Morphologic homogeneity is desirable in sample selection of clinical studies that evaluate methods of treating craniofacial discrepancies in orthodontics. The purposes of this study were to assess sample selection criteria commonly used in the orthodontic literature regarding their effectiveness in achieving morphologic homogeneity, and to propose a method that can guarantee selection of a homogeneous sample, for which the degree of homogeneity and the average skeletal pattern can be specified a priori.
Pretreatment lateral cephalograms from 170 consecutive patients (82 boys, 88 girls) aged 7 to 17 years were used. Sixteen skeletal and 4 dental landmarks were digitized and processed with Procrustes superimposition and principal component analysis. The sample was bootstrapped to a virtual population of 10,000 subjects by random sampling from the normal distribution for each principal component. A systematic literature search of randomized controlled trials showed that the most prevalent sample selection criteria, in addition to molar relationship, included overjet, ANB, and SN-GoGn. Each criterion was applied to the virtual population. The morphologic homogeneity of the samples was assessed as the percentage of shape variance of each sample relative to the shape variance of the population.
The first 3 principal components incorporated approximately 53% of shape variability. The evaluated criteria achieved low or moderate morphologic homogeneity scores (range, 28%-63%), and the selected patients were widely spread in the shape space. Although the criteria are commonly applied for selecting samples with skeletal discrepancies, a considerable number of subjects with an average shape were selected. The proposed procedure entails selecting a skeletal pattern appropriate for the study’s purpose, setting limits in shape space within which the sample should be confined, and testing candidate patients against these limits. The patients within these boundaries have, by definition, a similar shape to the selected skeletal pattern and form a homogeneous sample.
The cephalometric variables that have been used in randomized controlled trials do not result in samples of high morphologic homogeneity. The proposed method guarantees high morphologic homogeneity. The extent of homogeneity, the average shape of the sample, and the sample’s relationship to the general population’s average can be specified a priori.
We evaluated sample selection criteria of randomized controlled trials in orthodontics.
Conventional cephalometrics failed to select morphologically homogeneous samples.
Geometric morphometrics guarantees samples of high morphologic homogeneity.
The proposed method can predetermine homogeneity and average shape of the sample.
Clinical studies that evaluate orthodontic treatment methods usually require a homogeneous sample with regard not only to age and sex, but also to craniofacial morphology. There are 2 main reasons for this: (1) each of our treatments targets a specific morphologic type (eg, skeletal Class II), so we need to make certain that the selected patients actually conform to this craniofacial pattern; and (2) it is generally assumed that morphologically different patients respond differently to treatment and follow different growth patterns, whereas patients with comparable shape characteristics respond in a more similar way. Morphologic homogeneity is therefore desirable for establishing that the sample is appropriate to receive the treatment under investigation and for reducing variance in treatment response, which might otherwise overshadow significant results. Point 2 above is debatable, and evidence is limited ; however, until the extent of potential differences in growth and treatment responses is elucidated, it is prudent to consider morphologic homogeneity during sample selection.
A morphologically homogeneous sample can be selected by applying specific criteria related to cephalometric and dental measurements, such as ANB, mandibular plane angle, and overjet. The more criteria used and the narrower the limits set on each, the more homogeneous the sample will be, but it will also be harder to recruit enough conforming subjects. There are currently no guidelines or procedures to specify the number of criteria and their limits. The problem is difficult because the efficacy of each cephalometric variable in grouping together similar craniofacial types is unknown. One conventional cephalometric measurement can be similar among patients, yet the patients may exhibit quite different craniofacial patterns. This has been exemplified most notably by the ANB angle, an assumed indicator of anteroposterior jaw relationship heavily influenced, however, by extraneous factors. The problem is not specific to ANB; any linear or angular measurement is by its nature limited to describe the relative position of just a handful of landmarks in a craniofacial “complex” that clearly needs a much richer representation for comprehensive description.
Clinical trials, including randomized controlled trials (RCTs), may use only dental criteria (molar relationship or overjet) for selecting patients to be treated with purported “growth-modifying” appliances. Some studies add 1 or 2 craniofacial morphologic variables, with little justification for their selection or range limits. It is disturbing to consider that most of our evidence-based knowledge, which stems from RCTs, could be based on samples of questionable homogeneity and treatment suitability. Therefore, the aims of our study were (1) to evaluate sample selection criteria commonly used in orthodontic research regarding their effectiveness in achieving morphologically homogeneous samples; and (2) to propose a method that can guarantee selection of a homogeneous sample, for which the degree of homogeneity and the average skeletal pattern can be specified a priori.
Material and methods
For our first aim, we identified the RCTs most relevant to the orthodontic literature, extracted the sample selection morphologic criteria of each, and tabulated them. We selected the most prevalent criteria and assessed their effectiveness by applying them on a simulated population of 10,000 subjects and measuring the morphologic homogeneity of the resulting sample. Details of the procedure are presented below.
A systematic literature search was conducted in the PubMed database to collect RCTs that have sample selection criteria based on dentoskeletal pattern. The keywords “((randomized AND controlled AND clinical trials) OR RCTs) AND orthodontics” were inserted on October 24, 2014, and 1854 articles were identified. No date limits were applied, and 121 articles matched the inclusion criteria on a title basis, 119 matched according to the abstract, and 44 articles were kept after a full reading. The 18 inclusion criteria that were extracted from these articles are given in Table I . In almost all studies, the main criterion was dental: molar relationship. Additional criteria included overjet and 1 or 2 cephalometric measurements. Based on the number of citations of their source articles, criteria 1 through 4c were examined in this study. These involve 2 cephalometric angles, ANB and SN-GoGn, and 1 dental parameter, overjet. Criterion 4 was used for stratification rather than as an inclusion criterion ; however, we investigated its sample selection properties because the angle of the mandibular plane to the cranial base (measured as SN-MP, SN-GoGn, or SN-GoMe) has been used for both purposes in the literature.
|Criterion||Overjet (mm)||ANB angle (°)||Mandibular plane angle (°)||Other||Reference|
|1||≥7||Tulloch et al, 1998; Proffit and Tulloch, 2002; Thurman et al, 2011|
|2||>4.5||Ghafari et al, 1998|
|3||>7||>6||Illing et al, 1998; Morris et al, 1998|
|4a||SN-GoGn <30||Keeling et al, 1998; Pavlow et al, 2008|
|4b||SN-GoGn 30-40||Keeling et al, 1998; Pavlow et al, 2008|
|4c||SN-GoGn >40||Keeling et al, 1998; Pavlow et al, 2008|
|5||≥6||Thiruvenkatachari et al, 2010; Martina et al, 2013|
|6||4.5-10||Franco et al, 2002; Cevidanes et al, 2005|
|7||≥5||Cura and Saraç, 1997|
|8||>5||≥4.5||Efstratiadis et al, 2005|
|9||>6||>4||Trenouth and Desmond, 2012|
|10||<0||Wits <−2 mm||Ge at al, 2012|
|11||<0||<0||Wits <−2 mm||Saleh et al, 2013|
|12||>5||>4||SNB <78°||Showkatbakhsh et al, 2011|
|13||<−1||SN-GoMe 30-32||SNA ≤79°||Kurt et al, 2011|
|14||<0||Maxillomandibular angle <35°, lower face height <70 mm||Mandall et al, 2010; Mandall et al, 2012|
|15||≤0||≤0||Wits ≥3 mm, nasion perpendicular to A-point ≤2°||Vaughn et al, 2005|
|16||>4||>4||Wits >2 mm, mandibular incisor/mandibular plane 93° ± 5°, normal or reduced anterior facial height||Idris et al, 2012|
|17||≥5||>4||SN-GoGn 32 ± 6||SNB <78°||Baysal and Uysal, 2013|
|18||≥5||>4||SN-GoGn 32 ± 2||SNB <78°||Varlik et al, 2008|
To quantitatively evaluate the effectiveness of each criterion, we need a measure of morphologic homogeneity. We based our definition of morphologic homogeneity (MH) on the percentage of morphologic variation (MVar) that is selected by the criterion relative to the total variation of the population.
Mathematically, we define morphologic homogeneity as
MVar sample is the morphologic variation of the selected sample, and MVar population is the variation of the population. Morphologic homogeneity takes values from 0 to 1 and can be expressed as a percentage. Since MVar population is constant, the extreme values are obtained when MVar sample equals MVar population , in which case the sample is no more homogeneous than the population (0% homogeneity relative to the population). When MVar sample is 0, all subjects have exactly the same shape (100% homogeneity).
To measure shape and shape variance, we turned to geometric morphometrics, which provides quantitative and comprehensive measures of shape. Applied to tracings of cephalometric radiographs, geometric morphometrics first superimposes the landmark configurations of all patients, effectively removing differences in position, orientation, and size (Procrustes alignment). This alignment is different from conventional cephalometric superimpositions in that no specific points are made to coincide; instead, a best-fit alignment over all points is sought. The coordinates of the transformed landmarks (Procrustes coordinates) are then processed using principal component analysis and converted into principal components. These describe the shape patterns of the population, ordered by decreasing importance—from the most prominent, arising from inherent biologic variability (eg, low or high angle vertical pattern), to the least important, depicting insignificant variations, mostly caused by error. Each patient gets a set of principal components that describe his or her craniofacial shape. The principal components can be thought of as coordinates that position the patient in a so-called shape space. The shape space has the following properties: (1) each position in the shape space corresponds to a specific skeletal shape; (2) conversely, each patient occupies only one specific position in the shape space; (3) the shape space is continuous, with a gradual shape transition occurring from one position to another; and (4) the center of the shape space represents the average shape of the population from which the space was constructed.
The shape space is a quantitative construct where shape can be measured, and shape difference can be expressed by 1 number; the difference in shape between 2 patients is equal to the distance between them in shape space. Similarly, the distance between each patient and the center point of the space is mathematically equal to the patient’s shape deviation from the sample’s average skeletal pattern. Such distances in shape space are called Procrustes distances.
Since shape-space maps shape to space coordinates, variability of shape can be assessed by measuring a sample’s spatial extent in this space. Therefore, we can now modify our measure of morphologic homogeneity to the percentage of the volume occupied by a sample in relation to the volume of the whole population in shape space. To compute the volume occupied by a collection of points, we use the convex hull, the smallest convex region enclosing all points within it. Thus, equation 1 becomes