Two-way principal component analysis for matrix-variate data, with an application to functional magnetic resonance imaging data

Metabolomic Profiles in Childhood and Adolescence Are Associated with Fetal Overnutrition

Fetal overnutrition predisposes offspring to increased metabolic risk. The current study used metabolomics to assess sustained differences in serum metabolites across childhood and adolescence among youth exposed to three typologies of fetal overnutrition: maternal obesity only, gestational diabetes mellitus (GDM) only, and obesity + GDM. We included youth exposed in utero to obesity only (BMI ≥ 30; n = 66), GDM only (n = 56), obesity + GDM (n = 25), or unexposed (n = 297), with untargeted metabolomics measured at ages 10 and 16 years. We used linear mixed models to identify metabolites across both time-points associated with exposure to any overnutrition, using a false-discovery-rate correction (FDR) <0.20. These metabolites were included in a principal component analysis (PCA) to generate profiles and assess metabolite profile differences with respect to overnutrition typology (adjusted for prenatal smoking, offspring age, sex, and race/ethnicity). Fetal overnutrition was associated with 52 metabolites. PCA yielded four factors accounting for 17−27% of the variance, depending on age of measurement. We observed differences in three factor patterns with respect to overnutrition typology: sphingomyelin-mannose (8−13% variance), skeletal muscle metabolism (6−10% variance), and 3-carboxy-4-methyl-5-propyl-2-furanpropanoic acid (CMPF; 3−4% variance). The sphingomyelin-mannose factor score was higher among offspring exposed to obesity vs. GDM. Exposure to obesity + GDM (vs. GDM or obesity only) was associated with higher skeletal muscle metabolism and CMPF scores. Fetal overnutrition is associated with metabolic changes in the offspring, but differences between typologies of overnutrition account for a small amount of variation in the metabolome, suggesting there is likely greater pathophysiological overlap than difference.

A functional mixed model for scalar on function regression with application to a functional MRI study

Motivated by a functional magnetic resonance imaging (fMRI) study, we propose a new functional mixed model for scalar on function regression. The model extends the standard scalar on function regression for repeated outcomes by incorporating subject-specific random functional effects. Using functional principal component analysis, the new model can be reformulated as a mixed effects model and thus easily fit. A test is also proposed to assess the existence of the subject-specific random functional effects. We evaluate the performance of the model and test via a simulation study, as well as on data from the motivating fMRI study of thermal pain. The data application indicates significant subject-specific effects of the human brain hemodynamics related to pain and provides insights on how the effects might differ across subjects.

Hybrid principal components analysis for region-referenced longitudinal functional EEG data

Electroencephalography (EEG) data possess a complex structure that includes regional, functional, and longitudinal dimensions. Our motivating example is a word segmentation paradigm in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. For each subject, continuous EEG signals recorded at each electrode were divided into one-second segments and projected into the frequency domain via fast Fourier transform. Following a spectral principal components analysis, the resulting data consist of region-referenced principal power indexed regionally by scalp location, functionally across frequencies, and longitudinally by one-second segments. Standard EEG power analyses often collapse information across the longitudinal and functional dimensions by averaging power across segments and concentrating on specific frequency bands. We propose a hybrid principal components analysis for region-referenced longitudinal functional EEG data, which utilizes both vector and functional principal components analyses and does not collapse information along any of the three dimensions of the data. The proposed decomposition only assumes weak separability of the higher-dimensional covariance process and utilizes a product of one dimensional eigenvectors and eigenfunctions, obtained from the regional, functional, and longitudinal marginal covariances, to represent the observed data, providing a computationally feasible non-parametric approach. A mixed effects framework is proposed to estimate the model components coupled with a bootstrap test for group level inference, both geared towards sparse data applications. Analysis of the data from the word segmentation paradigm leads to valuable insights about group-region differences among the TD and verbal and minimally verbal children with ASD. Finite sample properties of the proposed estimation framework and bootstrap inference procedure are further studied via extensive simulations.

Extracting Voxel-Based Cartilage Relaxometry Features in Hip Osteoarthritis Subjects Using Principal Component Analysis

BACKGROUND

MRI-based relaxation time measurements provide quantitative assessment of cartilage biochemistry. Identifying distinctive relaxometry features in hip osteoarthritis (OA) might provide important information on regional disease variability.

PURPOSE

First, to incorporate fully automatic voxel-based relaxometry (VBR) with principal component analysis (PCA) to extract distinctive relaxometry features in subjects with radiographic hip OA and nondiseased controls. Second, to use the identified features to further distinguish subjects with cartilage compositional abnormalities.

STUDY TYPE

Cross-sectional.

SUBJECTS

Thirty-three subjects with radiographic hip OA (20 males; age, 50.2 ± 13.3 years) and 55 controls participated (28 males; 41.3 ± 12.0 years).

SEQUENCE

A 3.0T scanner using 3D SPGR, combined T_1ρ /T₂ , and fast spin echo sequences.

ASSESSMENT

Pelvic radiographs, patients' self-reported symptoms, physical function, and cartilage morphology were analyzed. Cartilage relaxation times were quantified using traditional regions of interest and VBR approaches. PCA was performed on VBR data to identify distinctive relaxometry features, and were subsequently used to identify a subgroup of subjects from the controls that exhibited compositional abnormalities.

STATISTICAL TESTS

Chi-square and independent t-tests were used to compare group characteristics. Logistic regression models were used to identify the possible principal components (PCs) that were able to predict OA vs. control classification.

RESULTS

In T_1ρ assessment, OA subjects demonstrated higher T_1ρ values in the posterior hip region and deep cartilage layer when compared with controls (P = 0.012 and 0.001, respectively). In T₂ assessment, OA subjects exhibited higher T₂ values in the posterior hip region (P < 0.001). Based on the PC score classification, 16 subjects without radiographic evidence of OA demonstrated relaxometry patterns similar to OA subjects, and exhibited worse physical function (P = 0.003) and cartilage lesions (P = 0.009-0.032) when compared with the remaining controls.

DATA CONCLUSION

The study identified distinctive cartilage relaxometry features that were able to discriminate subjects with and without radiographic hip OA effectively.

LEVEL OF EVIDENCE

1 Technical Efficacy Stage: 2 J. Magn. Reson. Imaging 2020;51:1708-1719.

Discussion of the paper ‘A general framework for functional regression modelling’

This discussion provides our reaction to the article by Greven and Scheipl. It contains an overview of their article and a description of the many areas of research that remain open and could benefit from further methodological and computational development.