*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 urcÏenõÂ skeletaÂlnõÂho veÏku podle vyÂvoje krcÏnõÂ paÂterÏe (cervical vertebrae maturation - CVM) v modifikaci Baccettiho. CõÂlem bylo proveÏrÏit spolehlivost metody CVM u võÂce hodnotiteluÊ i shodu prÏi opakovaneÂm hodnocenõÂ stejnyÂch hodnotiteluÊ.
MateriaÂl a metoda: Studie se zuÂcÏastnilo 11 ortodontistuÊ, kterÏõÂ hodnotili 50 bocÏnõÂch kefalometrickyÂch snõÂmkuÊ deÏtõÂ v obdobõÂ kolem pubertaÂlnõÂho ruÊstoveÂho spurtu. Byla u nich posuzovaÂna shoda v hodnocenõÂ sumaÂrneÏ pomocõÂ kappa podle Fleisse i shoda v hodnocenõÂ 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 nejvysÏsÏõ shoda u jedne dvojice u 68 % snõÂmkuÊ, nejnizÏsÏõ u 16% snõÂmkuÊ. PrÏi opakovaneÂm hodnocenõ titõÂzÏ hod- notõÂcõ 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 dalsÏõ 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 evalua- tion 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 as- sessed 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
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 treat- ment is during the adolescent growth spurt. Pubertal acceleration in jaw growth and in body growth correla- tes fully or almost fully [1, 2, 3].
Chronological or dental age of a patient in this pe- riod does not correlate well with his/her skeletal age.
There are two major methods used for the determi- nation of skeletal age: evaluation of radiographs of the hand and wrist, and evaluation of changes in morpho- logy of cervical vertebrae assessed on lateral cephalo- grams.
In orthodontic practice, the methods relating deve- lopment 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 bo- nes development, builds on the longitudinal study of patients monitored in a growth study with titanium im- plants.
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 radio- graphs 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 ra- diograph.
Baccetti's modification of skeletal age classifica- tion, 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 verte- brae 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 ve- rtebrae have the shape of either trapezoid or rectangu- lar 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 UÂvod
Intenzita ruÊstu cÏelistõ v obdobõ dospõÂvaÂnõ hraje rolive vyÂbeÏru zpuÊsobu leÂcÏby, ale iv urcÏenõ vhodneÂho veÏku pacienta pro zahaÂjenõ leÂcÏby. VeÏtsÏinou je optimaÂlnõ pro zahaÂjenõ ortodonticke leÂcÏby obdobõ pubertaÂlnõÂho ruÊ- stoveÂho zrychlenõÂ. PubertaÂlnõ zrychlenõ v ruÊstu cÏelist- nõÂch 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 nekore- luje prÏõÂlisÏ s jeho skeletaÂlnõÂm veÏkem.
V ortodoncii se pouzÏõÂvajõÂ dveÏ hlavnõÂ metody urcÏenõÂ skeletaÂlnõÂho veÏku: hodnocenõÂ rtg snõÂmku ruky se zaÂpeÏ- stõÂm a hodnocenõÂ zmeÏn morfologie krcÏnõÂch obratluÊ na bocÏnõÂm kefalogramu.
V ortodonticke praxise prÏevaÂzÏneÏ vyuzÏõÂvajõ metody charakterizujõÂcõ vyÂvoj kostõ ruky ve vztahu ke krÏivce in- tenzity 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 vzni- kla na zaÂkladeÏ longitudinaÂlnõ studie pacientuÊ sledova- nyÂch v ruÊstove studii s titanovyÂmiimplantaÂty.
Lamparskiv roce 1972 vydal atlas, kde popisuje zmeÏny tvaru krcÏnõÂch obratluÊ C2-C6 v obdobõ dospõÂ- vaÂnõÂ, zvlaÂsÏt' u dõÂvek a u chlapcuÊ, stejneÏ jako souvislost se skeletaÂlnõÂm veÏkem podle zmeÏn na rtg. snõÂmku ruky se zaÂpeÏstõÂm. PostupneÏ idalsÏõ autorÏipublikovalisve modifikovane metody [11, 12, 13, 14, 15, 16, 17, 18].
Tyto studie uvaÂdeÏjõÂ mozÏnost vyuzÏitõÂ zmeÏn tvaru krcÏnõÂch obratluÊ viditelnyÂch na bocÏnõÂch kefalogramech pro urcÏenõÂ kostnõÂho veÏku a prÏedpoveÏd'pubertaÂlnõÂho ruÊ- stoveÂho spurtu, stejneÏ jako mozÏnost pouzÏitõÂ hodno- cenõÂ vyÂvoje krcÏnõÂ paÂterÏe mõÂsto hodnocenõÂ rtg ruky se zaÂpeÏstõÂm, cÏõÂmzÏ se usÏetrÏõÂ 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 Verte- bral Maturation (CVM). PrÏifaÂziCS1 (Cervical Stage 1) jsou teÏla obratluÊ plochaÂ, majõ tvar lichobeÏzÏnõÂku, do ma- ximaÂlnõÂho pubertaÂlnõÂho ruÊstoveÂho zrychlenõ je 2 a võÂce rokuÊ. PrÏifaÂziCS2 se objevõ konkavita na spodnõ straneÏ obratle C2, nadaÂle jsou teÏla obratluÊ lichobeÏzÏnõÂkovaÂ. Do pocÏaÂtku pubertaÂlnõÂho spurtu je minimaÂlneÏ 1 rok. PrÏifaÂzi CS3 je konkavita na spodnõÂm povrchu C2 a C3. Tvar obratluÊ je lichobeÏzÏnõÂk nebo lezÏõÂcõ obdeÂlnõÂk. Podle Bac- cettiho 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 zakoncÏenõÂ
of lying rectangle. According to Baccetti, CS4 means the end of the maximum growth spurt. At CS5, verte- brae C3 or C4 have the shape of a square. The maxi- mum 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 maxi- mum pubertal growth spurt takes place between the stages CS3 and CS4 (Fig.1).
Baccettiet al. recommend cervical vertebrae matu- ration (CVM) as the indicator for optimal timing of treat- ment 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 im- mediately 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 effec- tive during CS1-CS2 period.
Predko et al. [20] published results of their study in which they compared methods of evaluation of skele- tal 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 accor- ding to CVM method correspond; the maximum corre- lation 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 re- peated evaluations by the same judges.
Material and method
50 scans of cephalograms of patients from Ortho- dontic Department of Clinic of Dental Medicine, Medi- cal 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 vi- sible in all pictures. Scans were placed in internet web- ruÊstoveÂho skoku. MaximaÂlnõÂ pubertaÂlnõÂ ruÊst nastaÂvaÂ
podle Baccettiho mezi faÂzemiCS3 a CS4 (Obr. 1). Baccettia kol. doporucÏujõ metodu CVM (cervical ve- rtebrae maturation) jako ukazatel pro vhodne zahaÂjenõ leÂcÏby funkcÏnõÂmiaparaÂty. UdaÂvajõÂ, zÏe uÂspeÏch ortodon- ticke leÂcÏby je zaÂvisly na tom, zda se skutecÏneÏ pouzÏil funkcÏnõ aparaÂt ve vhodne ruÊstove faÂzi[18]. PrÏileÂcÏbeÏ anomaÂliõ druhe trÏõÂdy, prvnõÂho oddeÏlenõ doporucÏujõ synchronizaci s obdobõÂm intervalu CS3-CS4, kdy jsou podle nich nejveÏtsÏõÂprÏõÂruÊstky na dolnõÂcÏelisti, 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 ob- ratluÊ 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 % pa- cientuÊ. Podle korelacÏnõ analyÂzy bylo take zjisÏteÏno, zÏe faÂziMP3cap (maximaÂlnõ pubertaÂlnõ spurt podle BjoÈrka) odpovõÂdajõ vsÏechny faÂze od CS1 do CS6 podle metody CVM, nejvõÂce faÂze CS4, cozÏ by podle Baccettiho zna- menalo konec maximaÂlnõÂho ruÊstu. U 76,2 % chlapcuÊ, kterÏõ meÏli faÂziMP3cap, byly nalezeny faÂze CS4, CS5 a CS6, ktere by meÏly ukazovat konec ruÊstu.
ZatõÂm nebylo publikovaÂno dostatek spolehlivyÂch vyÂzkumuÊ, ve kteryÂch se porovnaÂvajõÂ vyÂsledky hodno- cenõÂ stejnyÂch snõÂmkuÊ neÏkolika leÂkarÏi. Proto bylo cõÂlem teÂto studie proveÏrÏit spolehlivost metody CVM u võÂce hodnotiteluÊ ishodu prÏiopakovaneÂm hodnocenõÂ stej- nyÂch hodnotiteluÊ.
MateriaÂl a metoda
Bylo pouzÏito 50 skenuÊ kefalogramuÊ pacientuÊ orto- dontickeÂho 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 vidi- telne na vsÏech snõÂmcõÂch. Skeny byly umõÂsteÏny na inter- netove straÂnce, na ktere byl teÂzÏ prÏesny popis metody
Obr. 1. Cervical Vertebral Maturation (CVM ) podle Baccettiho Fig. 1. Cervical Vertebral Maturation (CVM ) according to Baccetti
site, where the precise description of 6 stages of cervi- cal 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 (interobser- ver agreement) was established for all 11 dentists by means of kappa according to Fleiss. The kappa accor- ding 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 ortho- dontist.
For each orthodontist, an intraindividual variability was determined by kappa according to Cohen, which shows the measure of agreement between two evalua- tions.
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 evalua- tors assessed by means of the kappa according to Fleiss was 0.325, which suggests only a mild agree- ment (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 bet- ween 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 determi- ned by kappa according to Cohen. Kappa values were between 0.300 and 0.597, which suggests mild to mo- derate agreement (tab. 5). The values of correlation coefficient between two evaluations by the same a prÏõÂklady vsÏech 6 faÂzõÂ zraÂnõÂ obratluÊ podle metody
CVM.
O urcÏovaÂnõÂ skeletaÂlnõÂho veÏku podle CVM bylo pozÏaÂ- daÂno 11 ortodontistuÊ (ve vyÂsledcõÂch oznacÏenipõÂsmeny A - K), z nichzÏ 6 udaÂvalo, zÏe tuto metodu pravidelneÏ pouzÏõÂvajõÂ.
Byl urcÏen stupenÏ interindividuaÂlnõ variability v prvnõ seÂrii mezi vsÏemi11 leÂkarÏipomocõ kappa podle Fleisse. Koeficient kappa podle Fleisse se pouzÏõÂva pro vyjaÂd- rÏenõ podõÂlu mõÂry skutecÏneÏ dosazÏene shody u võÂce hod- notiteluÊ.
RovneÏzÏ byla vypocÏõÂtaÂna mõÂra shody v hodnocenõÂ u vsÏech dvojic z 11 ortodontistuÊ, to jest 55 paÂruÊ leÂkarÏuÊ. U jednotlivyÂch dvojic bylo pocÏõÂtaÂno procento shod- nyÂch hodnocenõÂ.
LeÂkarÏipak bylipozÏaÂdaÂnio druhe hodnocenõ stej- nyÂch snõÂmkuÊ, prÏicÏemzÏ v druhe seÂrii bylo pro neÏ zmeÏ- neÏno porÏadõÂskenuÊ. Interval meziprvnõÂm a druhyÂm hod- nocenõÂm 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 meziprvyÂm a druhyÂm hodnocenõÂm ichyba metody pomocõ Dahlbergovy formule [21]. Chyba metody ukazuje velikost chybove variability dane metody. Dahlbergova formule je
,
kde d je rozdõÂl meziprvnõÂm a druhyÂm hodnocenõÂm jednotlivyÂch snõÂmkuÊ a n udaÂva mnozÏstvõ dvojic opako- vanyÂch hodnocenõÂ.
VyÂsledky
Shoda v hodnocenõ skeletaÂlnõÂho veÏku metodou CVM mezi11 hodnotõÂcõÂmi(interobserver agreement) vyjaÂdrÏena pomocõ ukazatele kappa podle Fleisse byla 0,325, cozÏ ukazuje v jejich hodnocenõ pouze mõÂrnou shodu (tab. 1).
Shoda v hodnocenõÂ pro 55 paÂruÊ leÂkarÏuÊ v procentech shodneÏ hodnocenyÂch snõÂmkuÊ je pruÊmeÏrneÏ 44 %
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 podstatná shoda 0.81 – 1.00
almost perfect agreement
téměř úplná shoda
Tab. 1. Interpretace spolehlivosti - mõÂry shody v hodnocenõÂ podle ukazatele kappy
Tab. 1. Interpretation of the agreement assessed with the kappa sta- tistics
orthodontist were between 0.541 and 0.868. The me- thod 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 ra- diographs, the average of 26.55%, by two stages bet- ween 2% and 24% of radiographs (the average = 11.27%). There were also pictures in which the devia- tion for the second evaluation was higher (maximum snõÂmkuÊ (tab. 2). NejvysÏsÏõÂ shoda byla 68 % (tab. 3) a nej-
nizÏsÏõÂ 16% (tab. 4).
PrÏiopakovaneÂm hodnocenõ teÏchtyÂzÏ leÂkarÏuÊ (intraob- server agreement) procento shodnyÂch hodnocenõ cÏi - nilo 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 po- mocõ kappa podle Cohena. Kappa se pohybovala od 0,300 do 0,597, cozÏ znamena mõÂrnou azÏ strÏednõ shodu
A B C D E F G H I J K A --- 48 16 48 54 54 36 50 54 38 66 B ---- --- 36 58 46 64 34 58 38 46 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
Tab. 2. MõÂra shody mezipaÂry hodnotiteluÊ v procentech stejneÏ hod- nocenyÂch snõÂmkuÊ (prÏes 50 % - tucÏneÏ)
Tab. 2. The percentage of identical evaluation between the pairs of evaluators (over 50% - in bold)
H 1 2 3 4 5 6 Total 1 8 8 2 1 1 3 3 7 10 4 1 3 2 14 20 5 1 2 2 5 1 11 6 0 F Total 14 5 9 16 5 1 50 (100 %)
Tab. 3. NejvysÏsÏõ shoda (pocÏet snõÂmkuÊ) pro paÂr hodnotiteluÊ (hodno- titele 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%).
C 1 2 3 4 5 6 Total 1 5 3 1 9 2 1 1 2 3 2 5 1 2 1 1 12 4 1 1 7 2 1 12 5 4 2 1 1 8 6 2 1 2 2 7 A Total 11 10 14 6 6 3 50 (100 %)
Tab. 4. NejnizÏsÏõ shoda (pocÏet snõÂmkuÊ)pro paÂr hodnotiteluÊ (hodnoti- tele 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%).
Procento snímků se stejným hodnocením Per cent of the same results kappa podle Cohena Cohen’s kappa korelační koeficient correlation coefficient chyba metody podle Dahlberga Dahlberg’s method error A 74 ----* 0.679** 0.70 B 56 ----* 0.740** 0.68 C 44 0.300 0.654** 0.79 D 50 ----* 0.662** 0.96 E 48 0.373 0.710** 0.93 F 78 0.707 0.868** 0.47 G 62 0.527 0.706** 0.75 H 68 0.597 0.779** 0.78 I 52 0.425 0.688** 0.91 J 48 0.363 0.541** 1.08 K 50 0.400 0.807** 0.83
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
* kappa nenõ mozÏne vypocÏõÂtat, k tomu je trÏeba tabulka se symetrickyÂmihod- notamiz prveÂho a ze druheÂho hodnocenõÂ; ** signifikantnõ na uÂrovnip < 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 as- sessment; ** significant at the level of p < 0.01
Obr. 2. Shoda prÏiopakovaneÂm hodnocenõ pro jednotlive ortodontisty