to use it as the serious information for treatment planning. The interobserver agreement as well as the intraobserver agreement is low. The error of the method (according the Dahlberg's formula) is high. The error of the method in our study is almost one phase (0.47 of a stage to 1.08 of a stage). However, in the treatment of patients with distoocclusion, the precise determination of the skeletal age is not usually necessary. According to Tulloch [27] and O'Brien [28] we usually start to treat Class II anomalies during the change of mixed dentition into the permanent one, and it is difficult to predict the amount of mandibular growth gain in an individual patient. Nevertheless, if the skeletal age (skeletal Class III, and skeletal open bite), is to decide about the method and timing of treatment, it is appropriate to support the skeletal age identification with the radiograph of the hand and wrist. The phases of uniting of epiphyses and diaphyses of DP3u, PP3u, MP3u inform us about the finished maximum growth spurt, and that the growth of body and jaws slows down [2]. Conclusions 1. The error of the CVM method in determination of the phases of skeletal age around the puberty is high. 2. A reliability of the classification of the skeletal age with the CVM method is too low to base on it the decisions in treatment planning. 3. In case the skeletal age is to decide about the treatment approach and its timing, (skeletal Class III, skeletal open bite), it is necessary to analyze the radiograph of the hand and wrist. Authors have no commercial, proprietary or financial interest in products or companies mentioned in the article.
Literatura/References 1. BjoÈrk, A.: Timing of interceptive measures based on stages of maturation, Trans. Eur. Orthodont. Soc. 1972, 48, s. 61-74. 2. Hunter, C. J.: The correlation of facial growth with body height and skeletal maturation at adolescence. Angle Orthodont .1966, 36, s. 44-54. 3. Bergersen, E. O.: The male adolescent facial growth spurt: its prediction and relations to skeletal maturation. Angle Orthodont. 1972, 42, s. 319-338. 4. BjoÈrk, A.; Helm, S.: Prediction of age of maximum of pubertal growth in body height. Angle Orthodont. 37, 1967, cÏ. 2, s. 134-143. www.orthodont-cz.cz e-mail:
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5. Helm, S.; Siersbaek-Nielsen, S.; Skieller, V.; BjoÈrk, A.: Skeletal maturation of the hand in relation to maximum pubertal growth in body height. Tandlaedgebladet 1971, 75, s. 1223-1234. 6. KamõÂnek, M.: SoucÏasne fixnõ ortodonticke aparaÂty. Praha, Avicenum 1976. 7. KamõÂnek, M.; SÏtefkovaÂ, M.: Ortodoncie I. Skriptum. 2nd ed. Olomouc, Univerzita PalackeÂho 2001. 8. Fishman, L. S.: Radiographic evaluation of skeletal maturation. A clinically oriented method based on handwrist films. Angle Orthodont. 1982, 52, s. 88-112. 225
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9. Fishman, L. S: Maturational patterns and prediction during adolescence. Angle Orthodont. 1987, 57, s. 178-193. 10. HaÈgg, U.; Taranger, J.: Maturation indicators and the pubertal growth spurt. Amer. J. Orthodont. 1982, 82, s. 299-309. 11. O'Reilly, M. T; Yanniello G. J: Mandibular growth changes and maturation of cervical vertebrae - a longitudinal study. Angle Orthodont. 1988, 58, s. 179-184. 12. Hassel, B.; Farman, A.: Skeletal maturation evaluation using cervical vertebrae. Amer. J. Orthodont. dentofacial Orthop. 1995, 107, s. 58-66. 13. Pancherz, H.; Szyska, M.: Analyse der HalswirbelkoÈrper statt der Handknochen zur Bestimmung der skelettalen und somatischen Reife. Informationen aus Orthodontie und KieferorthopaÈdie 2000, 32, cÏ. 2, s. 151-161. 14. Garcia-Fernandez, P.; Torre, H.: The cervical vertebrae as maturational indicators. J. Clin. Orthodont 1998, 32, s. 221-225. 15. Franchi, L.; Baccetti, T.; McNamara, J. A. Jr.: Mandibular growth as related to cervical vertebral maturation and body heigh. Amer. J. Orthodont. dentofacial Orthop. 2000, 118, s. 335-340. 16. San Roman, P.; Palma, J. C.; Oteo, D.; Nevado, E.: Skeletal maturation determined by cervical vertebrae development. Eur. J. Orthodont. 2002, 24, s. 303-311. 17. Baccetti, T.; Franchi, L.; McNamara, J. A. Jr.: An improved version of the cervical vertebral maturation (CVM) method for the assessment of mandibular growth. Angle Orthodont. 2002, 72, s. 316-323. 18. Baccetti, T.; Franchi, L.; McNamara, J. A. Jr.: The cervical vertebral maturation ( CVM) method for the assessment of optimal treatment timing in dentofacial orthopedics. Seminars in Orthodontics 2005. 19. Baccetti, T.; Franchi, L.; Toth, L. R.; McNamara, J. A. Jr.: Treatment timing for Twin-block therapy. Amer. J. Orthodont. dentofacial Orthop. 2000, 118, s. 159-70.
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20. Predko, A.; KamõÂnek, M.; LangovaÂ, K.: SkeletaÂlnõÂ veÏk v ortodoncii. CÏes. Stomat. 2011, 111, cÏ. 6, s. 154-159. 21. Dahlberg, G.: Statistical methods for medical and biological students. London: George Allen Unwin, 1940. 22. Gabriel, D. B.; Southard, K. A.; Qian, F.; Marshall, S. D.; Franciscus, R. D.; Southard, T. E.: Cervical vertebrae maturation method: poor reproducibility. Amer. J. Orthodont. dentofacial Orthop. 2009, 136, s. 478-480. 23. Ballrick, J.; Fields, H.; Vig, K. W. L.; Beck, F.; Germack, J.; Baccetti, T.: Reliability and validity of cervical vertebral maturation and hand-wrist radiographs. Proceedings of the 83rd General Session of the IADR/AADR/ CADR;2005, Mar. 9-12; Baltimore. 24. Gandini, P.; Mancini, M.; Andreani, F.: A comparison of hand-wrist bone and cervical vertebral analyses in measuring skeletal maturation. Angle Orthodont. 2006, 76, s. 984-989. 25. Flores -Mir, C.; Burgess, C. A.; Champney, M.; Jensen, R. J.; Pitcher, M. R.; Major, P. W.: Correlation of skeletal maturation stages determined by cervical vertebrae and hand-wrist evaluations. Angle Orthodont. 2006, 76, s.1-5. 26. Nestman, T. S.; Marshall, S. D.; Qian, F.; Holton, N.; Franciscus, R. G.; Southard, T. E.: Cervical vertebrae maturation method morphologic criteria: Poor reproducibility. Amer. J. Orthodont. Dentofacial Orthop. 2011, 140, s. 182-128. 27. Tulloch, J. F. C.; Philips, C.; Proffit, W.R.: Benefit of early Class II treatment: progress report of a two-phase randomized clinical trial. Amer. J. Orthodont. dentofacial Orthop. 1998, 113, cÏ.1, s.62-72. 28. O`Brien, K..; Wright, J..; Conboy, F. et al.: Early treatment for Class II Division 1 malocclusion with the Twin block appliance: a multi-center, randomized, controlled trial. Amer. J. Orthodont. dentofacial Orthop. 2009, 135, cÏ. 5, s. 573-579.
MUDr. Agnieszka Predko Klinika zubnõÂho leÂkarÏstvõÂ LF UP PalackeÂho 12, 772 00 Olomouc
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