Multilevel models of age-related changes in facial shape in adolescents

Here we study the effects of age on facial shape in adolescents by using a method called multilevel principal components analysis (mPCA). An associated multilevel multivariate probability distribution is derived and expressions for the (conditional) probability of age-group membership are presented. This formalism is explored via Monte Carlo (MC) simulated data in the first dataset; where age is taken to increase the overall scale of a three-dimensional facial shape represented by 21 landmark points and all other “subjective” variations are related to the width of the face. Eigenvalue plots make sense and modes of variation correctly identify these two main factors at appropriate levels of the mPCA model. Component scores for both single-level PCA and mPCA show a strong trend with age. Conditional probabilities are shown to predict membership by age group and the Pearson correlation coefficient between actual and predicted group membership is r = 0.99. The effects of outliers added to the MC training data are reduced by the use of robust covariance matrix estimation and robust averaging of matrices. These methods are applied to another dataset containing 12 GPA-scaled (3D) landmark points for 195 shapes from 27 white, male schoolchildren aged 11 to 16 years old. 21% of variation in the shapes for this dataset was accounted for by age. Mode 1 at level 1 (age) via mPCA appears to capture an increase in face height with age, which is consistent with reported pubertal changes in children. Component scores for both single-level PCA and mPCA again show a distinct trend with age. Conditional probabilities are again shown to reflect membership by age group and the Pearson correlation coefficient is given by r = 0.63 in this case. These analyses are an excellent first test of the ability of multilevel statistical methods to model age-related changes in facial shape in adolescents

Initial Investigations of the cranial size and shape of adult Eurasian otters (Lutra lutra) in Great Britain

Three-dimensional (3D) surface scans were carried out in order to determine the shapes of the upper sections of (skeletal) crania of adult Eurasian otters (Lutra lutra) from Great Britain. Landmark points were placed on these shapes using a graphical user interface (GUI) and distance measurements (i.e., the length, height, and width of the crania) were found by using the landmark points. Male otters had significantly larger skulls than females (P < 0.001). Differences in size also occurred by geographical area in Great Britain (P < 0.05). Multilevel Principal Components Analysis (mPCA) indicated that sex and geographical area explained 31.1% and 9.6% of shape variation in “unscaled” shape data and that they explained 17.2% and 9.7% of variation in “scaled” data. The first mode of variation at level 1 (sex) correctly reflected size changes between males and females for “unscaled” shape data. Modes at level 2 (geographical area) also showed possible changes in size and shape. Clustering by sex and geographical area was observed in standardized component scores. Such clustering in a cranial shape by geographical area might reflect genetic differences in otter populations in Great Britain, although other potentially confounding factors (e.g., population age-structure, diet, etc.) might also drive regional differences. This work provides a successful first test of the effectiveness of 3D surface scans and multivariate methods, such as mPCA, to study the cranial morphology of otters

Multilevel analysis of the influence of maternal smoking and alcohol consumption on the facial shape of English adolescents

This cross-sectional study aims to assess the influence of maternal smoking and alcohol consumption during pregnancy on the facial shape of non-syndromic English adolescents and demonstrate the potential benefits of using multilevel principal component analysis (mPCA). A cohort of 3755 non-syndromic 15-year-olds from the Avon Longitudinal Study of Parents and Children (ALSPAC), England, were included. Maternal smoking and alcohol consumption during the 1st and 2nd trimesters of pregnancy were determined via questionnaire at 18 weeks gestation. 21 facial landmarks, used as a proxy for the main facial features, were manually plotted onto 3D facial scans of the participants. The effect of maternal smoking and maternal alcohol consumption (average 1–2 glasses per week) was minimal, with 0.66% and 0.48% of the variation in the 21 landmarks of non-syndromic offspring explained, respectively. This study provides a further example of mPCA being used effectively as a descriptive analysis in facial shape research. This is the first example of mPCA being extended to four levels to assess the influence of environmental factors. Further work on the influence of high/low levels of smoking and alcohol and providing inferential evidence is required

Investigating facial shape using multilevel principal component analysis

SUMMARY Aims: 1. To determine the influence of geographical location, sex, height, Body Mass Index (BMI), age (14-16 years old), pubertal stage, metabolic factors, atopy, breathing disorders, maternal smoking and alcohol consumption during pregnancy on facial shape. 2. To explore the usefulness of Multilevel Principal Component Analysis (mPCA) in facial shape research. Method: The influence of geographical location and sex was assessed using 21 landmarks on 3D facial scans of subjects from Croatia (n=73), England (n=79), Wales (n=50) and Finland (n=47). The influence of sex, height, BMI, age (14-16 years old), pubertal stage, metabolic factors, atopy, breathing disorders, maternal smoking and alcohol consumption during pregnancy on adolescent facial shape was assessed using 1000 and 7160 quasi-landmarks on 3D facial scans of the Avon Longitudinal Study of Parents and Children (ALSPAC) cohort (n=1411). The results of mPCA were compared to those using landmarks only, conventional Principal Component Analysis (PCA), Discriminate Function Analysis (DFA) and Partial Least Squares Regression (PLSR). mPCA was also assessed as a variable selection tool prior to PLSR. Results: mPCA provided more meaningful information in the exploratory phase of data analysis than conventional PCA and DFA. However, the results must be interpreted with caution when group sizes are imbalanced. All variables reached significance, except for age, in their respective mPCA models. Geographical location, sex, height, BMI and fasting insulin explained greater than 5% of the total variation. These variables also reached significance in the PLSR models. Therefore 5% may be a useful threshold for PLSR variable selection. Conclusions: Sex, geographical location, height, BMI and fasting insulin had the most influence on facial shape. mPCA appears to be a useful tool for visualising the maximum variation between groups of subjects when group sizes are balanced and as a variable selection tool to inform more sophisticated models such as PLSR

An exploration of pathologies of multilevel principal components analysis in statistical models of shape

3D facial surface imaging is a useful tool in dentistry and in terms of diagnostics and treatment planning. Between-group PCA (bgPCA) is a method that has been used to analyse shapes in biological morphometrics, although various “pathologies” of bgPCA have recently been proposed. Monte Carlo (MC) simulated datasets were created here in order to explore “pathologies” of multilevel PCA (mPCA), where mPCA with two levels is equivalent to bgPCA. The first set of MC experiments involved 300 uncorrelated normally distributed variables, whereas the second set of MC experiments used correlated multivariate MC data describing 3D facial shape. We confirmed results of numerical experiments from other researchers that indicated that bgPCA (and so also mPCA) can give a false impression of strong differences in component scores between groups when there is none in reality. These spurious differences in component scores via mPCA decreased significantly as the sample sizes per group were increased. Eigenvalues via mPCA were also found to be strongly affected by imbalances in sample sizes per group, although this problem was removed by using weighted forms of covariance matrices suggested by the maximum likelihood solution of the two-level model. However, this did not solve problems of spurious differences between groups in these simulations, which was driven by very small sample sizes in one group. As a “rule of thumb” only, all of our experiments indicate that reasonable results are obtained when sample sizes per group in all groups are at least equal to the number of variables. Interestingly, the sum of all eigenvalues over both levels via mPCA scaled approximately linearly with the inverse of the sample size per group in all experiments. Finally, between-group variation was added explicitly to the MC data generation model in two experiments considered here. Results for the sum of all eigenvalues via mPCA predicted the asymptotic amount for the total amount of variance correctly in this case, whereas standard “single-level” PCA underestimated this quantity

Initial steps towards a multilevel functional principal components analysis model of dynamical shape changes

In this article, multilevel principal components analysis (mPCA) is used to treat dynamical changes in shape. Results of standard (single-level) PCA are also presented here as a comparison. Monte Carlo (MC) simulation is used to create univariate data (i.e., a single “outcome” variable) that contain two distinct classes of trajectory with time. MC simulation is also used to create multivariate data of sixteen 2D points that (broadly) represent an eye; these data also have two distinct classes of trajectory (an eye blinking and an eye widening in surprise). This is followed by an application of mPCA and single-level PCA to “real” data consisting of twelve 3D landmarks outlining the mouth that are tracked over all phases of a smile. By consideration of eigenvalues, results for the MC datasets find correctly that variation due to differences in groups between the two classes of trajectories are larger than variation within each group. In both cases, differences in standardized component scores between the two groups are observed as expected. Modes of variation are shown to model the univariate MC data correctly, and good model fits are found for both the “blinking” and “surprised” trajectories for the MC “eye” data. Results for the “smile” data show that the smile trajectory is modelled correctly; that is, the corners of the mouth are drawn backwards and wider during a smile. Furthermore, the first mode of variation at level 1 of the mPCA model shows only subtle and minor changes in mouth shape due to sex; whereas the first mode of variation at level 2 of the mPCA model governs whether the mouth is upturned or downturned. These results are all an excellent test of mPCA, showing that mPCA presents a viable method of modeling dynamical changes in shape

Heritability of facial soft tissue growth in mono- and dizygotic twins at 12 and 17 years of age: A retrospective cohort study

OBJECTIVE The purpose of this investigation of untreated monozygotic and dizygotic twins was to identify the genetic and environmental components to the facial soft tissue growth. SETTINGS AND SAMPLE POPULATION The sample consisted of 52 untreated monozygotic twins (36 male and 16 female) and 46 untreated dizygotic twins (23 male and 23 female) from the Forsyth Moorrees Twin Study (1959-1975). MATERIALS AND METHODS Lateral cephalograms were taken at 12 and 17 years of age and traced to analyse facial convexity, nasolabial angle, upper and lower lip thickness, upper and lower lip profile and nose prominence. The genetic and environmental components of variance were analysed with structural equation modelling for multilevel mixed-effects model. RESULTS At 12 years of age, strong additive genetic influence was seen for facial convexity (70%), upper lip profile (66%) and nose prominence (65%), whereas strong dominant genetic components were found for upper lip thickness (56%). Nevertheless, under unique environment influence were nasolabial angle (58%), lower lip profile (51%) and lower lip thickness (64%). At 17 years of age, only upper lip thickness (55%) and nose prominence (84%) were under strong additive genetic control, while the rest of the variables were under strong dominant genetic control. The only exception was lower lip thickness (61%), which is still influenced by the unique environment. CONCLUSION Although monozygotic/dizygotic twins share at least part of their genome, at both times either additive, dominant or environmental components were found. Nevertheless, at 17 years of age most of the variables are either under additive or dominant genetic influence

A review of the effectiveness of lower limb orthoses used in cerebral palsy

To produce this review, a systematic literature search was conducted for relevant articles published in the period between the date of the previous ISPO consensus conference report on cerebral palsy (1994) and April 2008. The search terms were 'cerebral and pals* (palsy, palsies), 'hemiplegia', 'diplegia', 'orthos*' (orthoses, orthosis) orthot* (orthotic, orthotics), brace or AFO