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Metabolomics has attracted the interest of the medical community for its potential in predicting early derangements from a healthy to a diseased metabolic phenotype. One key issue is the diversity observed in metabolic profiles of different healthy individuals, commonly attributed to the variation of intrinsic (such as (epi)genetic variation, gut microbiota, etc.) and extrinsic factors (such as dietary habits, life-style and environmental conditions). Understanding the relative contributions of these factors is essential to establish the robustness of the healthy individual metabolic phenotype. To assess the relative contribution of intrinsic and extrinsic factors we compared multilevel analysis results obtained from subjects of Homo sapiens and Macaca mulatta, the latter kept in a controlled environment with a standardized diet by making use of previously published data and results. We observed similarities for the two species and found the diversity of urinary metabolic phenotypes as identified by nuclear magnetic resonance (NMR) spectroscopy could be ascribed to the complex interplay of intrinsic factors and, to a lesser extent, of extrinsic factors in particular minimizing the role played by diet in shaping the metabolic phenotype. Moreover, we show that despite the standardization of diet as the most relevant extrinsic factor, a clear individual and discriminative metabolic fingerprint also exists for monkeys. We investigate the metabolic phenotype both at the static (i.e., at the level of the average metabolite concentration) and at the dynamic level (i.e., concerning their variation over time), and we show that these two components sum up to the overall phenotype with different relative contributions of about 1/4 and 3/4, respectively, for both species. Finally, we show that the great degree diversity observed in the urinary metabolic phenotype of both species can be attributed to differences in both the static and dynamic part of their phenotype.

The impact of diet and digestive disorders in flatus composition remains largely unexplored. This is partially due to the lack of standardized sampling collection methods, and the easy atmospheric contamination. This paper describes a method to quantitatively determine the major gases in flatus and their application in a nutritional intervention. We describe how to direct sample flatus into Tedlar bags, and simultaneous analysis by gas chromatography–thermal conductivity detection (GC–TCD). Results are analyzed by univariate hypothesis testing and by multilevel principal component analysis. The reported methodology allows simultaneous determination of the five major gases with root mean measurement errors of 0.8% for oxygen (O2), 0.9% for nitrogen (N2), 0.14% for carbon dioxide (CO2), 0.11% for methane (CH4), and 0.26% for hydrogen (H2). The atmospheric contamination was limited to 0.86 (95% CI: [0.7–1.0])% for oxygen and 3.4 (95% CI: [1.4–5.3])% for nitrogen. As an illustration, the method has been successfully applied to measure the response to a nutritional intervention in a reduced crossover study in healthy subjects.

In this article, we investigate clustering methods for multilevel functional data, which consist of repeated random functions observed for a large number of units (e.g., genes) at multiple subunits (e.g., bacteria types). To describe the within‐ and between variability induced by the hierarchical structure in the data, we take a multilevel functional principal component analysis (MFPCA) approach. We develop and compare a hard clustering method applied to the scores derived from the MFPCA and a soft clustering method using an MFPCA decomposition. In a simulation study, we assess the estimation accuracy of the clustering membership and the cluster patterns under a series of settings: small versus moderate number of time points; various noise levels; and varying number of subunits per unit. We demonstrate the applicability of the clustering analysis to a real data set consisting of expression profiles from genes activated by immunity system cells. Prevalent response patterns are identified by clustering the expression profiles using our multilevel clustering analysis.

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.

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.

Eye tracking (ET) experiments commonly record the continuous trajectory of a subject’s gaze on a two-dimensional screen throughout repeated presentations of stimuli (referred to as trials). Even though the continuous path of gaze is recorded during each trial, commonly derived outcomes for analysis collapse the data into simple summaries, such as looking times in regions of interest, latency to looking at stimuli, number of stimuli viewed, number of fixations, or fixation length. In order to retain information in trial time, we utilize functional data analysis (FDA) for the first time in literature in the analysis of ET data. More specifically, novel functional outcomes for ET data, referred to as viewing profiles, are introduced that capture the common gazing trends across trial time which are lost in traditional data summaries. Mean and variation of the proposed functional outcomes across subjects are then modeled using functional principal component analysis. Applications to data from a visual exploration paradigm conducted by the Autism Biomarkers Consortium for Clinical Trials showcase the novel insights gained from the proposed FDA approach, including significant group differences between children diagnosed with autism and their typically developing peers in their consistency of looking at faces early on in trial time.

In human metabolic profiling studies, between-subject variability is often the dominant feature and can mask the potential classifications of clinical interest. Conventional models such as principal component analysis (PCA) are usually not effective in such situations and it is therefore highly desirable to find a suitable model which is able to discover the underlying pattern hidden behind the high between-subject variability. In this study we employed two clinical metabolomics data sets as the testing grounds, in which such variability had been observed, and we demonstrate that a proper choice of chemometrics model can help to overcome this issue of high between-subject variability. Two data sets were used to represent two different types of experiment designs. The first data set was obtained from a small-scale study investigating volatile organic compounds (VOCs) collected from chronic wounds using a skin patch device and analysed by thermal desorption-gas chromatography-mass spectrometry. Five patients were recruited and for each patient three sites sampled in triplicate: healthy skin, boundary of the lesion and top of the lesion, the aim was to discriminate these three types of samples based on their VOC profile. The second data set was from a much larger study involving 35 healthy subjects, 47 patients with chronic obstructive pulmonary disease and 33 with asthma. The VOCs in the breath of each subject were collected using a mask device and analysed again by GC–MS with the aim of discriminating the three types of subjects based on breath VOC profiles. Multilevel simultaneous component analysis, multilevel partial least squares for discriminant analysis, ANOVA-PCA, and a novel simplified ANOVA-PCA model—which we have named ANOVA-Mean Centre (ANOVA-MC)—were applied on these two data sets. Significantly improved results were obtained by using these models. We also present a novel validation procedure to verify statistically the results obtained from those models.

Single-level principal component analysis (PCA) and multi-level PCA (mPCA) methods are applied here to a set of (2D frontal) facial images from a group of 80 Finnish subjects (34 male; 46 female) with two different facial expressions (smiling and neutral) per subject. Inspection of eigenvalues gives insight into the importance of different factors affecting shapes, including: biological sex, facial expression (neutral versus smiling), and all other variations. Biological sex and facial expression are shown to be reflected in those components at appropriate levels of the mPCA model. Dynamic 3D shape data for all phases of a smile made up a second dataset sampled from 60 adult British subjects (31 male; 29 female). Modes of variation reflected the act of smiling at the correct level of the mPCA model. Seven phases of the dynamic smiles are identified: rest pre-smile, onset 1 (acceleration), onset 2 (deceleration), apex, offset 1 (acceleration), offset 2 (deceleration), and rest post-smile. A clear cycle is observed in standardized scores at an appropriate level for mPCA and in single-level PCA. mPCA can be used to study static shapes and images, as well as dynamic changes in shape. It gave us much insight into the question “what’s in a smile?”.

When data sets are multilevel (group nesting or repeated measures), different sources of variations must be identified. In the framework of unsupervised analyses, multilevel simultaneous component analysis (MSCA) has recently been proposed as the most satisfactory option for analyzing multilevel data. MSCA estimates submodels for the different levels in data and thereby separates the “within”-subject and “between”-subject variations in the variables. Following the principles of MSCA and the strategy of decomposing the available data matrix into orthogonal blocks, and taking into account the between- and the within data structures, we generalize, in a multilevel perspective, multivariate models in which a matrix of response variables can be used to guide the projections (formed by responses predicted by explanatory variables or by a limited number of their combinations/composites) into choices of meaningful directions. To this end, the current paper proposes the multilevel version of the multivariate regression model and dimensionality-reduction methods (used to predict responses with fewer linear composites of explanatory variables). The principle findings of the study are that the minimization of the loss functions related to multivariate regression, principal-component regression, reduced-rank regression, and canonical-correlation regression are equivalent to the separate minimization of the sum of two separate loss functions corresponding to the between and within structures, under some constraints. The paper closes with a case study of an application focusing on the relationships between mental health severity and the intensity of care in the Lombardy region mental health system.

Despite the desire of adolescent girls and young women (AGYW) in sub-Saharan Africa (SSA) to use contraceptives, the majority of them have challenges with access to contraceptive services. This is more evident in high fertility countries in SSA. The purpose of this study was to examine the predictors of unmet need for contraception among AGYW in selected high fertility countries in SSA. Data from current Demographic and Health Surveys (DHS) carried out between 2010 and 2018 in 10 countries in SSA were analysed. A sample size of 24,898 AGYW who were either married or cohabiting was used. Unmet need for contraception was the outcome variable in this study. The explanatory variables were age, marital status, occupation, educational level, frequency of reading newspaper/magazine, frequency of listening to radio, frequency of watching television and parity (individual level variables) and wealth quintile, sex of household head, place of residence and decision-maker in healthcare (household/community level variables). Descriptive and multilevel logistic regression analyses were carried out. The results of the multilevel logistic regression analyses were reported using adjusted odds ratios at 95% confidence interval. The prevalence of unmet need for contraception in all the countries considered in this study was 24.9%, with Angola, recording the highest prevalence of 42.6% while Niger had the lowest prevalence of 17.8%. In terms of the individual level predictors, the likelihood of unmet need for contraception was low among AGYW aged 20-24 [aOR = 0.82; 95% CI = 0.76-0.88], those with primary [aOR = 1.22; 95% CI = 1.13-1.31] and secondary/higher levels of formal education [aOR = 1.18; 95% CI = 1.08-1.28, p < 0.001], cohabiting AGYW [aOR = 1.52; 95% CI = 1.42-1.63] and AGYW with three or more births [aOR = 3.41; 95% CI = 3.02-3.85]. At the household/community level, the odds of unmet need for contraception was highest among poorer AGYW [aOR = 1.36; 95% CI = 1.21-1.53], AGYW in female-headed households [aOR = 1.22; 95% CI = 1.13-1.33], urban AGYW [aOR = 1.21; 95% CI = 1.11-1.32] and AGYW who took healthcare decisions alone [aOR = 1.10; 95% CI = 1.01-1.21]. This study has identified disparities in unmet need for contraception among AGYW in high fertility countries in SSA, with AGYW in Angola having the highest prevalence. Both individual and household/community level factors predicted unmet need for contraception among AGYW in this study. However, based on the ICC values, household/community level factors prevailed the individual level factors. Enhancing access to contraception among poorer AGYW, those in female-headed households, those in urban areas and those who take healthcare decisions alone by both governmental and non-governmental organisations in high fertility countries is recommended.