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A LONGITUDINAL, MULTIVARIATE ANALYSIS OF ORTHODONTIC RELAPSE Nathan Daniel Mellion, D.D.S. An Abstract Presented to the Graduate Faculty of Saint Louis University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Dentistry 2011 Abstract Introduction: Orthodontic relapse is a complex problem that has troubled orthodontists throughout the history of the specialty. Although many studies have examined the various proposed causes of relapse, few have reported correlations that seem to support some sort of strong causal relationship. If no single factor can “explain” much of the variation in relapse, perhaps relapse can be predicted and/or modeled better by a linear combination of predictor variables--multiple regression and correlation. Subjects and Methods: Sixty-four posttreatment orthodontic patients of all four Angle classifications were recalled from one private practice. All had been treated with so-called “Tweed” mechanics, and all but five were treated with varying types of premolar extraction. Each subject had lateral cephalograms and study models taken prior to treatment, at deband/debond, and an average of 22.7 years posttreatment. From these records, various measurements of relapse and the factors that supposedly cause relapse were obtained. Backwards deletion multiple regression was employed to model/predict various types of relapse. In this process, posttreatment change in IMPA, incisal irregularity, maxillary intercanine width, and mandibular intercanine width served as dependent 1 variables, and ten skeletal and dental characteristics that are commonly thought to cause relapse served as independent variables. Results: There were five statistically significant multiple regression equations. Only one equation had more than one step of regression, the other four had only one predictor variable, and all featured small correlation coefficients (R or r between 0.32-0.48). During treatment, closing--“counterclockwise”-- rotations measured as Max-CB and Max-Mand angles were related to increased posttreatment incisal irregularity. Posttreatment maxillary or differential mandibular growth, alone or in combination, was not significantly related to any of the relapse measures. Supposed dental etiologies of relapse--treatment changes in IMPA, buccal-segment inclination, irregularity, mandibular intercanine width, and maxillary intercanine width--bore a weak, but statistically significant relationship to the studied relapse measures. Conclusions: The low correlation coefficients--both simple and multiple--suggest that the factors commonly thought to be important to orthodontic stability do not account for a significant portion of the variability in orthodontic relapse, at least in a “conservatively” treated sample. 2 A LONGITUDINAL, MULTIVARIATE ANALYSIS OF ORTHODONTIC RELAPSE Nathan Daniel Mellion, D.D.S. A Thesis Presented to the Graduate Faculty of Saint Louis University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Dentistry 2011 COMMITTEE IN CHARGE OF CANDIDACY: Professor Emeritus Lysle E. Johnston, Jr., Chairperson and Advisor Professor Eustaquio A. Araujo Professor Rolf G. Behrents Associate Clinical Professor Donald R. Oliver i DEDICATION To my wife, Tana, my family and teachers, for dedication and encouragement throughout my education that has enabled me to pursue my dreams. ii ACKNOWLEDGEMENTS The author would like to acknowledge: Dr. Lysle E. Johnston, Jr., for this thesis topic suggestion, tremendous dedication to all aspects of this thesis, and his passion to keep our specialty focused on science; Dr. Rolf G. Behrents, for assistance with the nuances of relapse covered in this thesis, and his guidance throughout my orthodontic education; Drs. Eustaquio A. Araujo and Donald R. Oliver, for their assistance with this thesis, and their guidance in my clinical education; Dr. Heidi Israel, for her assistance, and tremendous patience, with the statistical analysis for this thesis; and Dr. James Vaden, for the use of his records in this study, and the ability to examine truly remarkable treatment results. iii TABLE OF CONTENTS List of Tables. . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . .viii CHAPTER 1: CHAPTER 2: REVIEW OF THE LITERATURE. . . . . . . . . . Introduction . . . . . . . . . . . . . . . The Etiology of Relapse . . . . . . . . . . Soft Tissue Equilibrium . . . . . . . . Anterior Denture Displacement . . . Third Molar Eruption. . . . . . Anchorage Loss. . . . . . . . . Anterior Component of Occlusal Force . . . . . . . . . . . Differential Growth . . . . . . . . Incisor Procumbency . . . . . . . . Expansion . . . . . . . . . . . . . Periodontal Remodeling. . . . . . . . . Statement of Thesis . . . . . . . . . . . . Literature Cited. . . . . . . . . . . . . . JOURNAL ARTICLE . . . . . . . . . . . . . Abstract. . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . Subjects and Methods. . . . . . . . . . . Sample. . . . . . . . . . . . . . . . Cephalometric Technique and Analysis. Tracing Technique . . . . . . . . Digitization. . . . . . . . . . . Cephalometric Superimposition . . . . Cranial Base. . . . . . . . . . . Maxilla . . . . . . . . . . . . . Mandible. . . . . . . . . . . . . Measurement of Change . . . . . . Pitchfork Analysis. . . . . . Total Molar and Incisor Correction. . . . . . . . Skeletal and Molar Angles . . . . Model Analysis. . . . . . . . . . . . Error Study . . . . . . . . . . . . . Data Reduction. . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . Cephalometric Data. . . . . . . . . . Model Data. . . . . . . . . . . . . . iv 1 1 2 2 4 5 6 7 8 11 12 13 15 16 . . . . . . . . . . . . . . 21 21 23 26 26 28 28 31 32 32 33 34 35 35 . . . . . . . . 37 38 38 40 41 45 45 46 Results (cont.) Multiple Regression Error Study . . . . Discussion. . . . . . . Error Study . . . . Treatment Details . Skeletal Predictors Dental Predictors . Restricted Range. . Summary and Conclusions References. . . . . . . . . . . . . . . . . 46 47 60 60 60 62 65 69 70 72 Appendix A. . . . . . . . . . . . . . . . . . . . . . . Appendix B. . . . . . . . . . . . . . . . . . . . . . . 77 79 Vita Auctoris . . . . . . . . . . . . . . . . . . . . . 83 v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES Table 1.1. Table 1.2. Mesial movement of posterior buccal segments during Class II treatment (mm). . . . . . . 7 Saint Louis University treatment studies illustrating differential mandibular growth (ABCH). . . . . . . . . . . . . . . . . . . 10 Table 2.1. Angle classification by extraction pattern. 27 Table 2.2. Sample demographics . . . . . . . . . . . . 29 Table 2.3. Independent variables: potential causes of orthodontic relapse. . . . . . . . . . . 44 Angular cephalometric measures: means, standard deviations, and paired t-tests . . . . . . . . . . . . . . . . . . 48 Linear cephalometric measures: means, standard deviations, and paired t-tests . . 49 Fiducial and intermolar angle descriptive and inferential statistics. . . . . . . . . 53 Skeletal and dental components of molar and overjet change. . . . . . . . . . . . . 55 Model analysis: descriptive and inferential statistics. . . . . . . . . . . 57 Dependent and independent variables: means, standard deviations, and intra-class correlations. . . . . . . . . . . . . . . . 58 Table 2.10. Multiple regression analysis equations separated into proposed skeletal and dental etiologies of relapse. . . . . . . . 59 Table A. Customized cephalometric analysis . . . . . 78 Table B.1. Error Study: intra-class correlations (Cronbach’s α) for angular cephalometric measures. . . . . . . . . . . . . . . . . . 79 Table 2.4. Table 2.5. Table 2.6. Table 2.7. Table 2.8. Table 2.9. vi Table B.2. Table B.3. Table B.4. Table B.5. Error Study: intra-class correlations (Cronbach’s α) for linear cephalometric measures. . . . . . . . . . . . . . . . . . 80 Error study: intra-class correlations (Cronbach’s α) for the components of molar and overjet change. . . . . . . . . . . . . 81 Error study: intra-class correlations (Cronbach’s α) for fiducial and intermolar angles. . . . . . . . . . . . . . . . . . . 82 Error study: intra-class correlations (Cronbach’s α) for model analysis . . . . . 82 vii LIST OF FIGURES Figure 1.1. Soft tissue equilibrium pressures during swallowing and at rest. . . . . . . . . . 3 Anterior component of occlusal force (ACF) . . . . . . . . . . . . . . . . . . 9 Figure 2.1. Lateral cephalometric landmarks . . . . . 31 Figure 2.2. Regional superimpositions . . . . . . . . 36 Figure 2.3. Basal skeletal (hash mark) and intermolar angles. . . . . . . . . . . . . . . 39 Photocopied occlusal surfaces of a complete series T1-T3 (T1 on left, T2 middle, T3 right) with a 100 millimeter calibration rule . . . . . . . 41 Transverse intercanine (3-3) and intermolar (6-6) study model measurements. . . 42 Figure 2.6. The irregularity index. . . . . . . . . . 42 Figure 2.7. Mean facial outlines superimposed on the cranial base fiducial hash marks. . . . . 50 Mean facial outlines superimposed on the maxillary fiducial hash marks . . . . . . 51 Mean facial outlines superimposed on the mandibular fiducial hash marks. . . . . . 52 Figure 2.10. Average fiducial and intermolar angles. . 54 Figure 2.11. Pitchfork diagrams. . . . . . . . . . . . 56 Figure 2.12. Range restriction . . . . . . . . . . . . 70 Figure A. 77 Figure 1.2. Figure 2.4. Figure 2.5. Figure 2.8. Figure 2.9. Customized “Ricketts 71-point regimen”. . viii CHAPTER 1: REVIEW OF THE LITERATURE Introduction Over a century of orthodontic evolution has produced a high level of biomechanical efficiency; however, after active treatment is completed relapse is, and always has been, a common, little-understood problem. Dental crowding, loss of expansion in either arch, de-rotation, return of overbite and overjet, loss of molar correction, among many other untoward changes still plague the 21st century clinician. As noted by the historian, Weingberger,1 early orthodontic publications by Angell (1860), Coleman (1865), and Marvin (1866) emphasized the need for retention to prevent relapse. Because relapse is still a problem in modern orthodontics, the specialty’s response increasingly has been some form of permanent retention. Permanent retention, however, presents obvious problems. First of all, permanent retention diverts the specialty’s focus from understanding the causes of relapse. Secondly, even if determining the causes of relapse is not considered worthwhile, the long-term presence of bonded retainers presumably would increase our liability for problems such as periodontal disease and decalcification. It would seem, therefore, that understanding the causes of 1 relapse would be a service both to patients and the specialty. It will be the purpose of this study to examine longitudinally and simultaneously the proposed skeletal and dental etiologies of relapse in a large sample in which care was taken to avoid expansion and flaring and to preserve anchorage. This sample, in other words, was “conservatively” treated. The Etiology of Relapse Soft Tissue Equilibrium The dentition exists in an environment of soft tissue function--moving lips, cheeks, and muscles drape the outside while the tongue supports the inside of the dentition. This intimate contact allows the soft tissue, especially the muscles, to affect the shape of the alveolar bone and the position of the dentition, both of which are thought to be responsive to external forces. According to the “equilibrium theory of tooth position” as described by Weinstein and associates,2 teeth are in a position of balance in the envelope of motion of surrounding soft tissue. Movement of the dentition outside this equilibrium position/range thus would lead to movement that would serve to return the tooth to a position of equilibrium. 2 Although the existence and importance of a muscular equilibrium is a commonly-held belief in orthodontics, it has not yet been demonstrated experimentally. In a review of the equilibrium theory, Proffit3 has argued that the tongue and lip pressures that supposedly create the dental equilibrium cannot be shown to balance, either during rest or swallowing (Figure 1.1). Similarly, an assessment of normal subjects between ages 8 and 18 by Posen4 showed maximum tongue forces to be almost ten times maximum lip forces. As a result, Proffit argued that other factors, such as occlusion, dental eruption forces, and head posture might be responsible for the difference; as of yet, however, there has been no quantitative analysis that includes all of these potential factors. Figure 1.1. Soft tissue equilibrium pressures during swallowing and at rest. Lingual pressure is greater than lip pressure in both instances (units of measure not specified). Adopted from Proffit.3 3 Regardless of the algebraic sum of dental equilibrium forces, it is apparent that the soft tissues affect the position of the dentoalveolar complex. For example, to measure the effects of the disruption of the equilibrium, Weinstein and associates2 placed a 2 mm gold onlay either lingually or buccally on bicuspids set for extraction in eight subjects. They found that the bicuspids would move bucally when the gold onlay was placed lingually, and vice versa. It was concluded that a disruption of muscular equilibrium had caused the teeth to move toward a position of equilibrium. It seems reasonable to conclude, therefore, that expansion or a forward displacement of the dentition into the envelope of soft tissue function could lead to relapse. Anterior Denture Displacement Some orthodontic mechanics tend to move the dentition anteriorly, but the extent of movement is variable. Because a stable incisal position may be defined by the envelope of motion of the lips, cheeks, and tongue,4,5 anterior displacement might serve to upset the equilibrium. Ackerman and Proffit6 reviewed the literature on the tolerance of the dentition to anterior displacement and suggested that a movement of more than 2 mm would 4 initiate relapse. Causes of anterior displacement, however, are controversial and generally fall into one of three categories: third molar eruption, anchorage loss during treatment, and the anterior component of occlusal force. Third Molar Eruption Eruption of third molars is thought by many to push the dentition anteriorly and thus constitute a cause of relapse. The literature, however, does not provide a definitive causal link between third molar eruption and relapse, or, more specifically, anterior irregularity. Bergström and Jensen7 examined a sample with unilateral third molar agenesis and found more crowding on the side in which the third molar was present. Vego8 compared samples of bilateral third molar absence and presence and found 0.8 mm more crowding in the sample in which the third molars had erupted. An increase of 0.8 mm, however, seems to be too small an effect to explain the entirety of incisor relapse, were it to be due just to third molar eruption. More recent studies of patients with extracted third molars compared to non-extraction samples have reported that mandibular anterior irregularity is not statistically related to third molar eruption and/or 5 presence. Ades and co-workers9 compared the mandibular anterior crowding in four third molar samples (impacted, erupted, agenesis, and extracted). They found no statistically significant difference in irregularity among any of the four groups (F=0.313). Similarly, Harradine and co-workers10 reported no statistically significant difference in irregularity between groups with and without third molars (0.3 mm more crowding in those with third molars erupted). Given that recent, more extensive studies have failed to show a relationship between third molar eruption and anterior irregularity, the current consensus is that third molars are unlikely to be a cause of anterior dentition-displacement and relapse.11,12 Anchorage Loss The establishment of “Class I” canines and a reduction in incisor protrusion in Class II, Div. 1, extraction treatments commonly require mechanics that displace the buccal segments mesially. This mesial movement commonly is called “anchorage loss” and, if sufficient, might cause the dentition to encroach on the envelope of function of the lips and exceed the anterior 6 boundary of basal bone, both of which might lead to relapse of anterior alignment. Despite treatment goals of maintaining buccal segment position, Table 1.113-16 shows that maxillary and mandibular anchorage loss is a common event in bicuspid-extraction Class II treatment. Given that posttreatment skeletal growth continues throughout adulthood (vide infra), maxillary dentoalveolar compensations17 might also be a form of upper anterior relapse. The literature, however, has little to say concerning this possibility. Table 1.1. Mesial movement of posterior buccal segments during Class II extraction treatment (mm). Source Year Upper Lower Johnston, Lin, Peng13 1988 2.0 3.1 Harris, Dryer, Vaden14 1991 2.5 3.7 Paquette, Beattie, Johnston15 1992 3.1 4.6 Luppanapornlarp and Johnston16 1993 2.0 4.2 Anterior Component of Occlusal Force According to Proffit,18 intermittent forces, such as those from occlusal contact, are not of sufficient duration to cause tooth movement, let alone relapse. The obvious dentoalveolar compensations seen in Class III malocclusions, 7 however, seem to contradict the contention that intermittent occlusal forces cannot affect tooth position. It is probable, therefore, that occlusal forces, specifically those that produce an anterior occlusal vector, could displace the dentition mesially and thus be a cause of incisal relapse. Early orthodontic literature19,20 inferred an anterior component of occlusal force (ACF) from the mesial inclination of the buccal segments (Figure 1.2). Southard, Behrents, and Tolley21,22 measured changes in interproximal forces as result of biting on a force transducer and reported that there is a measureable ACF that is dissipated exponentially anterior to the second premolars. Southard’s group also reported a correlation between ACF and anterior crowding (r=0.54), although the authors stressed that this correlation does not prove a cause-and-effect relationship. To date, however, there are no studies relating the posttreatment inclinations of the buccal segments to anterior displacement and subsequent relapse. Differential Growth The normal facial skeletal growth pattern features excess mandibular growth relative to maxillary growth, even in Class II malocclusions.23 Differential mandibular growth, 8 Figure 1.2. Anterior component of occlusal force (ACF). Figure modified from Southard, Behrents, and Tolley.21 although helpful during Class II treatment (Table 1.215,16,2430 ), is considered by Proffit18 to be a contributor to posttreatment lower incisor irregularity. Specifically, Proffit has suggested that excess mandibular growth would force the mandibular anteriors against the lingual surfaces of the maxillary incisors, thus producing lower irregularity. If this phenomenon occurs posttreatment, it would be a form of relapse.18 Schudy31 studied a sample of 74 patients averaging 2.9 years posttreatment and found that condylar growth was significantly correlated with posttreatment incisal angulation (IMPA; r=-0.62). Accordingly, mandibular growth might tend to retrocline the mandibular incisors. righting, however, is not the same as increased 9 Up- irregularity. Glenn and associates32 went a step further and found a significant correlation between ANB reduction, as a measure of excess mandibular growth, and incisal crowding (r=0.65). Although these correlations support Proffit’s contention, differential maxillo-mandibular growth per se has not yet been shown to be related to incisor relapse. Table 1.2. Saint Louis University treatment studies illustrating differential mandibular growth (ABCH). Study Year ABCH (mm) Cohlmia24 1978 2.27 Ellis25 1979 2.25 Atkinson26 1980 3.10 Webb27 1981 2.17 Brown28 1985 2.68 extraction 2.32 nonextraction Phaerukkakit29 1985 2.68 Harper30 1986 1.75 Paquette et al.15 1992 1.94 extraction 2.51 nonextraction Luppanapornlarp, Johnston16 1993 2.74 extraction 1.95 nonextraction 10 Incisor Procumbency Whatever the cause of forward displacement of the buccal segments, incisor procumbency can be the end result following leveling and alignment. Tweed considered 80% of his nonextraction treatments failures because the results proved to be unstable. He attributed this relapse tendency to the mandibular incisors ending up too far forward relative to basal bone. He thus broke from Angle’s nonextraction treatment philosophy and re-treated a large group of his nonextraction cases in conjunction with premolar extraction.33 As a result of this “experiment,” Tweed concluded that stable posttreatment occlusions are dependent on the placement of mandibular incisors “upright over basal bone.” Numerous other workers agreed,34,35 and upright incisors remain, at least in theory, a common treatment goal. Failure to achieve this goal--incisal flaring--therefore could represent an encroachment on the labial soft tissue envelope of function and thus constitute a cause of relapse. Many studies support the contention that incisorflaring caused by treatment is prone to relapse. In a study of 56 patients whose incisors were intentionally flared during treatment, Mills36 showed that they relapsed lingually 4.8-8.6 degrees. Boley and associates37 went a 11 step further and found a significant correlation between incisor flaring during treatment to posttreatment incisal irregularity (r=0.43). It appears, therefore, that the labial muscular envelope of function is intolerant of incisal flaring; however, given that r2=0.18, treatmentinduced procumbency clearly does not explain much of the variation in incisor relapse and irregularity. As with flaring, transverse widening of the dental arches is also commonly thought to be a cause of relapse. Expansion Strang38 argued that stable posttreatment dentitions are dependent on the maintenance of the pretreatment intercanine dimension: There is no question in my mind that denture expansion as a treatment procedure in the correction of malocclusion should be discarded and every effort should be directed toward preserving the muscular balance that is the most important factor in establishing and maintaining tooth position. Many treatments, especially nonextraction treatments, commonly lead to transverse widening of the dental arch. For extraction treatments, some expansion can be attributed to canine retraction into a wider portion of the dental arch and, as such, would not obviously be prone to relapse, given that the final canine position would not encroach on the buccal envelope of motion. 12 Nonextraction treatments, however, often feature expansion that would displace the dentition into the functional buccal soft tissue envelope and thus might lead to relapse. There have been many studies designed to test the stability of treatment expansion. Burke and associates39 conducted a meta-analysis of twenty-six longitudinal clinical studies totaling 1,233 subjects. They found an average mandibular intercanine treatment expansion of 1.57 mm followed by a relapse of 1.24 mm posttreatment. It was concluded, therefore, that mandibular canine expansion is not stable. In an analysis of 28 patients eight years postretention, Glenn and associates32 reported a correlation between pretreatment and postretention intercanine and intermolar widths (r=0.57 and 0.63, respectively). They concluded that, although expansion is unstable, it could “explain” less than 40% of the observed “rebound.” Indeed, all orthodontic tooth movement seems prone to this type of relapse/reversion. Periodontal Remodeling In general, teeth moved orthodontically have a tendency to move back to their original position. Some types of “rebound” (especially de-rotation) are commonly 13 thought to be related to periodontal remodeling. The principal fibers of the periodontal ligament, specifically the apical and middle thirds, remodel between 50-80 days posttreatment.40,41 The supracrestal fibers, however, remodel much more slowly. Indeed, these fibers will not have fully remodeled a year posttreatment.40,42,43 The reason that supracrestal fibers are thought not to remodel quickly is that they can stretch. This stretch has been suggested as a cause of relapse,41 as the gingival fibers are stretched more in treatments with severe initial crowding;44 however, the literature is not in complete agreement with this assertion. In a study of 65 patients ten years postretention, Little and associates45 failed to show pretreatment incisal irregularity to be a predictor of posttreatment incisal relapse. Årtun and co-workers,46 on the other hand, examined a similar sample and found a statistically significant correlation between pretreatment and posttreatment incisal irregularity (r=-0.38). They noted that, although a statistically significant correlation was found, it could explain (i.e., it shared) only about 14% of the variance in posttreatment incisal irregularity. Periodontal remodeling and initial malocclusion severity--like all of the other “causes” 14 examined here--explain only a small portion of incisal relapse. Statement of Thesis Relapse in its various manifestations remains a phenomenon whose etiologies are still largely ill-defined, unproved, and thus highly controversial. There are a number of hypothesized causes of relapse, many of which have been shown to bear at least a weak relation to various types of relapse. Because of the considerable unexplained variation, however, it is clear that none of the proposed causes, when studied in isolation, supply an adequate explanation. It will be the purpose of this investigation, therefore, to examine the various proposed etiologies jointly in an effort to see if a multivariate approach will supply a more useful model of posttreatment relapse. 15 Literature Cited 1. Weinberger BW. Orthodontics: An Historical Review of Its Origin and Evolution. St. Louis: C.V. Mosby; 1926. 2. Weinstein S, Haack DC, Morris LY, Snyder BB, Attaway HE. On an equilibrium theory of tooth position. Angle Orthod. 1963;33:1-26. 3. Proffit WR. Equilibrium theory revisited: factors influencing position of the teeth. Angle Orthod. 1978;48:175-186. 4. Posen AL. The influence of maximum perioral and tongue force on the incisor teeth. Angle Orthod. 1972;42:285-309. 5. Posen AL. The application of quantitative perioral assessment to orthodontic case analysis and treatment planning. Angle Orthod. 1976;46:118-143. 6. Ackerman JL, Proffit WR. Soft tissue limitations in orthodontics: treatment planning guidelines. Angle Orthod. 1997;67:327-336. 7. Bergström K, Jensen R. Responsibility of the third molar for secondary crowding. Dent Abstr. 1961:544. 8. Vego L. A longitudinal study of mandibular arch perimeter. Angle Orthod. 1962;32:187-192. 9. Ades AG, Joondeph DR, Little RM, Chapko MK. A longterm study of the relationship of third molars to changes in the mandibular dental arch. Am J Orthod Dentofac Orthop. 1990;97:323-335. 10. Harradine NW, Pearson MH, Toth B. The effect of extraction of third molars on late lower incisor crowding: a randomized controlled trial. Br J Orthod. 1998;25:117-122. 11. Bishara SE, Andreasen G. Third molars: J Orthod. 1983;83:131-137. 16 a review. Am 12. Kandasamy S, Rinchuse DJ [sic], Rinchuse DJ [sic]. The wisdom behind third molar extractions. Aust Dent J. 2009;54:284-292. 13. Johnston LE Jr, Lin SS, Peng SJ. Anchorage loss: a comparative analysis. J Charles H. Tweed Int Found. 1988;16:23-27. 14. Harris EF, Dyer GS, Vaden JL. Age effects on orthodontic treatment: skeletodental assessments from the Johnston analysis. Am J Orthod Dentofac Orthop. 1991;100:531-6. 15. Paquette DE, Beattie JR, Johnston LE Jr. A long-term comparison of nonextraction and premolar extraction edgewise therapy in “borderline” Class II patients. Am J Orthod Dentofac Orthop. 1992;102:1-14. 16. Luppanapornlarp S, Johnston LE Jr. The effects of premolar-extraction: a long-term comparison of outcomes in “clear-cut” extraction and nonextraction Class II patients. Angle Orthod. 1993;63:257-272. 17. Solow B. The dentoalveolar compensatory mechanism: background and clinical implications. Br J Orthod. 1980;7:145-161. 18. Proffit WR, Fields HW, Sarver DM. Contemporary Orthodontics. 4th ed. St. Louis: Mosby; 2007. 19. Trauner F. The causes of progressive movement of the teeth toward the front. Am Orthod. 1912;3:144-158. 20. Stallard H. The anterior component of the force of mastication and its significance to the dental apparatus. Dent Cosmos. 1923;65:457-474. 21. Southard TE, Behrents RG, Tolley EA. The anterior component of occlusal force. Part 1. Measurement and distribution. Am J Orthod Dentofac Orthop. 1989;96:493-500. 22. Southard TE, Behrents RG, Tolley EA. The anterior component of occlusal force. Part 2. Relationship with dental malalignment. Am J Orthod Dentofac Orthop. 1990;97:41-44. 17 23. Bishara SE, Jakobsen JR, Vorhies B, Bayati P. Changes in dentofacial structures in untreated Class II, Division 1 and normal subjects: a longitudinal study. Angle Orthod. 1997;67:55-66. 24. Cohlmia GT. The relative contributions of growth and treatment in orthodontically corrected Class II malocclusion. [Unpublished Master’s Thesis] St. Louis: Saint Louis University; 1978. 25. Ellis CE. A quantitative evaluation of the role of growth and treatment in the correction of several Class II malocclusions. [Unpublished Master’s Thesis] St. Louis: Saint Louis University; 1979. 26. Atkinson BG. The relationship of skeletal morphology to molar correction in Class II, Division 1 malocclusions. [Unpublished Master’s Thesis] St. Louis: Saint Louis University; 1980. 27. Webb MA. The quantitative effects of maxillary second molar extraction in the correction of Class II, Division 1, malocclusion. [Unpublished Master’s Thesis] St. Louis: Saint Louis University; 1981. 28. Brown RK. A quantitative analysis of the relative contributions of maxillary and mandibular molar movement and growth to both the extraction and nonextraction correction of Class II, Division 1 malocclusions with the Begg technique. [Unpublished Master’s Thesis] St. Louis: Saint Louis University; 1985. 29. Phaerukkakit S. The relative effects of growth and tooth movement in the correction of Class II, Division 1 malocclusion. [Unpublished Master’s Thesis] St. Louis: Saint Louis University; 1985. 30. Harper DL. The affects [sic] of pretreatment morphology, treatment change, and posttreatment growth in relapse. [Unpublished Master’s Thesis] St. Louis: Saint Louis University; 1986. 31. Schudy GF. Posttreatment craniofacial growth: its implications in orthodontic treatment. Am J Orthod. 1974;65:39-57. 18 32. Glenn G, Sinclair PM, Alexander RG. Nonextraction orthodontic therapy: posttreatment dental and skeletal stability. Am J Orthod Dentofac Orthop. 1987;92:321-328. 33. Tweed CH. Indications for the extraction of teeth in orthodontic procedures. Am J Orthod Oral Surg. 1944;30:405-428. 34. Margolis HI. The axial inclination of the mandibular incisors. Am J Orthod Oral Surg. 1943;29:571-594. 35. Grieve GW. The stability of the treated denture. Orthod Oral Surg. 1944;30:171-195. Am J 36. Mills JRE. The long-term results of the proclination of lower incisors. Brit Dent J. 1966;120:355-363. 37. Boley JC, Mark JA, Sachdeva RC, Buschang PH. Long-term stability of Class I premolar extraction treatment. Am J Orthod Dentofac Orthop. 2003;124:277-87. 38. Strang RHW. The fallacy of denture expansion as a treatment procedure. Angle Orthod. 1949;19:12-22. 39. Burke SP, Silveira AM, Goldsmith LJ, Yancey JM, Van Steward A, Scarfe WC. A meta-analysis of mandibular intercanine width in treatment and postretention. Angle Orthod. 1998;68:53-60. 40. Reitan K. Tissue rearrangement during retention of orthodontically rotated teeth. Angle Orthod. 1959;29:105-113. 41. Edwards JG. A surgical procedure to eliminate rotational relapse. Am J Orthod. 1970;57:35-46. 42. Reitan K. Clinical and histologic observations on tooth movement during and after orthodontic treatment. Am J Orthod. 1967;53:721-745. 43. Blake M, Bibby K. Retention and stability: a review of the literature. Am J Orthod Dentofac Orthop. 1998;114:299-306. 19 44. Reitan K. Principles of retention and avoidance of posttreatment relapse. Am J Orthod. 1969;55:776790. 45. Little RM, Wallen TR, Riedel RA. Stability and relapse of mandibular anterior alignment-first premolar extraction cases treated by traditional edgewise orthodontics. Am J Orthod. 1981;80:349-65. 46. Årtun J, Garol JD, Little RM. Long-term stability of mandibular incisors following successful treatment of Class II, Division 1, malocclusions. Angle Orthod. 1996;66:229-238. 20 CHAPTER 2: JOURNAL ARTICLE Abstract Introduction: Orthodontic relapse is a complex problem that has troubled orthodontists throughout the history of the specialty. Although many studies have examined the various proposed causes of relapse, few have reported correlations that seem to support some sort of strong causal relationship. If no single factor can “explain” much of the variation in relapse, perhaps relapse can be predicted and/or modeled better by a linear combination of predictor variables--multiple regression and correlation. Subjects and Methods: Sixty-four posttreatment orthodontic patients of all four Angle classifications were recalled from one private practice. All had been treated with so-called “Tweed” mechanics, and all but five were treated with varying types of premolar extraction. Each subject had lateral cephalograms and study models taken prior to treatment, at deband/debond, and an average of 22.7 years posttreatment. From these records, various measurements of relapse and the factors that supposedly cause relapse were obtained. Backwards deletion multiple regression was employed to model/predict various types of relapse. In this process, posttreatment change in IMPA, incisal irregularity, maxillary intercanine 21 width, and mandibular intercanine width served as dependent variables, and ten skeletal and dental characteristics that are commonly thought to cause relapse served as independent variables. Results: There were five statistically significant multiple regression equations. Only one equation had more than one step of regression, the other four had only one predictor variable, and all featured small correlation coefficients (R or r between 0.32-0.48). During treatment, closing--“counterclockwise”--rotations measured as Max-CB and Max-Mand angles were related to increased posttreatment incisal irregularity. Posttreatment maxillary or differential mandibular growth, alone or in combination, was not significantly related to any of the relapse measures. Supposed dental etiologies of relapse--treatment changes in IMPA, buccal-segment inclination, irregularity, mandibular intercanine width, and maxillary intercanine width--bore a weak, but statistically significant relationship to the studied relapse measures. Conclusions: The low correlation coefficients--both simple and multiple--suggest that the factors commonly thought to be important to orthodontic stability do not account for a significant portion of the variability in orthodontic relapse, at least in a “conservatively” treated sample. 22 Introduction More than a century of orthodontic evolution has produced highly efficient treatments. Advancement in controlling posttreatment stability, however, as evidenced by reports from the earliest practitioners1 to those of today, has failed to keep pace; relapse remains a problem in modern orthodontics. Despite the potential problems of periodontal disease and decalcification, a popular solution in many of today’s treatments is some form of permanent retention. This approach implies that the precise causes of relapse are unknown or ignored, although many possible explanations have been presented in the literature. The dentition is surrounded by functioning soft tissue. It has been hypothesized that the dentition is positioned in equilibrium with the envelope of motion of these soft tissues.2 Disruption of this equilibrium by anterior and/or lateral displacement of the dentition during treatment thus would be a cause of relapse.3-5 Movement of the dentition mesially so that the incisors impinge on the labial muscular envelope of function is thought to cause relapse in the form of lingual tipping and crowding.6-10 Commonly hypothesized causes of anterior displacement are third molar eruption, anchorage loss, and the anterior component of occlusal force. 23 Third molar eruption was once generally thought to be a cause of lower anterior crowding.11,12 More recent literature, however, argues that the third molars are probably not a major cause of either anterior displacement or incisal relapse.13-16 Despite treatment goals of maintaining buccalsegment position, maxillary and mandibular anchorage loss is a common event in bicuspid-extraction Class II treatment.17-20 Given that posttreatment skeletal growth continues throughout adulthood (vide infra), maxillary dentoalveolar compensations21 might also contribute to relapse. The literature, however, has little to say about this possibility. The mesial inclination of the posterior occlusion is another possible cause of relapse. This inclination creates an anterior component of occlusal force (ACF). Southard, Behrents, and Tolley,22,23 however, only found a moderate correlation (r=0.54) between interproximal forces as a measure of ACF and incisal crowding. Although the various causes of displacement of the lower anterior dentition on basal bone have been shown individually to be slightly related to incisal relapse, none can account for a clinically useful portion of the 24 observed variability in posttreatment irregularity and crowding. Differential mandibular growth is another commonly cited cause of lower incisor relapse.24 Studies dealing with this conjecture, however, have tended to focus on condylar growth25 or ANB reduction.26 Little research has been conducted to measure its relation to actual differential jaw growth. Lateral displacement into the buccal muscular envelope of function--expansion--also is thought to be a cause of orthodontic relapse.3 Although recent studies26,27 are in agreement about its instability, all have concluded that dental expansion alone does not “explain” all the variation in the stability of expansion. Another commonly proposed cause of relapse-especially rotation--is the elastic nature of slowly remodeling periodontal tissues28-31 in relation to initial malocclusion severity.32 Severe initial crowding would likely require more movement during alignment, movement that would stretch the elastic periodontal fibers. The literature, however, has not demonstrated a strong correlation between initial malocclusion severity and relapse to be of clinical utility. 25 On balance, the various types of relapse remain phenomena whose etiologies are still largely unknown and/or unproved. There are a number of hypothesized causes, many of which have been shown to bear at least a weak relation to various types of relapse. Because of the considerable residual unexplained variation, however, it is clear that none of the proposed causes, in isolation, supply an adequate explanation. It will be the purpose of this investigation, therefore, to examine the various proposed etiologies jointly in an effort to see if a multivariate approach will supply a more useful model of posttreatment relapse. Subjects and Methods The purpose of this study was to test the nature of the relationship, if any, between hypothesized relapse etiologies and the various measures of relapse. To this end, data were obtained both from lateral cephalograms and study models. Sample The present sample consisted of 64 former orthodontic patients recalled by a single private-practice 26 orthodontist.A All Angle classifications were represented: 18 Class I; 39 Class II, Division 1; 6 Class II, Division 2; and 1 Class III. There also were a variety of extraction patterns, although the sample was predominately Class II, Division 1, treated in conjunction with the extraction of four first premolars (Table 2.1). The retention protocol was a mandibular bonded retainer from cuspid-to-cuspid, and a maxillary removable Hawley retainer. All subjects were out of retention at recall. Table 2.1. Angle classification by extraction pattern. Extraction Pattern Class 4/4 4/5 5/5 4/ Non-ext. I 10 1 4 1 2 II/1 16 12 8 2 1 II/2 2 1 2 0 1 III 0 0 0 0 1 There were no exclusion criteria; the subjects presented at their own discretion and expense between the years 2005 and 2008. Because it was assumed that relapse etiologies would be more or less common to all types of malocclusion, all Angle classes were included. The subjects presented in conjunction with their child’s A James L. Vaden 27 orthodontic treatment, during which time they consented to having follow-up orthodontic records taken. Because they had returned with their own children some 20-25 years later, the sample was presumably biased toward successful orthodontic treatment, at least as judged by laypersons. The fact that an outcome was liked by a patient, however, does not mean that there was no relapse or that the factors that cause relapse would not be operative. All had been treated with so-called “Tweed” mechanics featuring J-hook headgear, tip-back bends, and Class II elastics as needed. sample’s demographics. Table 2.2 summarizes the At the recall appointment, a lateral cephalogram, panoramic radiograph, alginate impressions for plaster study models, and intra-oral and extra-oral photographs were obtained. Cephalometric Technique and Analysis Tracing Technique Each subject’s treatment was documented by three lateral cephalograms: pretreatment, T1; immediate posttreatment/debond, T2; and long-term recall, T3. the 64 series was traced at a single sitting with a drafting pencil (2H lead) on tracing acetate (0.003” 28 Each of thickness). A second observerB examined the finished tracings and superimpositions before cephalometric digitization and numerical analysis. Disagreements were resolved by discussion and/or retracing and re-measurement. Table 2.2. Sample demographics (yrs) Time/Interval Mean S.D. Range Treatment T1 13.0 1.84 11-20 T2 15.3 1.84 13-22 2.3 0.40 1.8-3.8 T1-T2 Posttreatment T3 37.8 3.89 31-51 T2-T3 22.5 3.03 17-29 The tracing protocol of Johnston33 was employed here. Figure 2.1 shows the anatomical features traced in each lateral cephalogram. Johnston’s superimpositions were based on Björk’s structural method (vide infra). Specifically, unique trabecular patterns within the cranial base, maxilla, and mandible were included for each series. To optimize superimposition reliability, templates specific to each series were created for the key ridge, B L.E. Johnston, Jr. 29 pterygomaxillary fissure, third molar germ (if present), and the contour of the mandibular canal. Templates were also constructed for the most clearly discernable maxillary and mandibular first molars and incisors in each of the three film series (Figure 2.1). The incisors were traced as a long axis from apex to incisal edge. The molars were traced as a horizontal line connecting the mesial and distal contact points, and a vertical line representing the long axis connected to the midpoint of the horizontal line. Superimposition revealed that 22 of the 64 series featured a reduction in magnification between T2 and T3. This shrinkage probably was the result of a change in cephalostat and an inadvertent reduction in the object-film distance. In order to minimize the effect of this discrepancy, the T3 tracings were scanned into an image editing program (Adobe Photoshop CS3 Extended, version 10.0, Adobe Systems, Inc., San Jose, CA) and magnified an average of 2.5% so that Sella-Nasion of T3 matched that of T2. The T2 average age was 15, so it was assumed that there would have been relatively little growth between T2 and T3. enlarged T3 scan was then printed and measured. 30 The Digitization The cephalometric tracings were digitized on a transparent digitizer (Numonics digitizing board, Model A30Bl.H, Numonics Corporation, Montgomeryville, PA) and analyzed with a commercial software program (Dentofacial Planner, version 5.32, Dentofacial Software, Toronto, Canada). After the landmarks had been digitized according to a modified “Ricketts 71-point regimen,” a customized analysis of both linear and angular measures was executed (Appendix A). Figure 2.1. Lateral cephalometric landmarks. 31 Cephalometric Superimposition Because the goal of this study was to evaluate the various proposed causes of orthodontic relapse, it was necessary to quantify both the skeletal and dental changes that had occurred during and after treatment. These changes were estimated from cranial base, maxillary, and mandibular regional superimpositions33 based on stable structures as defined by Björk’s implant studies.34-36 For each regional superimposition, “fiducial hash marks,” arbitrary horizontal lines with vertical marks at both ends, were placed in cranial base, maxilla, and mandible of T2 and then passed through to T1 and T3 based on stable structural details (vide infra). hash marks: There were two purposes for these to record the regional superimposition,37 and to determine if vertical skeletal changes during treatment are a cause of relapse by depicting the pattern of displacement of the midface and mandibular basal bones relative to the cranial base and to each other. Cranial Base The commonly-utilized S-N cranial base superimposition was not used here because both landmarks remodel over time.33,38 Instead, Björk’s structural methods as implemented by Johnston,33 were used here: 32 1. the anterior wall of sella turcica, including the intersection with the anterior clinoid; 2. the cribriform plate; and 3. the greater wings of the sphenoid, especially near the intersection between it and the cranial base. An arbitrary point, the so-called “Wing point” (W),39 defined as the intersection between planum sphenoidale and the averaged greater wings of the sphenoid, was located on T2 and transferred to T1 and T3 by superimposition on the cranial base fiducial lines (Figure 2.2 A). Maxilla The maxillary superimposition was executed based on the best fit of: 1. the lingual cortical plate of the maxilla, specifically the anterior curvature; 2. common internal maxillary trabecula; and 3. the anterior surface of the key ridge. Fiducial lines were then placed along the T2 palatal plane (ANS-PNS), and then transferred to T1 and T3 based on best-fit superimposition (Figure 2.2 B). For the present study, the functional occlusal plane (FOP) served as the plane of orientation for the measurements of some dental and skeletal changes (vide infra). FOP (similar to the “average occlusal plane” described by Jenkins40), the bisection of the maxillary and mandibular buccal occlusion through the canines, represents 33 the relatively stable buccal occlusion, in contrast to the commonly used Downs occlusal plane,41 which is sensitive to changes in incisor position.33 The maxillary fiducial hash marks of T1 and T3 were superimposed and the FOPs were averaged by inspection to produce a mean functional occlusal plane (MFOP). The MFOP was then transferred to T2, also by way of a maxillary structural superimposition. Mandible The mandibular best-fit superimposition was based on: 1. trabecular patterns and the lingual endoesteal surface of the mandibular symphysis; 2. the outlines of the mandibular canals; and 3. the lower border of the mandibular third molar germs, if present. Fiducial hash marks were scribed on the T2 tracing at Gonion and the intersection of the mandibular plane with a line perpendicular to the mandibular plane dropped from Pogonion, and then transferred to T1 and T3 by way of mandibular structural superimposition. Similarly, the so-called “D- point,”42 the arbitrary center of the mandibular symphysis, was first marked on T2 and then transferred to T1 and T3 (Figure 2.2 C). 34 Measurement of Change Pitchfork Analysis The so-called “pitchfork analysis” was used to measure the skeletal and dental components of treatment and posttreatment change.33 These measurements were used to describe the changes during treatment and posttreatment, and determine if the tooth movements and the individual pattern of maxillo-mandibular growth are potential causes of relapse as well as measures of relapse, itself. The pitchfork analysis measures A-P changes that add up to the molar relationship and overjet, and both skeletal and dental changes are measured parallel to the MFOP. Based on the fiducial lines, the tracings were superimposed (T1 and T2 and T2 and T3) and measurements were taken to the nearest 0.01 mm with digital calipers under the control of a small magnifying glass. Net change (T1 to T3) was calculated by the algebraic sum of treatment and posttreatment changes. A common application of the pitchfork analysis is to quantify the components of the molar and overjet correction. In the present study, the vast majority were Class II and most underwent some overjet correction. Accordingly, a sign convention for the components of the molar and overjet corrections was employed as follows: 35 a positive sign was given to changes that would tend to produce a Normal molar occlusion or to reduce overjet in a Class II patient, and changes that would tend to a Class II molar relation or increase the overjet would be given a negative value. Figure 2.2. Regional superimpositions. T2 fiducial hash marks were placed along the S-N plane for the cranial base (A), palatal plane (ANS-PNS) for the maxilla (B), and Gonion to a line dropped from Pogonion perpendicular to the mandibular plane for the mandible (C). The hash marks were transferred to T1 and T3 by structural superimposition. 36 The tracings were superimposed on the maxillary fiducial hash marks (which would also ensure that each tracing’s MFOP were coincident) to measure: 1. maxillary displacement (MAX) relative to cranial base; 2. differential mandibular growth (ABCH); and 3. maxillary first molar (U6) and incisor (U1) displacement relative to maxillary basal bone. Mandibular displacement (MAND) relative to the cranial base was then determined algebraically: MAND=ABCH-MAX. Changes in position of mandibular first molar (L6) and incisor (L1) relative to mandibular basal bone were measured with two tracings oriented along the MFOP and registered on D-point. Total Molar and Incisor Correction Change in molar relationship was seen to be the algebraic sum of: 1. ABCH, 2. U6, and 3. L6. Similarly, the overjet change was calculated as the sum of: 2. U1, and 3. L1. 1. ABCH, As a check on measurement error, molar and overjet corrections were calculated directly and compared to the summed estimates. If the difference was greater than + 0.3mm, the measurements were repeated until the summed components were within these limits. 37 Skeletal and Molar Angles In order to estimate an anterior component of occlusal force (ACF) from posttreatment molar angulation and its effect, if any, on relapse, the intermolar angle was measured (Figure 2.3). The intermolar angle was measured from the long axes of the maxillary and mandibular molar templates (vide supra). To measure the effect on relapse of vertical skeletal change during treatment, the angles between the cranial base, maxillary, and mandibular fiducial hash marks were measured (Figure 2.3). Because fiducial hash marks represent underlying stable skeletal structures,33,37 these angles characterize the pattern of skeletal rotation during and after treatment, and given a “hyper-divergent” pattern, might have an impact on the A-P position of the dentition (a skeletal version of ACF). Model Analysis Study-models measurements were used to estimate treatment expansion of the maxillary and mandibular canines and molars and initial incisal irregularity as potential causes of relapse. Posttreatment changes in intercanine width and posttreatment incisal irregularity served as dental measures of relapse. 38 Figure 2.3. Basal skeletal (hash mark) and intermolar angles. 1. Cranial base to maxilla; 2. maxilla to mandible; 3. cranial base to mandible; and 4. intermolar angle as the angle between long axes of maxillary and mandibular first molars. The occlusal surfaces of the three maxillary and mandibular models in each series were photocopied (Ricoh Aficio MP5000, Ricoh Co., Ltd., Japan) along with a 100 millimeter calibration rule (Figure 2.4). These copies were then digitized on a transparent digitizer and analyzed with customized software in Dentofacial Planner version 5.32 (vide supra) to generate arch widths and mandibular incisor irregularity measures for T1, T2, and T3. 39 Arch width was calculated as the distance between cusp tips for the canines, and the middle of the central grooves for the molars (Figure 2.5). The “irregularity index” (Figure 2.6; Little43) was calculated as the cumulative displacements of the five mandibular anterior contact points from the mesial of the right cuspid to the mesial of the left cuspid. To verify the digitization measurements, arch width and irregularity were calculated by hand with a digital caliper for many of the T1 mandibular models. If the digitization and hand values differed by more than + 0.3 mm, the digitization was redone. The digital measurements were the ones that were used in the present analysis. Error Study To test the reliability of the cephalometric and model measurements, a random number generator (from www.random.org44) was used to select ten series (30 radiographs and sets of models) to be re-analyzed. Intra- class correlation was estimated by Cronbach’s α. Reliability is commonly considered “adequate” when the intra-class correlation coefficients are equal to or greater than 0.80. 40 Figure 2.4. Photocopied occlusal surfaces of a complete series T1-T3 (T1 on left, T2 middle, T3 right) with a 100 millimeter calibration rule. Data Reduction Statistical analysis was carried out by way of a commercially-available spreadsheet program (Microsoft Excel 2003) and statistical software (SPSS, version 15.0, SPSS Inc., Chicago, IL). 41 Figure 2.5. Transverse intercanine (3-3) and intermolar (6-6) study model measurements. Measurements were from the cusp tips for the canines, and the middle of the central grooves for the first molars. Figure 2.6. The irregularity index: the sum of the displacements of the five lower anterior contacts A+B+C+D+E. Modified from Little.43 42 Means and standard deviations were calculated for all cephalometric and model measurements. Paired t-tests were employed to test the null hypothesis that skeletal and dental changes during treatment (T1 to T2) and posttreatment (T2 to T3) did not differ significantly from zero--Ho:δ=0. To compensate for the family-wise error from repeated t-tests, the type-I error was set at α=0.0167 (α of 0.05 divided by 3 repeated measures, 0.05/3=0.0167) and 0.003 (α=0.01/3). Backwards elimination multiple regression was utilized to test the hypothesis that the cumulative effect of the proposed causes of relapse could explain a significant portion of the variability in the relapse seen here. Four posttreatment changes (T3 minus T2) served as measures/predictors of relapse (i.e., dependent variables): 1. mandibular incisor to mandibular plane angle (IMPA post tx∆); 2. Irregularity Index (Irr post tx∆); 3. mandibular intercuspid width (Mand 3-3 post tx∆); and 4. maxillary intercuspid width (Max 3-3 post tx∆). The potential relapse etiologies (the independent variables) as characterized by measures of treatment change are defined in Table 2.3. Given that the present sample size--N=64-- was too small to permit ten independent variables in one regression equation (Table 2.3), separate dental and 43 skeletal equations were generated. Thus, there were a total of eight equations, each with five potential independent variables--commonly assumed causes of relapse. The “probability in” (PIN) was 0.05 and the “probability out” (POUT) was 0.10, with a maximum of 2 independent variables to be allowed in each equation. Table 2.3. Independent variables: orthodontic relapse. Measure potential causes of Abbreviation Treatment change (T2 minus T1) Angularo Incisor to mandibular plane Intermolar angle IMPA tx∆ Intermolar Mandible to cranial base Maxilla to cranial base Mand-CB tx∆ Max-CB tx∆ Maxilla to mandible Max-Mand tx∆ Linear (mm) Irregularity Index IRR tx∆ Mandibular cuspid expansion Mand 3-3 tx∆ Maxillary cuspid expansion Max 3-3 tx∆ Posttreatment change (T3 minus T2) Maxilla to cranial base (mm) Differential mandibular Post tx∆ MAX Post tx∆ ABCH growth (mm) 44 Results Cephalometric Data Means and standard deviations for start, finish, and recall angular and linear cephalometric measures are presented in Tables 2.4 and 2.5. To depict changes between time points for each regional superimposition (cranial base, maxilla, and mandible), average tracings created from a customized utility within Dentofacial Planner version 5.32 (average.exe) are depicted in Figures 2.7-2.9 by superimposition on their respective fiducial marks. Descriptive statistics, means and standard deviations, for the angles amongst fiducial hash marks and the long axes of first molars are presented in Table 2.6. Figure 2.10 depicts the mean fiducial and intermolar angles for T1, T2, and T3. Means and standard deviations for the skeletal and dental components of molar and overjet change are presented in Table 2.7. The means for both groupings are also depicted in the “pitchfork” diagrams of Figure 2.11. To test whether the mean angular and linear cephalometric changes for all cephalometric data between T1 and T2 and between T2 and T3 differed significantly from zero (Ho:δ=0), repeated-measures t-tests are presented in Tables 2.4-2.6. Because of an increased family-wise error 45 from multiple t-tests, the conventional 0.05 and 0.01 significance levels were adjusted to P<0.0167 and P<0.003. Model Data Irregularity index, intercanine width, and intermolar width descriptive statistics (means and standard deviations) for T1, T2, T3, treatment change (T2–T1), posttreatment change (T3–T2), and net change (T3–T1) are presented in Table 2.8. Repeated measures t-tests (Ho:δ=0), with the above-described α-adjustments, for T1 to T2 and T2 to T3 are also summarized in Table 2.8. Multiple Regression Means and standard deviations for each dependent variable (measure of relapse) and independent variable (commonly proposed causes of relapse) are shown in Table 2.9. The results of the backwards deletion multiple regression analysis is presented in Table 2.10. It is worth noting here that all of the relapse measures are significantly related to one or more of the dental independent variables. Only one relapse measure, incisal irregularity, however, was significantly related to any of the proposed skeletal etiologies. 46 Error Study Intra-class correlations (Cronbach’s α) for all duplicate measures are presented in the last column of Table 2.9 and Appendix B. 47 Table 2.4. Angular cephalometric measures: and paired t-tests. T1 T2 means, standard deviations, T3 Paired t (Ho:δ=0) Measure Mean S.D. Mean S.D. Mean S.D. T1 to T2 SNA 81.43 3.67 79.20 3.52 79.73 3.61 7.19** SNB 77.28 3.26 77.19 3.21 77.21 3.45 0.44 ANB 4.16 2.29 2.02 2.25 2.52 2.34 9.29** Y-axis 57.40 3.66 57.31 3.57 56.58 3.51 0.29 2.38 U1-SN 104.59 6.74 104.27 7.00 102.15 6.88 0.28 3.65** U1-NA 23.15 6.81 25.08 7.37 22.42 6.96 -1.53 4.33** L1-NB 21.92 5.70 20.29 5.50 19.32 5.92 2.50 1.79 1/1 130.77 9.21 132.62 6.86 135.74 7.85 -1.35 -3.73* FMA 20.82 6.16 20.22 6.53 18.92 6.51 1.95 3.17** IMPA 93.16 6.86 91.89 6.43 91.62 5.76 1.91 0.53 FMIA 66.02 6.06 67.92 6.49 69.16 7.05 -2.76* -2.06 Z 76.06 9.43 82.72 8.53 87.58 8.85 -8.23** -6.41** SN-PP 8.19 3.36 8.40 3.15 8.93 3.40 -1.02 -3.01* SN-FOP 18.16 4.83 17.01 4.43 16.50 4.77 * P<0.0167 ** P<0.003 48 2.81* T2 to T3 -2.40 0.07 -3.25** 1.36 Table 2.5. Linear cephalometric measures: and paired t-tests Ho:δ=0. T1 means, standard deviations, T2 T3 Paired t (Ho:δ=0) Measure Mean S.D. Mean S.D. Mean S.D. T1 to T2 T2 to T3 Wits A/B 2.73 3.34 -1.07 2.75 0.49 3.32 9.46** -5.37** PNS-A pt 49.56 2.87 48.53 3.16 49.74 2.82 3.80** -5.26** S-Ar 34.81 3.44 35.72 3.80 35.25 3.52 -3.65** 2.66* S-Go 80.51 5.75 85.77 6.13 86.00 6.52 -10.63** -0.21 Ar-Gn 108.12 6.27 113.41 5.59 113.45 6.18 -10.06** 0.57 Pg-NB 1.89 1.97 3.07 2.36 3.60 2.26 -6.22** -2.73* U6-PTV 16.73 3.74 20.62 3.58 22.68 3.80 -13.55** -7.50** U1-NA 4.09 2.85 4.01 2.69 3.23 2.51 0.17 3.25** L1-APg 0.52 2.22 1.12 2.05 0.05 2.20 -2.60 6.36** Overjet 6.34 2.60 3.53 0.91 4.10 0.90 8.44** -4.45** Overbite 2.39 2.15 1.50 1.10 2.83 1.55 3.30** -6.96** N-Me 118.54 6.15 124.44 6.81 123.70 6.52 -10.93** 1.52 N-ANS 53.11 3.02 55.04 3.26 55.12 3.59 -6.64** 0.66 ANS-Me 66.97 5.33 70.30 5.63 69.48 5.43 -8.70** 2.16 UFH (%) 44.85 2.21 44.23 2.22 44.59 2.47 3.52** -1.77 LFH (%) 56.45 2.78 56.44 2.41 56.13 2.60 0.02 1.62 LL-E line -1.24 3.28 -3.98 2.77 -6.29 2.86 9.00** 9.28** * P<0.0167 ** P<0.003 49 Figure 2.7. Mean facial outlines superimposed on the cranial base fiducial hash marks. Start, black; finish, red; and recall, green. 50 Figure 2.8. Mean facial outlines superimposed on the maxillary fiducial hash marks. Start, black; finish, red; and recall, green. Note the maxillary dentoalveolar compensations, specifically the maxillary molars continue to come forward with the mandible. 51 Figure 2.9. Mean facial outlines superimposed on the mandibular fiducial hash marks. Start, black; finish, red; and recall, green. 52 Table 2.6. Fiducial and intermolar angle descriptive and inferential statistics. T1 T2 T3 Treatment Measure Mean 53 Maxilla-CB S.D. Mean S.D. Mean Paired t (Ho:δ=0) Change S.D. T2 minus T1 Posttreatment T3 minus T2 Net T3 minus T1 Mean S.D. Mean S.D. Mean S.D. T1 to T2 T2 to T3 7.38 2.99 8.01 3.07 7.98 3.16 0.62 1.53 -0.06 2.59 0.34 2.59 -3.26** -0.47 MaxillaMandible 27.03 6.59 25.84 7.02 25.41 7.16 -1.19 1.99 -0.18 2.56 -1.30 2.56 4.77** 0.85 Mandible-CB 34.40 6.86 33.83 7.43 33.52 7.40 -0.57 2.30 -0.61 5.65 -1.2 5.65 1.95 0.34 Intermolar 170.73 4.86 171.35 4.53 169.74 4.87 0.61 4.14 -1.70 3.91 -1.01 3.91 -1.18 * P<0.0167 ** P<0.003 3.89** 54 Figure 2.10. Average fiducial and intermolar angles. Table 2.7. Skeletal and dental components of molar and overjet change. Change Measurement Treatment Posttreatment Net T2 minus T1 T3 minus T2 T3 minus T1 Mean S.D. Mean S.D. Mean S.D. Skeletal ABCH 2.50 1.94 1.06 1.70 3.56 2.63 Maxilla -1.31 1.34 -0.47 1.03 -1.78 1.78 Mandible 3.81 2.68 1.52 1.85 5.33 3.52 Dental Upper 6 -3.20 1.70 -1.96 1.52 -5.22 2.09 Lower 6 2.44 1.96 1.13 1.22 3.57 2.06 Upper Incisor 2.32 3.10 -0.71 1.48 1.61 3.17 Lower Incisor -1.74 2.18 -0.98 1.61 -2.72 2.25 Total Molar correction 1.72 1.56 0.23 1.19 1.95 1.92 Overjet change 3.13 2.65 -0.70 0.97 2.43 2.39 55 Figure 2.11. Pitchfork diagrams. A. Components of molar and overjet change; B. Treatment change; C. Posttreatment change; and D. Net change (in mm). Note that the maxillary molars came forward more than the mandibular molars, ABCH was greater in the posttreatment interval, and the maxillary and mandibular incisors moved lingually posttreatment. 56 Table 2.8. Model analysis: descriptive and inferential statistics. T1 T2 T3 Change Paired t Measure Mean Irregularity Mandibular Intercuspid Maxillary 57 Intercuspid Mandibular Intermolar Maxillary Intermolar * P<0.0167 ** P<0.003 S.D. Mean S.D. Mean S.D. Treatment Posttreatment Net T2 minus T1 T3 minus T2 T3 minus T1 Mean S.D. Mean S.D. Mean S.D. T1 to T2 T2 to T3 (Ho:δ=0) 4.80 3.12 0.74 0.80 2.57 1.60 -4.10 3.17 1.81 1.71 -2.23 3.23 10.28** -8.42** 24.95 1.52 26.24 1.44 24.47 1.43 1.29 1.49 -1.76 1.15 -0.48 1.46 -6.83** 12.19** 31.91 2.22 33.34 1.58 32.31 1.76 1.43 1.91 -1.01 1.18 0.40 1.77 -5.95** 6.82** 40.60 2.54 38.21 2.30 37.90 2.66 -2.41 2.36 -0.31 1.39 -2.70 2.06 8.12** 1.76 44.93 2.96 43.79 2.27 43.44 2.55 -1.15 2.20 -0.36 1.32 -1.50 2.11 4.14** 2.16 Table 2.9. Dependent and independent variables: standard deviations, and intra-class correlations. Item Abbreviation Mean means, S.D. Cronbach’s α Dependent Variables (Relapse) Incisor to mandibular plane Post tx∆ IMPA -0.27 3.98 0.71 Post tx∆ IRR 1.81 1.71 0.76 Mandibular intercuspid width Post tx∆ Mand 3-3 -1.76 1.15 0.76 Maxillary intercuspid width Post tx∆ Max 3-3 -1.01 1.18 0.70 Irregularity Index Skeletal Independent Variables (Predictors) Mandible to cranial base Mand-CB tx∆ -0.56 2.30 0.84 Maxilla to cranial base Max-CB tx∆ 0.62 1.53 0.75 Maxilla to mandible Max-Mand tx∆ -1.19 1.99 0.81 Maxilla to cranial base Post tx∆ MAX -0.47 1.03 0.98 Differential mandibular growth Post tx∆ ABCH 1.06 1.70 0.59 Dental Independent Variables (Predictors) Incisor to mandibular plane IMPA tx∆ -1.31 5.46 0.73 Intermolar angle 171.35 4.53 0.89 Irregularity Index IRR tx∆ -4.10 3.17 0.94 Mandibular cuspid expansion Mand 3-3 tx∆ 1.29 1.49 0.76 Maxillary cuspid expansion Max 3-3 tx∆ 1.43 1.91 0.82 Intermolar angle 58 Table 2.10. Multiple regression analysis equations separated into proposed skeletal and dental causes of relapse. Dependent Variable Constant Regression Coefficients r/R r2/R2 F-Ratio Skeletal Predictors Post tx∆ IMPA . . None significant . . . . . . Post tx∆ IRR 1.76 -0.28 MAX-Mand tx∆ -0.26 CB-MAX tx∆ 0.35 0.12 3.91* Post tx∆ Mand 3-3 . . None significant . . . . . . Post tx∆ Max 3-3 . . None significant . . . . . . 59 Dental Predictors Post tx∆ IMPA Post tx∆ IRR Post tx∆ Mand 3-3 Post tx∆ Max 3-3 * P<0.05 ** P<0.01 *** P<0.001 -0.36 -0.32 IMPA tx∆ -0.32 0.10 6.70* -0.36 Intermolar Angle -0.36 0.13 8.83** -1.36 -0.40 Mand 3-3 tx∆ -0.40 0.16 11.41*** -0.59 -0.48 Max 3-3 tx∆ -0.48 0.23 8.81** 1.92 Discussion Error Study The intra-class correlations for the double determinations show that most of the measurements are acceptably reliable (Cronbach’s α above 0.80). There were, however, some measures for which the reliability correlations were low. It must be noted at the outset that a lack of technical reliability may be, in certain instances, a contributor to the generally low and clinically non-significant correlations seen here. Unfortunately, at present there really is no other source of data than lateral cephalograms and study models. Another possible reason for the low correlations in the present study is the method utilized to correct the T3 cephalometric magnification reduction present in 22 of the 64 series. If, in some subjects, growth was not minimal between T2 and T3, as was assumed, the resulting T3 measurements may have slightly under-estimated the posttreatment changes. Treatment Details The descriptive statistics imply that the present sample was treated conservatively in accord with the precepts of the Tweed technique. 60 Cephalometric data summarized in Tables 2.4 and 2.5 illustrate relatively small, often statistically non-significant, treatment changes: the mandibular incisors were up-righted 1.27 degrees (IMPA) and retracted 0.60 mm (L1-APg); the interincisal angle (1/1) was increased 1.85 degrees; and the common vertical measurements, Y-axis and FMA, each decreased less than 1 degree. Linear measures of size generally showed statistically significant increases, as did measures of molar movement, overjet reduction, profile protrusion, and maxillary size/position (SNA). From the study-model measurements (Table 2.8), it may be seen that the canines were expanded on average 1.29 mm in the mandible and 1.43 mm in the maxilla. Both upper and lower intermolar dimensions were decreased during treatment (Table 2.8), 2.41 mm in the mandible and 1.15 mm in the maxilla. These small changes were statistically significant and perhaps can be attributed to the fact that, because of the mechanics of space closure, the canines moved distally and the buccal segments moved mesially along a “V-shaped” basal arch (vide infra). As measured from the fiducial hash mark angles, there were also minimal, and mostly non-significant, vertical changes (Table 2.6 and Figure 2.10). It is perhaps worthwhile to note that there was a slight closing 61 rotation of the mandible during treatment (Mand-CB angle treatment change of -0.57o). This change, however, was not significantly different from zero. This finding contradicts a popular assertion in the Tweed literature that their approach to vertical control allows the mandible to auto-rotate upwards and forwards, the so-called “mandibular response.”45-47 Conversely, the lack of an opening rotation suggests, at the very least, that the present treatment mechanics produced results that counter the common claim that “all orthodontic mechanics are extrusive.” Apparently, it need not be so. From the present descriptive data, it is evident that care was taken by the treating orthodontist to avoid many of the classically-proposed causes of relapse. Despite conservative treatment, however, there were instances in which there was a relationship between even these small treatment changes and subsequent relapse. Further, there were skeletal causes that were beyond the control of the clinician. Skeletal Predictors The multiple regression equations summarized in Table 2.10 show that most of the hypothesized skeletal 62 causes of relapse did not account for a significant portion of the actual incisor relapse seen here. Schudy,25 reported a significant correlation between condylar growth and a decrease in IMPA. The skeletal predictor variables studied here were considerably more complex--differential maxillo-mandibular relations, maxillary displacement, and angular measures of basal rotation (changes in Mand-CB, Max-CB, and Max-Mand angles). The lack of a significant relationship suggests that posttreatment incisal inclination is relatively independent of the overall pattern of skeletal change. As was noted earlier, whatever the change in incisor inclination, it is not the same as change in incisor irregularity, as the two might be relatively independent. As shown in Table 2.8, irregularity increased 1.81 mm in the posttreatment interval to a recall value of 2.57 mm, a result that is similar to several other longterm recall studies of similarly-treated patients.19,20,48 Indeed, 51 of the 64 subjects had posttreatment irregularity below Little’s success/failure borderline of 3.5 mm.49 Although irregularity relapse was small, it was correlated with posttreatment change in ABCH (r=0.218, 63 P=0.047C) and negatively correlated with treatment changes in Max-CB (r=-0.340, P=0.004) and Max-Mand (r=-0.238, P=0.033). These relationships, although weak, are statistically significant and thus require comment. The Pitchfork Analysis (Table 2.7) showed that the mandible outgrew/out-advanced the maxilla (ABCH) in treatment and posttreatment intervals, a pattern of change that is thought by some to be a potential cause of incisal relapse.24,26 The weak positive correlation between ABCH and irregularity suggests that excessive mandibular growth is, at best, a minor factor. ABCH, however, was not part of the multiple regression equation, suggesting that mandibular excess did not supply significant, unduplicated information beyond that supplied by the skeletal variables that did enter. The regression equation for irregularity relapse was statistically significant and included treatment changes in the Max-Mand and Max-CB basal-bone angles. The multiple correlation coefficient, however, was only 0.35; R2, only 0.12. The negative correlation of these angles to incisal crowding inferred from regression coefficients (vide supra) suggests that a forward basal rotation during C Given the intent to employ multivariate analysis, the simple correlation matrix was not tabulated. 64 treatment would serve to increase posttreatment irregularity. The fact that the model can only account for 12% of the observed variation, however, suggests that this sample’s favorable pattern of skeletal rotation is not a clinically significant predictor of irregularity relapse. Further, regardless of predictive significance, posttreatment maxillo-mandibular rotations would seem beyond the control of the clinician. The proposed dental etiologies, however, were more significantly related to relapse and presumably are clinically modifiable. Dental Predictors The results summarized in Table 2.10 show that the multiple regression equation for each measure of relapse had only one statistically significant dental independent variable. In these instances, therefore, multiple regression was really simple regression. For posttreatment change in IMPA, treatment change in IMPA was the only statistically significant predictor (r=-0.32; r2=0.10; P=0.006; Table 2.10). The negative correlation implies that changes in incisor angulation will have a slight tendency to “rebound.” This outcome is in agreement with Tweed,8 Ackerman and Proffit,50 Blake and Bibby,31 and many others who have argued that the original 65 mandibular incisor inclination is the most stable position. In the present sample, the incisors were uprighted during treatment and continued this trend posttreatment. Both effects, however, were small and non-significant. It was the same with irregularity relapse. The posttreatment increase in Little’s Irregularity Index was small and consistent with previous long-term recall studies of similar treatments (vide supra). Regression analysis found only a single significant dental predictor, the intermolar angle at debond; hence, R=r (Table 2.10; r=-0.36, r2=0.13). The negative correlation suggests that more mesially inclined buccal segments will have a slight tendency to increase the posttreatment irregularity, perhaps because of an increased anterior component of occlusal force. The intermolar angle did not change significantly during treatment (Table 2.6), the buccal segments remained mesially inclined, and thus the occlusal forces in this sample would feature an anterior component of force (ACF) that might serve to displace the dentition anteriorly into the labial soft tissue envelope of function. The mesially inclined buccal segment as a potential cause of irregularity is in agreement with a two-part paper by Southard, Behrents, and Tolley.22,23 66 They found a correlation between interproximal forces during occlusion, a measure of anterior occlusal force, and incisor irregularity (r=0.54). Their correlation was greater than seen here, possibly suggesting that a measure of occlusal force in combination with mesial buccal segment inclination might have provided an improved prediction in the present study. It is also worthwhile to note here that initial irregularityD was not correlated to posttreatment irregularity relapse. This finding disagrees with Årtun and co-workers,32 a difference that might be due to the nature of Årtun’s sample, which had both nonextraction and extraction treatments, as compared to the present sample, which was almost all extraction. Presumably, nonextraction treatments of patients with modest anterior space deficiencies often would align the dentition by flaring the incisors into the labial soft tissue envelope of function.4,5,51 In contrast, extraction treatments probably would procline the incisors less frequently and thus would decrease the variation to be predicted. Canine expansion is a kind of lateral “flaring,” and it too, was examined with respect to “dental etiologies.” D Because treatment generally reduced irregularity to zero at T2, treatment change with the sign reversed served as the measurement of initial irregularity in the regression analysis. 67 Of the five dental independent variables, there was only one significant predictor of the stability of mandibular and maxillary canine expansion--the extent of the expansion during treatment (mandible, r=-0.40. r2=0.16; maxilla, r=-0.48, r2=0.23). Thus, even the small, seemingly unavoidable canine expansion seen here appears to be, to a degree, unstable. This outcome is in agreement with Strang’s classic observation about the “inviolability” of lower intercanine width.3 The present study’s expansion relapse is also similar to the results of Little, Wallen, and Riedel,49 who found an average of 2.02 mm of canine relapse. The small r2 values for both expansion equations, however, suggest that, at least in this sample, canine expansion during treatment is not a clinically significant predictor of relapse. A possible reason for this low correlation is that retraction of the canines into a wider portion of the arch would be measured as expansion, but at the same time might not impinge on the buccal soft tissue envelope of function. Another possibility for the small r2 values in the expansion equations is the restricted range of the treatment changes seen here (Table 2.8; standard deviations for treatment changes in mandibular intercanine width was 1.49 mm and for maxillary intercanine width was 1.91 mm). For the present study, if there is little 68 expansion, there is little relapse; if there is little relapse there is almost nothing to predict. Restricted Range Only one of the five statistically significant regression equations featured more than one predictor variable, and all featured weak, seemingly clinically insignificant correlations. One possible reason for the weak correlations is the conservative treatment that was employed. For example, there was little expansion and no incisor flaring. Correlation measures the covariance of standard scores, and if one variable is relatively constant, there is little covariance, and the resulting correlation coefficients must, of necessity, be small (Figure 2.12 A). The combination of nonextraction and extraction treatments might serve to increase the range and perhaps increase the correlation. If, say, 70-80% of the sample were to have been treated with contemporary non-extraction mechanics, there would be deliberate canine expansion, and an increase in range. If such treatments were to be examined 10-20 years posttreatment, this increased range perhaps would lead to much stronger correlation between expansion and relapse (Figure 2.12 B). Time will tell. 69 Figure 2.12. Range restriction. Abscissa is expansion; the ordinate, the relapse associated with a change in width. The narrow grouping of results from conservative Tweed mechanics (A) would tend to obscure any correlation between expansion and relapse; however, the range of results produced by a trend to non-extraction/expansion mechanics (B), might show a more obvious relation between expansion and relapse. Summary and Conclusions The present investigation was a multivariate statistical evaluation of commonly-hypothesized causes of relapse in a longitudinal sample of treated cases recalled over 20 years posttreatment. Despite conservative treatments and relatively small changes in many of the factors thought to cause relapse, a few isolated relationships proved to be statistically significant: 1. Forward basal rotation of the maxilla and mandible during treatment was correlated with an increase in incisal irregularity; 70 2. Treatment change in mandibular incisal angulation was negatively correlated to posttreatment change in incisal angulation; 3. Perhaps as a result of the anterior component of occlusal force, mesial buccal-segment inclination was negatively correlated to posttreatment mandibular incisor irregularity; and 4. Maxillary and mandibular canine expansion during treatment will tend to relapse. Despite scattered instances of statistical significance, no clinically significant prediction equations could be generated from this conservatively treated sample. Perhaps the relapse seen here was too small to be detected by the statistical power of a conventional cephalometrics study. If so, future studies of more marked treatment effects may reveal relationships that are of greater clinical significance. Alternatively perhaps the causes of relapse are more subtle than contemporary methods and conjectures can address. 71 References 1. Weinberger BW. Orthodontics: An Historical Review of Its Origin and Evolution. St. Louis: C.V. Mosby; 1926. 2. Weinstein S, Haack DC, Morris LY, Snyder BB, Attaway HE. On an equilibrium theory of tooth position. Angle Orthod. 1963;33:1-26. 3. Strang RHW. The fallacy of denture expansion as a treatment procedure. Angle Orthod. 1949;19:12-22. 4. Posen AL. The influence of maximum perioral and tongue force on the incisor teeth. Angle Orthod. 1972;42:285-309. 5. Posen AL. The application of quantitative perioral assessment to orthodontic case analysis and treatment planning. Angle Orthod. 1976;46:118-143. 6. Margolis HI. The axial inclination of the mandibular incisors. Am J Orthod Oral Surg. 1943;29:571-594. 7. Grieve GW. 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Angle Orthod. 1997;67:327-336. 51. Proffit WR. Equilibrium theory revisited: factors influencing position of the teeth. Angle Orthod. 1978;48:175-186. 76 APPENDIX A Cephalometric Digitization Regimen Appendix A depicts a customized “Ricketts 71-point regimen” from Dentofacial Planner version 5.32 (Figure A), and the corresponding cephalometric analysis (Table A). Figure A. Customized “Ricketts 71-point regimen” from Dentofacial Planner version 5.32. Point 65 defined the anterior extent of the functional occlusal plane. 77 Table A. Customized cephalometric analysis. Measures Angular Linear SNA Wits A/B SNB PNS-A pt ANB S-Ar Y-axis S-Go U1-SN Ar-Gn U1-NA Pg-NB L1-NB U6-PTV Interincisal (1/1) U1-NA FMA L1-APg IMPA Overjet FMIA Overbite Z N-Me SN-Palatal Plane (ANS-PNS) N-ANS SN-Functional Occlusal Plane ANS-Me UFH (%) LFH (%) LL-E line Wits A/B PNS-A pt 78 APPENDIX B Error Study Appendix B contains the intra-class correlations (Cronbach’s α) for both cephalometric and model duplicate measures. Table B.1. Error Study: intra-class correlations (Cronbach’s α) for angular cephalometric measures. Measures T1 T2 T3 SNA 0.91 0.81 0.83 SNB 0.89 0.85 0.74 ANB 0.94 0.97 0.97 Y-axis 0.92 0.83 0.81 U1-SN 0.94 0.72 0.86 U1-NA 0.94 0.82 0.90 L1-NB 0.94 0.95 0.96 Interincisal 0.94 0.84 0.82 FMA 0.93 0.95 0.95 IMPA 0.97 0.92 0.97 FMIA 0.85 0.71 0.77 Z 0.97 0.94 0.96 SN-PP 0.90 0.92 0.79 SN-FOP 0.93 0.96 0.81 79 Table B.2. Error Study: intra-class correlations (Cronbach’s α) for linear cephalometric measures. Measures T1 T2 T3 Wits A/B 0.95 0.87 0.87 PNS-A pt 0.86 0.93 0.95 S-Ar 0.93 0.98 0.98 S-Go 0.87 0.98 0.99 Ar-Gn 0.99 0.99 0.98 Pg-NB 0.95 0.96 0.92 U6-PTV 0.85 0.93 0.91 U1-NA 0.93 0.97 0.94 L1-APg 0.86 0.95 0.96 Overjet 0.96 0.89 0.79 Overbite 0.88 0.87 0.70 N-Me 0.96 0.97 0.98 N-ANS 0.88 0.95 0.94 ANS-Me 0.99 0.98 0.99 UFH (%) 0.90 0.88 0.92 LFH (%) 0.83 0.80 0.90 LL-E line 0.92 0.98 0.97 80 Table B.3. Measure Error study: intra-class correlations (Cronbach’s α) for the components of molar and overjet change. Treatment Post-treatment Net Skeletal MAX 0.70 0.98 0.94 ABCH 0.57 0.59 0.69 MAND 0.51 0.80 0.76 Dental U6 0.88 0.78 0.74 L6 0.93 0.80 0.83 U1 0.99 0.78 0.97 L1 0.90 0.90 0.84 Total Molar 0.80 0.66 0.90 Overjet 0.97 0.75 0.96 81 Table B.4. Error study: intra-class correlations (Cronbach’s α) for fiducial and intermolar angles. Measures T1 T2 T3 Maxilla-CB 0.76 0.84 0.86 Maxilla-Mandible 0.84 0.94 0.94 Mandible-CB 0.95 0.98 0.96 Intermolar 0.59 0.89 0.85 Table B.5. Error study: intra-class correlations (Cronbach’s α) for model analysis Measures Irregularity Mandibular Intercuspid Maxillary Intercuspid Mandibular Intermolar Maxillary Intermolar T1 T2 T3 0.97 0.95 0.94 0.97 0.97 0.98 0.87 0.96 0.92 0.97 0.98 0.98 0.99 0.98 0.98 82 VITA AUCTORIS Nathan Daniel Mellion was born on September 13, 1982 in Akron, Ohio. He received his undergraduate education at Denison University in Granville, Ohio. He received his dental education at The Ohio State University, and graduated with a degree of Doctor of Dental Surgery in 2008. Immediately after graduation from dental school, he began his graduate orthodontic education at the Center for Advanced Dental Education at Saint Louis University, in St. Louis, Missouri. He is currently a candidate for the degree of Master of Science in Dentistry. to Tana Marie Mellion on December 27, 2008. He was married 83