- Email: [email protected]
Reliability and validity of a transverse horizontal axis location instrument
DIAZ-ARNOLDANDWILCOX
5. McLean JW, Wilson AD. The clinical development of the glass ionomer cement. II. Some clinical applications. Aust Dent J 1977;22:120-7. 6. McLean JW, Wilson AD. The clinical development of the glass ionomer cement. III. The erosion lesion. Auat Dent J 1977;22:190-5. 7. Mount GJ. Glass ionomer cements: clinical considerations. In: Clark JW, ed. Clinical dentistry. vol 4. Philadelphia: JB Lippincott Co, 19841-24. 8. McLean JW, Presser HJ, Wilson AD. The use of glass-ionomer cements in bonding composite resins to dentine. Br Dent J 1985;158:410-4. 9. McLean JW. Limitations of posterior composite resins and extending their use with glass ionomer cements. Quintessence Intl1987;18:517-29. 10. McLean JW. New concepts in cosmetic dentistry using glass-ionomer cements and composites. Can Dent Assoc J 1986;14:20-7. 11. Wu W, Cobb E, Dermann K. Detecting margin leakage of dental composite restorations. J Biomed Mater Res 1983;17:37-43. 12. Marosky JE, Patterson SS, Swartx M. Marginal leakage of temporary sealing materials used between endodontic appointments and assessed by calcium 45-an in vitro study. J Endodont 1977;3:110-3. 13. Wilcox LR, Diax-Arnold AM. Coronal microleakage of permanent lingual access restorations in endodontically treated anterior teeth. J Endodont 1989;15:584-7.
Reliability and validity location instrument
14. Tamse A, Ben-Amar A, Gover A. Sealing properties of temporary filling materials used in endodontics. J Endodont 1982;8:332-5. 15. Alperstein KS, Graver HT, Herold RCB. Marginal leakage of glass-ionomer cement restorations. J PROSTHET DENT 1983;50:803-7. 16. Baez RJ, Weed RM, Morales F. Microleakage of glass ionomer restorations. J Dent Rest 1984;63(special issueh294. 17. Hembree JH, Andrews JT. Marginal leakage of anterior restorative materials: a five-year study. J Tenn Dent Assoc 1984;64:28-30. 18. Herrin KH, Shen C. Microleakage of root caries restorations. Geriodontics 1985;1:156-9. 19. Welsh EL, Hembree JH. Microleakage at the gingival wall with four class V anterior restorative materials. J PROSTHET DENT 1985;54:370-2. 20. Robbins JW, Cooley RL. Microleakage of Ketac-Silver in the tunnel preparation. Oper Dent 198&13:8-11. Reprint requests to: DR. A. M. DLU-ARNOLD COILEGE OF DENTJSTRY UNlVERSlTY OF IOWA IOWA CITY, IA 52242
of a transverse
horizontal
axis
John F. Bowley,
D.D.S., M.S.,* and Calvin J. Pierce, D.M.D., Ph.D.** College of Dentistry, Columbus, Ohio; and University of Pittsburgh, School of Dental Medicine, Pittsburgh, Pa.
Ohio
State
University,
Previous studies have demonstrated a relatively accurate location of the transverse horizontal axis (THA) with several different instrument systems. This study statistically evaluated the reliability and validity of an instrument used to locate a known THA on a mannequin. Three experienced prosthodontists were the subjects. Each operator used 15 mm of interincisal arc to locate the THA. The mandibular stylus was aligned by the investigator with the known horizontal axis. The vertical microdot flags were positioned so the stylus was over a known coordinate and were repositioned so the operator could attempt to locate the axis. The known coordinates were varied with each of four trials. Subjects No. 1 and 3 demonstrated the best coefficient of reliability, 0.25. The 96% confidence interval for linear deviation from the known was 0.44 + 0.10 mm on the right side and 0.97 ? 0.10 mm on the left side. These confidence intervals did not include zero. A statistically better result was achieved on the right side compared with the left side (Fl$ = 131.24, p = 0.0014). The results of this study indicate that a random error factor of 0.3 to 1.2 mm can be expected when this instrument system is used clinically. (J PROSTHET DENT 1990;64:646-50.)
T
he transverse horizontal axis (THA) as defined in the Glossary of Prosthodontic Terms1 is “an imaginary line around which the mandible may rotate through the sagittal plane.“l This axis is important clinically to properly mount the maxillary cast on an articulator with a face-bow transfer.2 *Assistant Professor, Restorative tion, The Ohio State University,
and Prosthetic Dentistry College of Dentistry.
Sec-
**Assistant Professor,Behavioral SciencesDepartment, University
of Pittsburgh,
10/1/22011 646
School
of Dental
Medicine.
Preston2 presented the problems associated with a maxillary cast mounted with a face-bow inconsistent with this axis. In this case, interocclusal records at an open vertical dimension or an arbitrary increase in the occlusal vertical dimension will result in occlusal errors. These occlusal errors result from differences in the arc of closure on the articulator compared with that on the patient. The inferior and superior deviations were the most critical errors, assuming colinearity. The precision of the location of the THA has been widely investigated to determine the reliability and validity of various operators.3-6 The variation among these studies was DECEMBER1990
VOLUME64
NUMBER6
TRANSVERSE
HORIZONTAL
AXIS
LOCATION
in a range of less than 0.2 to 2.4 mm. Experience, good lighting, and magnification have been suggested as methods to improve the accuracy of this technique.5 Previous studies have shown a degree of variability in the THA location, but none have demonstrated the reliability or the validity of this technique by statistical evaluation. This investigation objectively determined the statistical reliability and validity of an instrument system on a mannequin by experienced operators.
METHODS Subjects
AND
MATERIAL
patient
A mannequin with a metallic skull and maxillary and mandibular typodont dentitions (“Fletcher” Plassein, Columbia Dentiform Corp., New York, N.Y.) served as the experimental patient. The experimental patient was mounted on a vertical support of the headrest of a dental operatory chair so the head was positioned in the same place as a patient’s head would be positioned during a dental procedure. The mandibular typodont rotated around a 5 mm diameter cylinder that was perpendicular to the sagittal plane. The mandibular typodont was fastened to a bilateral metallic structure that simulated both rami, which were of identical size and shape. Each ramus had a V-shaped surface that seated against the round rod and was maintained in place with a spring retainer. The maxillary typodont was mounted perpendicular to a vertical pole and the cylindrically shaped rod, the maxillary assembly was parallel to the cylindrical rod in the frontal and horizontal planes. The cylindrically shaped rod was machined from a brass alloy to be round throughout its entire length. Also, the cylinder had a central point machined at each end of the rod and both points were designed to be colinear. This maxillary-mandibular complex simulated the theoretical pure rotation phase of opening and closing the mandible in the sagittal plane.
Equipment The Denar Mini-Recording Device for Orthodontists (Denar Corp., Anaheim, Calif.) instrument was used by the subjects to locate the THA on the experimental patient. This system was used in this investigation due to its availability and its similarities with the Denar Hinge Axis Locator (Denar Corp.) instrument.‘j A chemically activated acrylic resin (Formatray, Kerr, Romulus, Mich.) jig was made to maintain an interincisal opening of 5 mm. Maxillary and mandibular clutches were made with the same material at the known vertical dimenTEE
JOURNAL
Subject 1 %-
Trial
OF PROSTHETIC
DENTISTRY
No.
No.
3
2 X-
Y-
0 -0.6
X-
Y’-
Y-
+o.s +1.7
0
0
+0.4
+03
-0.8 -0.4
-0.9
+0.7
0
0
0
2
Right Left Trial No. Right Left Trial No. Right Left
No.
1
Right Left Trial
Three educationally qualified prosthodontists at The Ohio State University, College of Dentistry, served as subjects for this study. Each subject had prior experience in the THA location technique using the kinematic face-bow on patients.
Experimental
I. x and y Coordinates for deviations from known THA on left and right sides for three subjects and four trials
Table
0 -0.4
0 -0.9
0
-0.2 -0.8
-0.4 -0.4
0 0
-0.8 -0.2
+0.1 -0.8
0
+0.1 -1.2
-0.6 +0.6
3 0
0
0
-1.3
-0.7
-0.2
-0.5 -0.1
+0.1 -0.9
-0.6 +0.2
4 -1.3
sion of a 5 mm interincisal opening. The acrylic resin was allowed to set completely in place to assure stable positioning of the clutches throughout the experiment. The clutches were made according to The Denar Mini-Recorder instruction manual. The fabrication of the clutches was completed by one of the investigators (JFB). The completed clutches allowed the subjects 15 mm of interincisal arcing to determine the THA. Both clutches were made so that the maxillary and mandibular crossbars were parallel to each other as well as to the THA in the horizontal and frontal planes.
Procedure After clutch fabrication, the mandibular right stylus was positioned within the THA hole on the mannequin and was secured by tightening the set screws. The stylus was then withdrawn slightly to enable the positioning of the maxillary vertical table so the stylus was over a black dot as the known position. After the right maxillary table was positioned and secured by tightening the set screws, the known position was recorded and the same procedure was performed on the left side. Prior to the experimental trial location of the THA by the subject, the mandibular styli were loosened and allowed to hang in an inferior direction; then the metallic skull cap was positioned. Each subject attempted to locate the THA on the mannequin with the same method used on patients but independent from the other subjecti and without help from the investigators. All three subjects attempted to locate the same known axis point during the same trial, but the known axis point was varied from trial to trial for four trials. The known axis points on the right and left vertical tables were varied within the same trial so that each trial represented two independent location attempts to preclude obvious visual cues from symmetrical positioning. 647
BOWLEY
Table
II.
AND
PIERCE
Linear distance deviations and two-way ANOVA* Right side Subject
Trial No. Trial No. Trial No. Trial No. Mean
1 2 3 4
2
3
0.80 0 0 0.51 0.33
0 0.80 0 0.60 0.35
0.70 0.45 0.81 0.61 0.64
Error
Subject No.
No.
1
Between groups Mean Error Within group Right/left Error Subjects Error Right/left X subjects
Left side
Mean
0.50 0.42 0.27 0.57 0.44
df
ss
MS
1 3
11.896 0.328
0.1095
1 3 2 6
1.682 0.0385 0.1775 1.7855
1.682 0.0128 0.0887 0.02976
2 6
0.7088 1.0339
0.3544 0.1723
1
2
3
1.80 0.98 1.48 0.91 1.29
0.89 0.98 0.20 1.32 0.84
0 0.89 0.82 1.34 0.76
Mean
0.90 0.95 0.83 1.19 0.97
F
P
131.24
0.0014
0.30
2.06
0.2088
*Significance level, p <0.05. MS, Mean squares; SS, sum of squares; SS, sum of squares.
After each subject trial, one of the investigators (JFB) would assessthe deviation from the known THA point on each side and release the mandibular slide arm to the inferior vertical position before beginning the next subject’s trial. After completion of each trial by all three subjects, the same procedure was followed for the subsequent trials except a new vertical table THA known position was selected compared with that of the previous trial.
Method of assessment After each subject had completed the attempt to locate the THA, the distance of deviation from the known axis position was visually estimated to the nearest 0.1 mm in both the x and y axes. Each dot on the maxillary vertical table was 1 mm apart, both vertically and horizontally in rows. The alternate rows in both axes had been positioned by the manufacturer 0.5 mm out of line from every other row. This microdot arrangement aided the visual estimation of the distance from the known axis in the x and y axes.
RESULTS A repeated measures analysis of variance (ANOVA) was used to compare the three variables (x and y axis coordinates and linear distance) with each other and the known THA points on the right and left sides for four trials by three subjects. The t values for a two-tailed test at the 0.05 level and the mean square error from the ANOVA were used to compute the various confidence intervals in the va-
648
lidity determinations. An interrater reliability coefficient was determined from the covariancelvariance product divided by its ratio. All statistical evaluations were done with the absolute values of the magnitudes of the deviation values. The raw data for x and y coordinates of the deviations from the known THA appear in Table I.
Linear distance validity The linear distance from the known THA was computed from the x and y axis coordinates by trigonometric functions. The raw data appear in Table II and the range of linear deviation on the right and left sides was 0 to 1.8 mm. The three subjects were significantly closer to the known position on the right side compared with the left (Fi,e = 131.24, p = 0.0014). The 95% confidence interval (ta,c.c2s= 3.182, MSE = 0.0128) for linear deviation was 0.34 to 0.54 mm on the right and 0.87 to 1.07 mm on the left. These values did not include the known THA point and varied significantly from zero (p < 0.05).
x and y Coordinate validity Both right-side x and y axis coordinate deviation values were significantly
closer to the known
axis coordinates
than
the left-side values to their respective known axis coordinates. The raw data appear in Table III and the range of values were a low of 0 mm in some trials on both axes on both sides to a high of 1.7 mm on the left-side y axis. The 95% confidence intervals for the right-side x and y axis coordinates
were xR = 0.17 to 0.45 mm and ya = 0.03
DECEMBER
1000
VOLUME
64
NUMBER
6
TRANSVERSE
AORIZONTAL
AXIS
LOCATION
III. x and y Coordinates of deviation from known THA and MSE values* from ANOVA used to compute confidence intervals at the 95% level
Table
Y-
X-
Subject
Right side Trial No. 1 Trial No. 2 Trial No. 3 Trial No. 4 Mean MS between MS between MS Error: Left Side Trial No. 1 Trial No. 2 Trial No. 3 Trial No. 4 Mean MS between MS between MS error: *Pooled
1
2
0 0 0 0.5 0.13
0 0.8 0
0.6 0.4 1.3 0.1 0.60
0.4 0.4 0.2 0.2 0.30
0.6 0.35
trials: subjects:
trials: subjects:
No.
Subject
interval
0.7
0.23 0.33 0.27 0.40 0.31
0.8 0 0 0 0 0 0.1 0 0.23 0 MS between trials: MS between subjects: MS Error:
0 0.4 0.l 0.6 0.!28
0.27 0.13 0.03 0.23 0.17 0.03333 0.08583 0.09583
0.33 0.53 0.57 0.50 0.48
1.7 0.8 0.9 0.9 0 0.7 1.3 0.9 1.10 0.75 MS between trials: MS between subjects: MS Error:
0 0.4 0.8
0.83 0.73 0.50 0.93 0.75 0.10333 0.36000 0.25333
0.2 0.8 0.1 0.45 0.01639 0.11083 0.16972
0 0.8 0.2 1.2 0.55 0.03222
Table
IV.
Covariance matrix for right-side linear
deviation Subject 1 Subject Subject Subject
No. No. No.
1 2 3
0.157
No.
2
3
-0.051 0.170
0.010 -0.088 0.020
reliability
DISCUSSION The Denar Mini-Recording Device for Orthodontists indemonstrated a large random error factor when used by these subjects in this experiment. This study demonstrated similar results to those found by Kurth and Feinstein,3 Borgh and Posselt,4 and Winstanley. Winstanley also recorded deviation values in the vertical and horizontal axes similar to those found in the present investigation. In contrast, Lauritzen and Wolford5 found that experienced operators with visual magnification could strument
JOURNAL
0.6 0.45
computations.
The highest correlation between subjects was demonstrated by subjects No. 1 and 3, with a coefficient of reliability of 0.25. Subject No. 2 was negatively correlated with subjects No. 1 and 3. The covariance matrix can be found in Table IV.
THE
Mean
Mean
to 0.31 mm (t.3,0.025= 3.182, MSE = 0.02465); these values were not significantly different from each other. Neither interval included the known THA and both were significantly different from zero. The 95% confidence intervals for the left side x and y axis coordinate values were XL = 0.34 to 0.62 mm and ye = 0.61 to 0.89 mm (ts,s.sz~= 3.182, MSE = 0.02465). These values were significantly different from each other. Neither interval included the known THA and both were significantly different from zero.
Interrater
3
3
0.10333 0.27222
MSE = 0.02465 used in confidence
2
1
No.
OF PROSTHETIC
DENTISTBY
locate the known THA to within 0.2 m:m in linear distance from the known position. The errors in the inferior and superior directions along the y axis were pointed out by Preston2 as being the most significant in terms of occlusal errors. The current study demonstrated a large THA location technique error factor on the left side of the mannequin in the range of 0.6 to 0.9 mm at a point 110 mm from the anterior clutch connection point; a y axis error of this magnitude may produce an infraocclusion at 55 mm anterior to the THA or the second molar region in a patient of this size. The coefficient of reliability indicated a relatively wide range of values among these subjects during the location of the same THA. Deviation of each subject’s scores relative to those of other subjects and the low validity indicate that a large random error factor exists when using this device.
649
BOWLEY
These results support the conclusion that this THA location instrument is unreliable. Although other THA-locating devices may appear to be easier to use as well as more accurate and consistent, the statistical validity and reliability have not been demonstrated. The results of this study tend to support the concept that an instrument error factor might exist in other THA location instrumentation. This study reinforces the clinical practice of making interocclusal records at the desired vertical dimension of occlusion, whenever possible, in restoring a patient to mitigate the inherent error of this step. Errors of this type might be of an even larger magnitude in patients due to other uncontrollable factors, for example, muscular tension, inadequate arcing of the mandible, thick and/or unstable clutches, etc. Further investigation is necessary to determine the cause of differences between left- and right-sided results as well as the demonstration of these errors in normal human subjects.
CONCLUSIONS A reliability and validity study has been presented to determine the error factor inherent within a THA location instrument. The following conclusions can be drawn from this investigation: 1. A large random error factor has been demonstrated and is inherent within the instrument. This factor is independent of operator and patient variables. 2. Inferior, negative y-axis deviations produce an in-
Availability
of JOURNAL
AND
PIERCE
fraocclusion in the second molar region due to the equipment in a patient of this size. 3. The left side appears to be more difficult for righthanded operators in locating the THA, it will require further investigation to definitively evaluate the cause of this phenomenon. The authors thank Mr. James Ashtcn and Dr. Melvin Moeschberger, Biometrics Laboratory, Preventive Medicine, College of Medicine, for help in statistical evaluation of the data and Drs. Chu, Padilla, and Peregrina, Restorative and Prosthetic Dentistry Section, The Ohio State University College of Dentistry, for their participation.
REFERENCES 1. Glossary of prosthodontic terms. J PROSTHET DENT 1987;58:721. 2. Preston JD. A reassessment of the mandibular transverse horizontal axis theory. J PROSTHET DENT 1979;41:605-13. 3. Kurth LE, F&stein IK. The hinge axis of the mandible. J PROSTHEY DENT 1951;1:327-32. 4. Borgh 0, Posselt U. Hinge axis registration: experiments on the articulator. J PROSTHET DENT 1958;8:35-40. 5. Lauritzen AG, Wolford LW. Hinge axis location on an experimental basis. J PROSTHET DENT 1961;11:1059-67. 6. Winstanley RB. Hinge axis location on the articulator. J PROSTHET DENT 1979;42:135-42.
Reprint
requests
to:
DR. JOHN F. BOWLEY THE OHIO STATE UNIVEFWTY COLLEXE OF DENTETRY COLUMBUS, OH 43210-1241
back issues, 1986-1989
Back issues of the JOURNAL OF PROSTHETIC DENTISTRY are available for purchase from the publisher, Mosby-Year Book, Inc., at a cost of $6.50 per issue. (Foreign postage is not included.) The following quantity discounts are available: 25% off on quantities of 12 to 23, and one third off on quantities of 24 or more. Please write to the Mosby-Year Book, Inc., Circulation Department, 11830 Westline Industrial Drive, St. Louis, MO 63146-3318, or call (314)872-8370, ext. 7351 for information on availability of particular issues for that period from 1978 to 1989. If unavailable from the publisher, photocopies of complete issues are available from University Microforms International, 300 N. Zeeb Rd., Ann Arbor, MI 48106, (313)761-4700.
650
DECEMBER
1990
VOLUME
84
NUMBER
6
5. McLean JW, Wilson AD. The clinical development of the glass ionomer cement. II. Some clinical applications. Aust Dent J 1977;22:120-7. 6. McLean JW, Wilson AD. The clinical development of the glass ionomer cement. III. The erosion lesion. Auat Dent J 1977;22:190-5. 7. Mount GJ. Glass ionomer cements: clinical considerations. In: Clark JW, ed. Clinical dentistry. vol 4. Philadelphia: JB Lippincott Co, 19841-24. 8. McLean JW, Presser HJ, Wilson AD. The use of glass-ionomer cements in bonding composite resins to dentine. Br Dent J 1985;158:410-4. 9. McLean JW. Limitations of posterior composite resins and extending their use with glass ionomer cements. Quintessence Intl1987;18:517-29. 10. McLean JW. New concepts in cosmetic dentistry using glass-ionomer cements and composites. Can Dent Assoc J 1986;14:20-7. 11. Wu W, Cobb E, Dermann K. Detecting margin leakage of dental composite restorations. J Biomed Mater Res 1983;17:37-43. 12. Marosky JE, Patterson SS, Swartx M. Marginal leakage of temporary sealing materials used between endodontic appointments and assessed by calcium 45-an in vitro study. J Endodont 1977;3:110-3. 13. Wilcox LR, Diax-Arnold AM. Coronal microleakage of permanent lingual access restorations in endodontically treated anterior teeth. J Endodont 1989;15:584-7.
Reliability and validity location instrument
14. Tamse A, Ben-Amar A, Gover A. Sealing properties of temporary filling materials used in endodontics. J Endodont 1982;8:332-5. 15. Alperstein KS, Graver HT, Herold RCB. Marginal leakage of glass-ionomer cement restorations. J PROSTHET DENT 1983;50:803-7. 16. Baez RJ, Weed RM, Morales F. Microleakage of glass ionomer restorations. J Dent Rest 1984;63(special issueh294. 17. Hembree JH, Andrews JT. Marginal leakage of anterior restorative materials: a five-year study. J Tenn Dent Assoc 1984;64:28-30. 18. Herrin KH, Shen C. Microleakage of root caries restorations. Geriodontics 1985;1:156-9. 19. Welsh EL, Hembree JH. Microleakage at the gingival wall with four class V anterior restorative materials. J PROSTHET DENT 1985;54:370-2. 20. Robbins JW, Cooley RL. Microleakage of Ketac-Silver in the tunnel preparation. Oper Dent 198&13:8-11. Reprint requests to: DR. A. M. DLU-ARNOLD COILEGE OF DENTJSTRY UNlVERSlTY OF IOWA IOWA CITY, IA 52242
of a transverse
horizontal
axis
John F. Bowley,
D.D.S., M.S.,* and Calvin J. Pierce, D.M.D., Ph.D.** College of Dentistry, Columbus, Ohio; and University of Pittsburgh, School of Dental Medicine, Pittsburgh, Pa.
Ohio
State
University,
Previous studies have demonstrated a relatively accurate location of the transverse horizontal axis (THA) with several different instrument systems. This study statistically evaluated the reliability and validity of an instrument used to locate a known THA on a mannequin. Three experienced prosthodontists were the subjects. Each operator used 15 mm of interincisal arc to locate the THA. The mandibular stylus was aligned by the investigator with the known horizontal axis. The vertical microdot flags were positioned so the stylus was over a known coordinate and were repositioned so the operator could attempt to locate the axis. The known coordinates were varied with each of four trials. Subjects No. 1 and 3 demonstrated the best coefficient of reliability, 0.25. The 96% confidence interval for linear deviation from the known was 0.44 + 0.10 mm on the right side and 0.97 ? 0.10 mm on the left side. These confidence intervals did not include zero. A statistically better result was achieved on the right side compared with the left side (Fl$ = 131.24, p = 0.0014). The results of this study indicate that a random error factor of 0.3 to 1.2 mm can be expected when this instrument system is used clinically. (J PROSTHET DENT 1990;64:646-50.)
T
he transverse horizontal axis (THA) as defined in the Glossary of Prosthodontic Terms1 is “an imaginary line around which the mandible may rotate through the sagittal plane.“l This axis is important clinically to properly mount the maxillary cast on an articulator with a face-bow transfer.2 *Assistant Professor, Restorative tion, The Ohio State University,
and Prosthetic Dentistry College of Dentistry.
Sec-
**Assistant Professor,Behavioral SciencesDepartment, University
of Pittsburgh,
10/1/22011 646
School
of Dental
Medicine.
Preston2 presented the problems associated with a maxillary cast mounted with a face-bow inconsistent with this axis. In this case, interocclusal records at an open vertical dimension or an arbitrary increase in the occlusal vertical dimension will result in occlusal errors. These occlusal errors result from differences in the arc of closure on the articulator compared with that on the patient. The inferior and superior deviations were the most critical errors, assuming colinearity. The precision of the location of the THA has been widely investigated to determine the reliability and validity of various operators.3-6 The variation among these studies was DECEMBER1990
VOLUME64
NUMBER6
TRANSVERSE
HORIZONTAL
AXIS
LOCATION
in a range of less than 0.2 to 2.4 mm. Experience, good lighting, and magnification have been suggested as methods to improve the accuracy of this technique.5 Previous studies have shown a degree of variability in the THA location, but none have demonstrated the reliability or the validity of this technique by statistical evaluation. This investigation objectively determined the statistical reliability and validity of an instrument system on a mannequin by experienced operators.
METHODS Subjects
AND
MATERIAL
patient
A mannequin with a metallic skull and maxillary and mandibular typodont dentitions (“Fletcher” Plassein, Columbia Dentiform Corp., New York, N.Y.) served as the experimental patient. The experimental patient was mounted on a vertical support of the headrest of a dental operatory chair so the head was positioned in the same place as a patient’s head would be positioned during a dental procedure. The mandibular typodont rotated around a 5 mm diameter cylinder that was perpendicular to the sagittal plane. The mandibular typodont was fastened to a bilateral metallic structure that simulated both rami, which were of identical size and shape. Each ramus had a V-shaped surface that seated against the round rod and was maintained in place with a spring retainer. The maxillary typodont was mounted perpendicular to a vertical pole and the cylindrically shaped rod, the maxillary assembly was parallel to the cylindrical rod in the frontal and horizontal planes. The cylindrically shaped rod was machined from a brass alloy to be round throughout its entire length. Also, the cylinder had a central point machined at each end of the rod and both points were designed to be colinear. This maxillary-mandibular complex simulated the theoretical pure rotation phase of opening and closing the mandible in the sagittal plane.
Equipment The Denar Mini-Recording Device for Orthodontists (Denar Corp., Anaheim, Calif.) instrument was used by the subjects to locate the THA on the experimental patient. This system was used in this investigation due to its availability and its similarities with the Denar Hinge Axis Locator (Denar Corp.) instrument.‘j A chemically activated acrylic resin (Formatray, Kerr, Romulus, Mich.) jig was made to maintain an interincisal opening of 5 mm. Maxillary and mandibular clutches were made with the same material at the known vertical dimenTEE
JOURNAL
Subject 1 %-
Trial
OF PROSTHETIC
DENTISTRY
No.
No.
3
2 X-
Y-
0 -0.6
X-
Y’-
Y-
+o.s +1.7
0
0
+0.4
+03
-0.8 -0.4
-0.9
+0.7
0
0
0
2
Right Left Trial No. Right Left Trial No. Right Left
No.
1
Right Left Trial
Three educationally qualified prosthodontists at The Ohio State University, College of Dentistry, served as subjects for this study. Each subject had prior experience in the THA location technique using the kinematic face-bow on patients.
Experimental
I. x and y Coordinates for deviations from known THA on left and right sides for three subjects and four trials
Table
0 -0.4
0 -0.9
0
-0.2 -0.8
-0.4 -0.4
0 0
-0.8 -0.2
+0.1 -0.8
0
+0.1 -1.2
-0.6 +0.6
3 0
0
0
-1.3
-0.7
-0.2
-0.5 -0.1
+0.1 -0.9
-0.6 +0.2
4 -1.3
sion of a 5 mm interincisal opening. The acrylic resin was allowed to set completely in place to assure stable positioning of the clutches throughout the experiment. The clutches were made according to The Denar Mini-Recorder instruction manual. The fabrication of the clutches was completed by one of the investigators (JFB). The completed clutches allowed the subjects 15 mm of interincisal arcing to determine the THA. Both clutches were made so that the maxillary and mandibular crossbars were parallel to each other as well as to the THA in the horizontal and frontal planes.
Procedure After clutch fabrication, the mandibular right stylus was positioned within the THA hole on the mannequin and was secured by tightening the set screws. The stylus was then withdrawn slightly to enable the positioning of the maxillary vertical table so the stylus was over a black dot as the known position. After the right maxillary table was positioned and secured by tightening the set screws, the known position was recorded and the same procedure was performed on the left side. Prior to the experimental trial location of the THA by the subject, the mandibular styli were loosened and allowed to hang in an inferior direction; then the metallic skull cap was positioned. Each subject attempted to locate the THA on the mannequin with the same method used on patients but independent from the other subjecti and without help from the investigators. All three subjects attempted to locate the same known axis point during the same trial, but the known axis point was varied from trial to trial for four trials. The known axis points on the right and left vertical tables were varied within the same trial so that each trial represented two independent location attempts to preclude obvious visual cues from symmetrical positioning. 647
BOWLEY
Table
II.
AND
PIERCE
Linear distance deviations and two-way ANOVA* Right side Subject
Trial No. Trial No. Trial No. Trial No. Mean
1 2 3 4
2
3
0.80 0 0 0.51 0.33
0 0.80 0 0.60 0.35
0.70 0.45 0.81 0.61 0.64
Error
Subject No.
No.
1
Between groups Mean Error Within group Right/left Error Subjects Error Right/left X subjects
Left side
Mean
0.50 0.42 0.27 0.57 0.44
df
ss
MS
1 3
11.896 0.328
0.1095
1 3 2 6
1.682 0.0385 0.1775 1.7855
1.682 0.0128 0.0887 0.02976
2 6
0.7088 1.0339
0.3544 0.1723
1
2
3
1.80 0.98 1.48 0.91 1.29
0.89 0.98 0.20 1.32 0.84
0 0.89 0.82 1.34 0.76
Mean
0.90 0.95 0.83 1.19 0.97
F
P
131.24
0.0014
0.30
2.06
0.2088
*Significance level, p <0.05. MS, Mean squares; SS, sum of squares; SS, sum of squares.
After each subject trial, one of the investigators (JFB) would assessthe deviation from the known THA point on each side and release the mandibular slide arm to the inferior vertical position before beginning the next subject’s trial. After completion of each trial by all three subjects, the same procedure was followed for the subsequent trials except a new vertical table THA known position was selected compared with that of the previous trial.
Method of assessment After each subject had completed the attempt to locate the THA, the distance of deviation from the known axis position was visually estimated to the nearest 0.1 mm in both the x and y axes. Each dot on the maxillary vertical table was 1 mm apart, both vertically and horizontally in rows. The alternate rows in both axes had been positioned by the manufacturer 0.5 mm out of line from every other row. This microdot arrangement aided the visual estimation of the distance from the known axis in the x and y axes.
RESULTS A repeated measures analysis of variance (ANOVA) was used to compare the three variables (x and y axis coordinates and linear distance) with each other and the known THA points on the right and left sides for four trials by three subjects. The t values for a two-tailed test at the 0.05 level and the mean square error from the ANOVA were used to compute the various confidence intervals in the va-
648
lidity determinations. An interrater reliability coefficient was determined from the covariancelvariance product divided by its ratio. All statistical evaluations were done with the absolute values of the magnitudes of the deviation values. The raw data for x and y coordinates of the deviations from the known THA appear in Table I.
Linear distance validity The linear distance from the known THA was computed from the x and y axis coordinates by trigonometric functions. The raw data appear in Table II and the range of linear deviation on the right and left sides was 0 to 1.8 mm. The three subjects were significantly closer to the known position on the right side compared with the left (Fi,e = 131.24, p = 0.0014). The 95% confidence interval (ta,c.c2s= 3.182, MSE = 0.0128) for linear deviation was 0.34 to 0.54 mm on the right and 0.87 to 1.07 mm on the left. These values did not include the known THA point and varied significantly from zero (p < 0.05).
x and y Coordinate validity Both right-side x and y axis coordinate deviation values were significantly
closer to the known
axis coordinates
than
the left-side values to their respective known axis coordinates. The raw data appear in Table III and the range of values were a low of 0 mm in some trials on both axes on both sides to a high of 1.7 mm on the left-side y axis. The 95% confidence intervals for the right-side x and y axis coordinates
were xR = 0.17 to 0.45 mm and ya = 0.03
DECEMBER
1000
VOLUME
64
NUMBER
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TRANSVERSE
AORIZONTAL
AXIS
LOCATION
III. x and y Coordinates of deviation from known THA and MSE values* from ANOVA used to compute confidence intervals at the 95% level
Table
Y-
X-
Subject
Right side Trial No. 1 Trial No. 2 Trial No. 3 Trial No. 4 Mean MS between MS between MS Error: Left Side Trial No. 1 Trial No. 2 Trial No. 3 Trial No. 4 Mean MS between MS between MS error: *Pooled
1
2
0 0 0 0.5 0.13
0 0.8 0
0.6 0.4 1.3 0.1 0.60
0.4 0.4 0.2 0.2 0.30
0.6 0.35
trials: subjects:
trials: subjects:
No.
Subject
interval
0.7
0.23 0.33 0.27 0.40 0.31
0.8 0 0 0 0 0 0.1 0 0.23 0 MS between trials: MS between subjects: MS Error:
0 0.4 0.l 0.6 0.!28
0.27 0.13 0.03 0.23 0.17 0.03333 0.08583 0.09583
0.33 0.53 0.57 0.50 0.48
1.7 0.8 0.9 0.9 0 0.7 1.3 0.9 1.10 0.75 MS between trials: MS between subjects: MS Error:
0 0.4 0.8
0.83 0.73 0.50 0.93 0.75 0.10333 0.36000 0.25333
0.2 0.8 0.1 0.45 0.01639 0.11083 0.16972
0 0.8 0.2 1.2 0.55 0.03222
Table
IV.
Covariance matrix for right-side linear
deviation Subject 1 Subject Subject Subject
No. No. No.
1 2 3
0.157
No.
2
3
-0.051 0.170
0.010 -0.088 0.020
reliability
DISCUSSION The Denar Mini-Recording Device for Orthodontists indemonstrated a large random error factor when used by these subjects in this experiment. This study demonstrated similar results to those found by Kurth and Feinstein,3 Borgh and Posselt,4 and Winstanley. Winstanley also recorded deviation values in the vertical and horizontal axes similar to those found in the present investigation. In contrast, Lauritzen and Wolford5 found that experienced operators with visual magnification could strument
JOURNAL
0.6 0.45
computations.
The highest correlation between subjects was demonstrated by subjects No. 1 and 3, with a coefficient of reliability of 0.25. Subject No. 2 was negatively correlated with subjects No. 1 and 3. The covariance matrix can be found in Table IV.
THE
Mean
Mean
to 0.31 mm (t.3,0.025= 3.182, MSE = 0.02465); these values were not significantly different from each other. Neither interval included the known THA and both were significantly different from zero. The 95% confidence intervals for the left side x and y axis coordinate values were XL = 0.34 to 0.62 mm and ye = 0.61 to 0.89 mm (ts,s.sz~= 3.182, MSE = 0.02465). These values were significantly different from each other. Neither interval included the known THA and both were significantly different from zero.
Interrater
3
3
0.10333 0.27222
MSE = 0.02465 used in confidence
2
1
No.
OF PROSTHETIC
DENTISTBY
locate the known THA to within 0.2 m:m in linear distance from the known position. The errors in the inferior and superior directions along the y axis were pointed out by Preston2 as being the most significant in terms of occlusal errors. The current study demonstrated a large THA location technique error factor on the left side of the mannequin in the range of 0.6 to 0.9 mm at a point 110 mm from the anterior clutch connection point; a y axis error of this magnitude may produce an infraocclusion at 55 mm anterior to the THA or the second molar region in a patient of this size. The coefficient of reliability indicated a relatively wide range of values among these subjects during the location of the same THA. Deviation of each subject’s scores relative to those of other subjects and the low validity indicate that a large random error factor exists when using this device.
649
BOWLEY
These results support the conclusion that this THA location instrument is unreliable. Although other THA-locating devices may appear to be easier to use as well as more accurate and consistent, the statistical validity and reliability have not been demonstrated. The results of this study tend to support the concept that an instrument error factor might exist in other THA location instrumentation. This study reinforces the clinical practice of making interocclusal records at the desired vertical dimension of occlusion, whenever possible, in restoring a patient to mitigate the inherent error of this step. Errors of this type might be of an even larger magnitude in patients due to other uncontrollable factors, for example, muscular tension, inadequate arcing of the mandible, thick and/or unstable clutches, etc. Further investigation is necessary to determine the cause of differences between left- and right-sided results as well as the demonstration of these errors in normal human subjects.
CONCLUSIONS A reliability and validity study has been presented to determine the error factor inherent within a THA location instrument. The following conclusions can be drawn from this investigation: 1. A large random error factor has been demonstrated and is inherent within the instrument. This factor is independent of operator and patient variables. 2. Inferior, negative y-axis deviations produce an in-
Availability
of JOURNAL
AND
PIERCE
fraocclusion in the second molar region due to the equipment in a patient of this size. 3. The left side appears to be more difficult for righthanded operators in locating the THA, it will require further investigation to definitively evaluate the cause of this phenomenon. The authors thank Mr. James Ashtcn and Dr. Melvin Moeschberger, Biometrics Laboratory, Preventive Medicine, College of Medicine, for help in statistical evaluation of the data and Drs. Chu, Padilla, and Peregrina, Restorative and Prosthetic Dentistry Section, The Ohio State University College of Dentistry, for their participation.
REFERENCES 1. Glossary of prosthodontic terms. J PROSTHET DENT 1987;58:721. 2. Preston JD. A reassessment of the mandibular transverse horizontal axis theory. J PROSTHET DENT 1979;41:605-13. 3. Kurth LE, F&stein IK. The hinge axis of the mandible. J PROSTHEY DENT 1951;1:327-32. 4. Borgh 0, Posselt U. Hinge axis registration: experiments on the articulator. J PROSTHET DENT 1958;8:35-40. 5. Lauritzen AG, Wolford LW. Hinge axis location on an experimental basis. J PROSTHET DENT 1961;11:1059-67. 6. Winstanley RB. Hinge axis location on the articulator. J PROSTHET DENT 1979;42:135-42.
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DR. JOHN F. BOWLEY THE OHIO STATE UNIVEFWTY COLLEXE OF DENTETRY COLUMBUS, OH 43210-1241
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650
DECEMBER
1990
VOLUME
84
NUMBER
6