Gradient synchronization for multivariate functional data, with application to brain connectivity.

Quantifying the association between components of multivariate random curves is of general interest and is a ubiquitous and basic problem that can be addressed with functional data analysis. An important application is the problem of assessing functional connectivity based on functional magnetic resonance imaging (fMRI), where one aims to determine the similarity of fMRI time courses that are recorded on anatomically separated brain regions. In the functional brain connectivity literature, the static temporal Pearson correlation has been the prevailing measure for functional connectivity. However, recent research has revealed temporally changing patterns of functional connectivity, leading to the study of dynamic functional connectivity. This motivates new similarity measures for pairs of random curves that reflect the dynamic features of functional similarity. Specifically, we introduce gradient synchronization measures in a general setting. These similarity measures are based on the concordance and discordance of the gradients between paired smooth random functions. Asymptotic normality of the proposed estimates is obtained under regularity conditions. We illustrate the proposed synchronization measures via simulations and an application to resting-state fMRI signals from the Alzheimer's Disease Neuroimaging Initiative and they are found to improve discrimination between subjects with different disease status.

DeepIDA-GRU: a deep learning pipeline for integrative discriminant analysis of cross-sectional and longitudinal multiview data with applications to inflammatory bowel disease classification.

Biomedical research now commonly integrates diverse data types or views from the same individuals to better understand the pathobiology of complex diseases, but the challenge lies in meaningfully integrating these diverse views. Existing methods often require the same type of data from all views (cross-sectional data only or longitudinal data only) or do not consider any class outcome in the integration method, which presents limitations. To overcome these limitations, we have developed a pipeline that harnesses the power of statistical and deep learning methods to integrate cross-sectional and longitudinal data from multiple sources. In addition, it identifies key variables that contribute to the association between views and the separation between classes, providing deeper biological insights. This pipeline includes variable selection/ranking using linear and nonlinear methods, feature extraction using functional principal component analysis and Euler characteristics, and joint integration and classification using dense feed-forward networks for cross-sectional data and recurrent neural networks for longitudinal data. We applied this pipeline to cross-sectional and longitudinal multiomics data (metagenomics, transcriptomics and metabolomics) from an inflammatory bowel disease (IBD) study and identified microbial pathways, metabolites and genes that discriminate by IBD status, providing information on the etiology of IBD. We conducted simulations to compare the two feature extraction methods.

Functional data geometric morphometrics with machine learning for craniodental shape classification in shrews.

This work proposes a functional data analysis approach for morphometrics in classifying three shrew species (S. murinus, C. monticola, and C. malayana) from Peninsular Malaysia. Functional data geometric morphometrics (FDGM) for 2D landmark data is introduced and its performance is compared with classical geometric morphometrics (GM). The FDGM approach converts 2D landmark data into continuous curves, which are then represented as linear combinations of basis functions. The landmark data was obtained from 89 crania of shrew specimens based on three craniodental views (dorsal, jaw, and lateral). Principal component analysis and linear discriminant analysis were applied to both GM and FDGM methods to classify the three shrew species. This study also compared four machine learning approaches (naïve Bayes, support vector machine, random forest, and generalised linear model) using predicted PC scores obtained from both methods (a combination of all three craniodental views and individual views). The analyses favoured FDGM and the dorsal view was the best view for distinguishing the three species.

Profiling biomechanical abilities during sprint front-crawl swimming using IMU and functional clustering of variabilities.

This study aims to profile biomechanical abilities during sprint front crawl by identifying technical stroke characteristics, in light of performance level. Ninety-one recreational to world-class swimmers equipped with a sacrum-worn IMU performed 25 m all-out. Intra and inter-cyclic 3D kinematical variabilities were clustered using a functional double partition model. Clusters were analysed according to (1) swimming technique using continuous visualisation and discrete features (standard deviation and jerk cost) and (2) performance regarding speed and competition calibre using respectively one-way ANOVA and Chi-squared test as well as Gamma statistics. Swimmers displayed specific technical profiles of intra-cyclic (smoothy and jerky) and inter-cyclic stroke regulation (low, moderate and high repeatability) significantly discriminated by speed (p < 0.001, η2 = 0.62) and performance calibre (p < 0.001, V = 0.53). We showed that combining high levels of both kinds of variability (jerky + low repeatability) are associated with highest speed (1.86 ± 0.12 m/s) and competition calibre (ℽ = 0.75, p < 0.001). It highlights the crucial importance of variabilities combination. Technical skills might be driven by a specific alignment of stroke pattern and its associated dispersion according to the task constraints. This data-driven approach can assist eyes-based technical evaluation. Targeting the development of an explosive swimming style with a high level of body stability should be considered during training of sprinters.

Instrumental variable estimation for functional concurrent regression models.

In this work we propose a functional concurrent regression model to estimate labor supply elasticities over the years 1988 through 2014 using Current Population Survey data. Assuming, as is common, that individuals' wages are endogenous, we introduce instrumental variables in a two-stage least squares approach to estimate the desired labor supply elasticities. Furthermore, we tailor our estimation method to sparse functional data. Though recent work has incorporated instrumental variables into other functional regression models, to our knowledge this has not yet been done in the functional concurrent regression model, and most existing literature is not suited for sparse functional data. We show through simulations that this two-stage least squares approach greatly eliminates the bias introduced by a naive model (i.e. one that does not acknowledge endogeneity) and produces accurate coefficient estimates for moderate sample sizes.

Robust scalar-on-function partial quantile regression.

Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). This is because the influence function of the regression quantiles is bounded in the response variable but unbounded in the predictor space. The leverage points may alter the eigenstructure of the predictor matrix, leading to poor estimation and prediction results. This study proposes a robust procedure to estimate the model parameters in the scalar-on-function quantile regression method and produce reliable predictions in the presence of both outliers and leverage points. The proposed method is based on a functional partial quantile regression procedure. We propose a weighted partial quantile covariance to obtain functional partial quantile components of the scalar-on-function quantile regression model. After the decomposition, the model parameters are estimated via a weighted loss function, where the robustness is obtained by iteratively reweighting the partial quantile components. The estimation and prediction performance of the proposed method is evaluated by a series of Monte-Carlo experiments and an empirical data example. The results are compared favorably with several existing methods. The method is implemented in an R package robfpqr.

Multilevel functional data analysis modeling of human glucose response to meal intake.

Glucose meal response information collected via Continuous Glucose Monitoring (CGM) is relevant to the assessment of individual metabolic status and the support of personalized diet prescriptions. However, the complexity of the data produced by CGM monitors pushes the limits of existing analytic methods. CGM data often exhibits substantial within-person variability and has a natural multilevel structure. This research is motivated by the analysis of CGM data from individuals without diabetes in the AEGIS study. The dataset includes detailed information on meal timing and nutrition for each individual over different days. The primary focus of this study is to examine CGM glucose responses following patients' meals and explore the time-dependent associations with dietary and patient characteristics. Motivated by this problem, we propose a new analytical framework based on multilevel functional models, including a new functional mixed R-square coefficient. The use of these models illustrates 3 key points: (i) The importance of analyzing glucose responses across the entire functional domain when making diet recommendations; (ii) The differential metabolic responses between normoglycemic and prediabetic patients, particularly with regards to lipid intake; (iii) The importance of including random, person-level effects when modelling this scientific problem.

Perspectives on the future of host-microbe biology from the Council on Microbial Sciences of the American Society for Microbiology.

Host-microbe biology (HMB) stands on the cusp of redefinition, challenging conventional paradigms to instead embrace a more holistic understanding of the microbial sciences. The American Society for Microbiology (ASM) Council on Microbial Sciences hosted a virtual retreat in 2023 to identify the future of the HMB field and innovations needed to advance the microbial sciences. The retreat presentations and discussions collectively emphasized the interconnectedness of microbes and their profound influence on humans, animals, and environmental health, as well as the need to broaden perspectives to fully embrace the complexity of these interactions. To advance HMB research, microbial scientists would benefit from enhancing interdisciplinary and transdisciplinary research to utilize expertise in diverse fields, integrate different disciplines, and promote equity and accessibility within HMB. Data integration will be pivotal in shaping the future of HMB research by bringing together varied scientific perspectives, new and innovative techniques, and 'omics approaches. ASM can empower under-resourced groups with the goal of ensuring that the benefits of cutting-edge research reach every corner of the scientific community. Thus, ASM will be poised to steer HMB toward a future that champions inclusivity, innovation, and accessible scientific progress.

Testing conditional quantile independence with functional covariate.

We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer-von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the "curse of dimensionality" under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

Data-Fusion-Based Quality Enhancement for HR Measurements Collected by Wearable Sensors.

The advancements of Internet of Things (IoT) technologies have enabled the implementation of smart and wearable sensors, which can be employed to provide older adults with affordable and accessible continuous biophysiological status monitoring. The quality of such monitoring data, however, is unsatisfactory due to excessive noise induced by various disturbances, such as motion artifacts. Existing methods take advantage of summary statistics, such as mean or median values, for denoising, without taking into account the biophysiological patterns embedded in data. In this research, a functional data analysis modeling method was proposed to enhance the data quality by learning individual subjects' diurnal heart rate (HR) patterns from historical data, which were further improved by fusing newly collected data. This proposed data-fusion approach was developed based on a Bayesian inference framework. Its effectiveness was demonstrated in an HR analysis from a prospective study involving older adults residing in assisted living or home settings. The results indicate that it is imperative to conduct personalized healthcare by estimating individualized HR patterns. Furthermore, the proposed calibration method provides a more accurate (smaller mean errors) and more precise (smaller error standard deviations) HR estimation than raw HR and conventional methods, such as the mean.

Discrimination of Genetic Biomarkers of Disease through Machine-Learning-Based Hypothesis Testing of Direct SERS Spectra of DNA and RNA.

Cancer is globally a leading cause of death that would benefit from diagnostic approaches detecting it in its early stages. However, despite much research and investment, cancer early diagnosis is still underdeveloped. Owing to its high sensitivity, surface-enhanced Raman spectroscopy (SERS)-based detection of biomarkers has attracted growing interest in this area. Oligonucleotides are an important type of genetic biomarkers as their alterations can be linked to the disease prior to symptom onset. We propose a machine-learning (ML)-enabled framework to analyze complex direct SERS spectra of short, single-stranded DNA and RNA targets to identify relevant mutations occurring in genetic biomarkers, which are key disease indicators. First, by employing ad hoc-synthesized colloidal silver nanoparticles as SERS substrates, we analyze single-base mutations in ssDNA and RNA sequences using a direct SERS-sensing approach. Then, an ML-based hypothesis test is proposed to identify these changes and differentiate the mutated sequences from the corresponding native ones. Rooted in "functional data analysis," this ML approach fully leverages the rich information and dependencies within SERS spectral data for improved modeling and detection capability. Tested on a large set of DNA and RNA SERS data, including from miR-21 (a known cancer miRNA biomarker), our approach is shown to accurately differentiate SERS spectra obtained from different oligonucleotides, outperforming various data-driven methods across several performance metrics, including accuracy, sensitivity, specificity, and F1-scores. Hence, this work represents a step forward in the development of the combined use of SERS and ML as effective methods for disease diagnosis with real applicability in the clinic.

Utilizing the Glucose and Insulin Response Shape of an Oral Glucose Tolerance Test to Predict Dysglycemia in Children with Overweight and Obesity, Ages 8-18 Years.

Common dysglycemia measurements including fasting plasma glucose (FPG), oral glucose tolerance test (OGTT)-derived 2 h plasma glucose, and hemoglobin A1c (HbA1c) have limitations for children. Dynamic OGTT glucose and insulin responses may better reflect underlying physiology. This analysis assessed glucose and insulin curve shapes utilizing classifications-biphasic, monophasic, or monotonically increasing-and functional principal components (FPCs) to predict future dysglycemia. The prospective cohort included 671 participants with no previous diabetes diagnosis (BMI percentile ≥ 85th, 8-18 years old); 193 returned for follow-up (median 14.5 months). Blood was collected every 30 min during the 2 h OGTT. Functional data analysis was performed on curves summarizing glucose and insulin responses. FPCs described variation in curve height (FPC1), time of peak (FPC2), and oscillation (FPC3). At baseline, both glucose and insulin FPC1 were significantly correlated with BMI percentile (Spearman correlation r = 0.22 and 0.48), triglycerides (r = 0.30 and 0.39), and HbA1c (r = 0.25 and 0.17). In longitudinal logistic regression analyses, glucose and insulin FPCs predicted future dysglycemia (AUC = 0.80) better than shape classifications (AUC = 0.69), HbA1c (AUC = 0.72), or FPG (AUC = 0.50). Further research should evaluate the utility of FPCs to predict metabolic diseases.

The relationship between joint kinematic patterns during single-leg drop landing and perceived instability in individuals with chronic ankle instability.

BACKGROUND: Perceived instability is a primary symptom among individuals with chronic ankle instability. However, the relationship between joint kinematics during landing remains unclear. Therefore, we investigated the relationships between landing kinematics and perceived instability in individuals with chronic ankle instability. METHODS: In 32 individuals with chronic ankle instability, we recorded ankle, knee, and hip joint angles during a single-leg drop landing. Joint angle waveforms during 200 ms before and after initial contact were summarized into single values using two methods: peak joint angles and principal component scores via principal component analysis. Using Spearman's rank correlation coefficient (ρ), we examined the relationships of peak joint angles and principal component scores with the Cumberland Ankle Instability Tool score, with a lower score indicating a greater perceived instability (α = 0.05). FINDINGS: The second principal component scores of ankle angle in the horizontal and sagittal planes significantly correlated with the Cumberland Ankle Instability Tool score (Horizontal: ρ = 0.507, P = 0.003; Sagittal: ρ = -0.359, P = 0.044). These scores indicated the differences in the magnitude of angles before and after landing. Significant correlations indicated a greater perceived instability correlated with smaller internal rotation and plantarflexion before landing and smaller external rotation and dorsiflexion after landing. In contrast, no peak joint angles correlated with the Cumberland Ankle Instability Tool score (P > 0.05). INTERPRETATION: In individuals with chronic ankle instability, ankle movements during landing associated with perceived instability may be a protective strategy before landing and potentially cause ankle instability after landing.

Strategies for knee stabilising and pivot-shift avoidance in a step-down and cross-over task observed sub-acutely after anterior cruciate ligament reconstruction.

BACKGROUND: Individuals with a recent anterior cruciate ligament reconstruction may demonstrate an altered movement strategy for protecting the knee and maintaining stability. Altered knee movement might lead to abnormal intra-articular load, potentially contributing to early knee osteoarthritis onset. A protective strategy may be particularly evident during active tasks that induce a pivot-shift manoeuvre, such as a step-down and cross-over task. In this study, we investigated whether knee joint mechanics and muscle activity differed between participants early (∼3 months) following reconstruction (n = 35) to uninjured controls (n = 35) during a step-down and cross-over task with a 45° change-of-direction. METHODS: We used motion capture, force plates and surface electromyography to compare time-normalised curves of sagittal and transverse-plane knee mechanics and muscle activity during the cross-over phase between groups using functional t-tests. We also compared knee mechanics between sides within the injured group and compared discrete outcomes describing the cross-over phase between groups. FINDINGS: Compared to controls, the injured participants had greater knee flexion angle and moment, lower internal rotation moment, more preparatory foot rotation of the pivoting leg, a smaller cross-over angle, and a longer cross-over phase for both the injured and uninjured sides. The injured leg also had greater biceps femoris and vastus medialis muscle activity compared to controls and different knee mechanics than the uninjured leg. INTERPRETATION: Individuals with anterior cruciate ligament reconstruction showed a knee-stabilising and pivot-shift avoidance strategy for both legs early in rehabilitation. These results may reflect an altered motor representation and motivate considerations early in rehabilitation.

A Study of Pupil Response to Light as a Digital Biomarker of Recent Cannabis Use.

Introduction: Given the traffic safety and occupational injury prevention implications associated with cannabis impairment, there is a need for objective and validated measures of recent cannabis use. Pupillary light response may offer an approach for detection. Method: Eighty-four participants (mean age: 32, 42% female) with daily, occasional, and no-use cannabis use histories participated in pupillary light response tests before and after smoking cannabis ad libitum or relaxing for 15 min (no use). The impact of recent cannabis consumption on trajectories of the pupillary light response was modeled using functional data analysis tools. Logistic regression models for detecting recent cannabis use were compared, and average pupil trajectories across cannabis use groups and times since light test administration were estimated. Results: Models revealed small, significant differences in pupil response to light after cannabis use comparing the occasional use group to the no-use control group, and similar statistically significant differences in pupil response patterns comparing the daily use group to the no-use comparison group. Trajectories of pupillary light response estimated using functional data analysis found that acute cannabis smoking was associated with less initial and sustained pupil constriction compared to no cannabis smoking. Conclusion: These analyses show the promise of pairing pupillary light response and functional data analysis methods to assess recent cannabis use.

Predicting Driver's mental workload using physiological signals: A functional data analysis approach.

This study investigates the impact of advanced driver-assistance systems on drivers' mental workload. Using a combination of physiological signals including ECG, EMG, EDA, EEG (af4 and fc6 channels from the theta band), and eye diameter data, this study aims to predict and categorize drivers' mental workload into low, adequate, and high levels. Data were collected from five different driving situations with varying cognitive demands. A functional linear regression model was employed for prediction, and the accuracy rate was calculated. Among the 31 tested combinations of physiological variables, 9 combinations achieved the highest accuracy result of 90%. These results highlight the potential benefits of utilizing raw physiological signal data and employing functional data analysis methods to understand and assess driver mental workload. The findings of this study have implications for the design and improvement of driver-assistance systems to optimize safety and performance.

Functional support vector machine.

Linear and generalized linear scalar-on-function modeling have been commonly used to understand the relationship between a scalar response variable (e.g. continuous, binary outcomes) and functional predictors. Such techniques are sensitive to model misspecification when the relationship between the response variable and the functional predictors is complex. On the other hand, support vector machines (SVMs) are among the most robust prediction models but do not take account of the high correlations between repeated measurements and cannot be used for irregular data. In this work, we propose a novel method to integrate functional principal component analysis with SVM techniques for classification and regression to account for the continuous nature of functional data and the nonlinear relationship between the scalar response variable and the functional predictors. We demonstrate the performance of our method through extensive simulation experiments and two real data applications: the classification of alcoholics using electroencephalography signals and the prediction of glucobrassicin concentration using near-infrared reflectance spectroscopy. Our methods especially have more advantages when the measurement errors in functional predictors are relatively large.

A scalar-on-quantile-function approach for estimating short-term health effects of environmental exposures.

Environmental epidemiologic studies routinely utilize aggregate health outcomes to estimate effects of short-term (eg, daily) exposures that are available at increasingly fine spatial resolutions. However, areal averages are typically used to derive population-level exposure, which cannot capture the spatial variation and individual heterogeneity in exposures that may occur within the spatial and temporal unit of interest (eg, within a day or ZIP code). We propose a general modeling approach to incorporate within-unit exposure heterogeneity in health analyses via exposure quantile functions. Furthermore, by viewing the exposure quantile function as a functional covariate, our approach provides additional flexibility in characterizing associations at different quantile levels. We apply the proposed approach to an analysis of air pollution and emergency department (ED) visits in Atlanta over 4 years. The analysis utilizes daily ZIP code-level distributions of personal exposures to 4 traffic-related ambient air pollutants simulated from the Stochastic Human Exposure and Dose Simulator. Our analyses find that effects of carbon monoxide on respiratory and cardiovascular disease ED visits are more pronounced with changes in lower quantiles of the population's exposure. Software for implement is provided in the R package nbRegQF.

Bayesian adaptive selection of basis functions for functional data representation.

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via the Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent variables to assign zero to some of the basis function coefficients with a positive probability. This procedure allows for an adaptive basis selection since it can determine the number of bases and which ones should be selected to represent functional data. Moreover, the proposed procedure measures the uncertainty of the selection process and can be applied to multiple curves simultaneously. The methodology developed can deal with observed curves that may differ due to experimental error and random individual differences between subjects, which one can observe in a real dataset application involving daily numbers of COVID-19 cases in Brazil. Simulation studies show the main properties of the proposed method, such as its accuracy in estimating the coefficients and the strength of the procedure to find the true set of basis functions. Despite having been developed in the context of functional data analysis, we also compared the proposed model via simulation with the well-established LASSO and Bayesian LASSO, which are methods developed for non-functional data.

Projection-based two-sample inference for sparsely observed multivariate functional data.

Modern longitudinal studies collect multiple outcomes as the primary endpoints to understand the complex dynamics of the diseases. Oftentimes, especially in clinical trials, the joint variation among the multidimensional responses plays a significant role in assessing the differential characteristics between two or more groups, rather than drawing inferences based on a single outcome. We develop a projection-based two-sample significance test to identify the population-level difference between the multivariate profiles observed under a sparse longitudinal design. The methodology is built upon widely adopted multivariate functional principal component analysis to reduce the dimension of the infinite-dimensional multi-modal functions while preserving the dynamic correlation between the components. The test applies to a wide class of (non-stationary) covariance structures of the response, and it detects a significant group difference based on a single p-value, thereby overcoming the issue of adjusting for multiple p-values that arise due to comparing the means in each of components separately. Finite-sample numerical studies demonstrate that the test maintains the type-I error, and is powerful to detect significant group differences, compared to the state-of-the-art testing procedures. The test is carried out on two significant longitudinal studies for Alzheimer's disease and Parkinson's disease (PD) patients, namely, TOMMORROW study of individuals at high risk of mild cognitive impairment to detect differences in the cognitive test scores between the pioglitazone and the placebo groups, and Azillect study to assess the efficacy of rasagiline as a potential treatment to slow down the progression of PD.