Testing homogeneity: the trouble with sparse functional data.

Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.

Trajectories of brain volumes in young children are associated with maternal education.

Brain growth in early childhood is reflected in the evolution of proportional cerebrospinal fluid volumes (pCSF), grey matter (pGM), and white matter (pWM). We study brain development as reflected in the relative fractions of these three tissues for a cohort of 388 children that were longitudinally followed between the ages of 18 and 96 months. We introduce statistical methodology (Riemannian Principal Analysis through Conditional Expectation, RPACE) that addresses major challenges that are of general interest for the analysis of longitudinal neuroimaging data, including the sparsity of the longitudinal observations over time and the compositional structure of the relative brain volumes. Applying the RPACE methodology, we find that longitudinal growth as reflected by tissue composition differs significantly for children of mothers with higher and lower maternal education levels.

Network evolution of regional brain volumes in young children reflects neurocognitive scores and mother's education.

The maturation of regional brain volumes from birth to preadolescence is a critical developmental process that underlies emerging brain structural connectivity and function. Regulated by genes and environment, the coordinated growth of different brain regions plays an important role in cognitive development. Current knowledge about structural network evolution is limited, partly due to the sparse and irregular nature of most longitudinal neuroimaging data. In particular, it is unknown how factors such as mother's education or sex of the child impact the structural network evolution. To address this issue, we propose a method to construct evolving structural networks and study how the evolving connections among brain regions as reflected at the network level are related to maternal education and biological sex of the child and also how they are associated with cognitive development. Our methodology is based on applying local Fréchet regression to longitudinal neuroimaging data acquired from the RESONANCE cohort, a cohort of healthy children (245 females and 309 males) ranging in age from 9 weeks to 10 years. Our findings reveal that sustained highly coordinated volume growth across brain regions is associated with lower maternal education and lower cognitive development. This suggests that higher neurocognitive performance levels in children are associated with increased variability of regional growth patterns as children age.

Mean and Covariance Estimation for Functional Snippets.

We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation of the covariance function for functional snippets is challenging since information for the far off-diagonal regions of the covariance structure is completely missing. We address this difficulty by decomposing the covariance function into a variance function component and a correlation function component. The variance function can be effectively estimated nonparametrically, while the correlation part is modeled parametrically, possibly with an increasing number of parameters, to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this hybrid strategy is effective. In addition, we propose a new estimator for the variance of measurement errors and analyze its asymptotic properties. This estimator is required for the estimation of the variance function from noisy measurements.

Modeling sparse longitudinal data in early neurodevelopment.

Early childhood is a period marked by rapid brain growth accompanied by cognitive and motor development. However, it remains unclear how early developmental skills relate to neuroanatomical growth across time with no growth quantile trajectories of typical brain development currently available to place and compare individual neuroanatomical development. Even though longitudinal neuroimaging data have become more common, they are often sparse, making dynamic analyses at subject level a challenging task. Using the Principal Analysis through Conditional Expectation (PACE) approach geared towards sparse longitudinal data, we investigate the evolution of gray matter, white matter and cerebrospinal fluid volumes in a cohort of 446 children between the ages of 1 and 120 months. For each child, we calculate their dynamic age-varying association between the growing brain and scores that assess cognitive functioning, applying the functional varying coefficient model. Using local Fréchet regression, we construct age-varying growth percentiles to reveal the evolution of brain development across the population. To further demonstrate its utility, we apply PACE to predict individual trajectories of brain development.

Time dynamics of COVID-19.

We apply tools from functional data analysis to model cumulative trajectories of COVID-19 cases across countries, establishing a framework for quantifying and comparing cases and deaths across countries longitudinally. It emerges that a country's trajectory during an initial first month "priming period" largely determines how the situation unfolds subsequently. We also propose a method for forecasting case counts, which takes advantage of the common, latent information in the entire sample of curves, instead of just the history of a single country. Our framework facilitates to quantify the effects of demographic covariates and social mobility on doubling rates and case fatality rates through a time-varying regression model. Decreased workplace mobility is associated with lower doubling rates with a roughly 2 week delay, and case fatality rates exhibit a positive feedback pattern.

Mountaineers on Mount Everest: Effects of age, sex, experience, and crowding on rates of success and death.

Mount Everest is an extreme environment for humans. Nevertheless, hundreds of mountaineers attempt to summit Everest each year. In a previous study we analyzed interview data for all climbers (2,211) making their first attempt on Everest during 1990-2005. Probabilities of summiting were similar for men and women, declined progressively for climbers about 40 and older, but were elevated for climbers with experience climbing in Nepal. Probabilities of dying were also similar for men and women, increased for climbers about 60 and older (especially for the few that had summited), and were independent of experience. Since 2005, many more climbers (3,620) have attempted Everest. Here our primary goal is to quantify recent patterns of success and death and to evaluate changes over time. Also, we investigate whether patterns relate to key socio-demographic covariates (age, sex, host country, prior experience). Recent climbers were more diverse both in gender (women = 14.6% vs. 9.1% for 1990-2005) and in age (climbers ≥ 40 = 54.1% vs. 38.7%). Strikingly, recent climbers of both sexes were almost twice as likely to summit-and slightly less likely to die-than were comparable climbers in the previous survey. Temporal shifts may reflect improved weather forecasting, installation of fixed ropes on much of the route, and accumulative logistic equipment and experience. We add two new analyses. The probability of dying from illness or non-traumas (e.g., high-altitude illness, hypothermia), relative to dying from falling or from 'objective hazards' (avalanche, rock or ice fall), increased marginally with age. Recent crowding during summit bids was four-fold greater than in the prior sample, but surprisingly crowding has no evident effect on success or death during summit bids. Our results inform prospective climbers as to their current odds of success and of death, as well as inform governments of Nepal and China of the safety consequences and economic impacts of periodically debated restrictions based on climber age and experience.

Emotional EEG classification using connectivity features and convolutional neural networks.

Convolutional neural networks (CNNs) are widely used to recognize the user's state through electroencephalography (EEG) signals. In the previous studies, the EEG signals are usually fed into the CNNs in the form of high-dimensional raw data. However, this approach makes it difficult to exploit the brain connectivity information that can be effective in describing the functional brain network and estimating the perceptual state of the user. We introduce a new classification system that utilizes brain connectivity with a CNN and validate its effectiveness via the emotional video classification by using three different types of connectivity measures. Furthermore, two data-driven methods to construct the connectivity matrix are proposed to maximize classification performance. Further analysis reveals that the level of concentration of the brain connectivity related to the emotional property of the target video is correlated with classification performance.

FMEM: Functional Mixed Effects Models for Longitudinal Functional Responses.

The aim of this paper is to conduct a systematic and theoretical analysis of estimation and inference for a class of functional mixed effects models (FMEM). Such FMEMs consist of fixed effects that characterize the association between longitudinal functional responses and covariates of interest and random effects that capture the spatial-temporal correlations of longitudinal functional responses. We propose local linear estimates of refined fixed effect functions and establish their weak convergence along with a simultaneous confidence band for each fixed-effect function. We propose a global test for the linear hypotheses of varying coefficient functions and derive the associated asymptotic distribution under the null hypothesis and the asymptotic power under the alternative hypothesis are derived. We also establish the convergence rates of the estimated spatial-temporal covariance operators and their associated eigenvalues and eigenfunctions. We conduct extensive simulations and apply our method to a white-matter fiber data set from a national database for autism research to examine the finite-sample performance of the proposed estimation and inference procedures.

A New Approach for Functional Connectivity via Alignment of Blood Oxygen Level-Dependent Signals.

Due to technological advances, spatially indexed objects, such as blood oxygen level-dependent time series or electroencephalography data, are commonly observed across different scientific disciplines. Such object data are typically high dimensional and therefore challenging to handle. We propose a new approach for spatially indexed object data by mapping their spatial locations to a targeted one-dimensional interval so objects that are similar are placed near each other on the new target space. The proposed alignment not only provides a visualization tool for such complex object data but also facilitates a new way to study brain functional connectivity. Specifically, we introduce a new concept of path length to quantify the functional connectivity and a new community detection method. The advantages of the proposed methods are illustrated by simulations and in a study of functional connectivity for Alzheimer's disease.

Longitudinal associations between white matter maturation and cognitive development across early childhood.

From birth to 5 years of age, brain structure matures and evolves alongside emerging cognitive and behavioral abilities. In relating concurrent cognitive functioning and measures of brain structure, a major challenge that has impeded prior investigation of their time-dynamic relationships is the sparse and irregular nature of most longitudinal neuroimaging data. We demonstrate how this problem can be addressed by applying functional concurrent regression models (FCRMs) to longitudinal cognitive and neuroimaging data. The application of FCRM in neuroimaging is illustrated with longitudinal neuroimaging and cognitive data acquired from a large cohort (n = 210) of healthy children, 2-48 months of age. Quantifying white matter myelination by using myelin water fraction (MWF) as imaging metric derived from MRI scans, application of this methodology reveals an early period (200-500 days) during which whole brain and regional white matter structure, as quantified by MWF, is positively associated with cognitive ability, while we found no such association for whole brain white matter volume. Adjusting for baseline covariates including socioeconomic status as measured by maternal education (SES-ME), infant feeding practice, gender, and birth weight further reveals an increasing association between SES-ME and cognitive development with child age. These results shed new light on the emerging patterns of brain and cognitive development, indicating that FCRM provides a useful tool for investigating these evolving relationships.

LCox: a tool for selecting genes related to survival outcomes using longitudinal gene expression data.

Longitudinal genomics data and survival outcome are common in biomedical studies, where the genomics data are often of high dimension. It is of great interest to select informative longitudinal biomarkers (e.g. genes) related to the survival outcome. In this paper, we develop a computationally efficient tool, LCox, for selecting informative biomarkers related to the survival outcome using the longitudinal genomics data. LCox is powerful to detect different forms of dependence between the longitudinal biomarkers and the survival outcome. We show that LCox has improved performance compared to existing methods through extensive simulation studies. In addition, by applying LCox to a dataset of patients with idiopathic pulmonary fibrosis, we are able to identify biologically meaningful genes while all other methods fail to make any discovery. An R package to perform LCox is freely available at https://CRAN.R-project.org/package=LCox.

Age-dynamic networks and functional correlation for early white matter myelination.

The maturation of the myelinated white matter throughout childhood is a critical developmental process that underlies emerging connectivity and brain function. In response to genetic influences and neuronal activities, myelination helps establish the mature neural networks that support cognitive and behavioral skills. The emergence and refinement of brain networks, traditionally investigated using functional imaging data, can also be interrogated using longitudinal structural imaging data. However, few studies of structural network development throughout infancy and early childhood have been presented, likely owing to the sparse and irregular nature of most longitudinal neuroimaging data, which complicates dynamic analysis. Here, we overcome this limitation and investigate through concurrent correlation the co-development of white matter myelination and volume, and structural network development of white matter myelination between brain regions as a function of age, using statistically well-supported methods. We show that the concurrent correlation of white matter myelination and volume is overall positive and reaches a peak at 580 days. Brain regions are found to differ in overall magnitudes and patterns of time-varying association throughout early childhood. We introduce time-dynamic developmental networks based on temporal similarity of association patterns in the levels of myelination across brain regions. These networks reflect groups of brain regions that share similar patterns of evolving intra-regional connectivity, as evidenced by levels of myelination, are biologically interpretable and provide novel visualizations of brain development. Comparing the constructed networks between different maternal education groups, we found that children with higher and lower maternal education differ significantly in the overall magnitude of the time-dynamic correlations.

Lysozyme-rich milk mitigates effects of malnutrition in a pig model of malnutrition and infection.

Malnutrition remains a leading contributor to the morbidity and mortality of children under the age of 5 years and can weaken the immune system and increase the severity of concurrent infections. Livestock milk with the protective properties of human milk is a potential therapeutic to modulate intestinal microbiota and improve outcomes. The aim of this study was to develop an infection model of childhood malnutrition in the pig to investigate the clinical, intestinal and microbiota changes associated with malnutrition and enterotoxigenic Escherichia coli (ETEC) infection and to test the ability of goat milk and milk from genetically engineered goats expressing the antimicrobial human lysozyme (hLZ) milk to mitigate these effects. Pigs were weaned onto a protein-energy-restricted diet and after 3 weeks were supplemented daily with goat, hLZ or no milk for a further 2 weeks and then challenged with ETEC. The restricted diet enriched faecal microbiota in Proteobacteria as seen in stunted children. Before infection, hLZ milk supplementation improved barrier function and villous height to a greater extent than goat milk. Both goat and hLZ milk enriched for taxa (Ruminococcaceae) associated with weight gain. Post-ETEC infection, pigs supplemented with hLZ milk weighed more, had improved Z-scores, longer villi and showed more stable bacterial populations during ETEC challenge than both the goat and no milk groups. This model of childhood disease was developed to test the confounding effects of malnutrition and infection and demonstrated the potential use of hLZ goat milk to mitigate the impacts of malnutrition and infection.

Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development.

For longitudinal studies with multivariate observations, we propose statistical methods to identify clusters of archetypal subjects by using techniques from functional data analysis and to relate longitudinal patterns to outcomes. We demonstrate how this approach can be applied to examine associations between multiple time-varying exposures and subsequent health outcomes, where the former are recorded sparsely and irregularly in time, with emphasis on the utility of multiple longitudinal observations in the framework of dimension reduction techniques. In applications to children's growth data, we investigate archetypes of infant growth patterns and identify subgroups that are related to cognitive development in childhood. Specifically, "Stunting" and "Faltering" time-dynamic patterns of head circumference, body length and weight in the first 12 months are associated with lower levels of long-term cognitive development in comparison to "Generally Large" and "Catch-up" growth. Our findings provide evidence for the statistical association between multivariate growth patterns in infancy and long-term cognitive development.

Young Pigs Consuming Lysozyme Transgenic Goat Milk Are Protected from Clinical Symptoms of Enterotoxigenic Escherichia coli Infection.

Background: Diarrheal diseases in infancy and childhood are responsible for substantial morbidity and mortality in developing nations. Lysozyme, an antimicrobial component of human milk, is thought to play a role in establishing a healthy intestinal microbiota and immune system. Consumption of breast milk has been shown to prevent intestinal infections and is a recommended treatment for infants with diarrhea.Objective: This study aimed to examine the ability of lysozyme-rich goat milk to prevent intestinal infection.Methods: Six-week-old Hampshire-Yorkshire pigs were assigned to treatment groups balanced for weight, sex, and litter and were fed milk from nontransgenic control goats (GM group) or human lysozyme transgenic goats (hLZM group) for 2 wk before they were challenged with porcine-specific enterotoxigenic Escherichia coli (ETEC). Fecal consistency, complete blood counts, intestinal histology, and microbial populations were evaluated.Results: Pigs in the hLZM group had less severe diarrhea than did GM pigs at 24 and 48 h after ETEC infection (P = 0.01 and 0.05, respectively), indicating a less severe clinical disease state. Relative to baseline, postmilk hLZM pigs had 19.9% and 137% enrichment in fecal Bacteroidetes (P = 0.028) and Paraprevotellaceae (P = 0.003), respectively, and a 93.8% reduction in Enterobacteriaceae (P = 0.007), whereas GM pigs had a 60.9% decrease in Lactobacillales (P = 0.003) and an 83.3% enrichment in Burkholderiales (P = 0.010). After ETEC infection, hLZM pigs tended to have lower amounts (68.7% less) of fecal Enterobacteriaceae than did GM pigs (P = 0.058). There were 83.1% fewer bacteria translocated into the mesenteric lymph nodes of hLZM pigs than into those of GM pigs (P = 0.039), and hLZM pigs had 34% lower mucin 1 and 61% higher tumor necrosis factor-α expression in the ileum than did GM pigs (P = 0.046 and 0.034, respectively).Conclusion: Results of this study indicate that human lysozyme milk consumption before and during ETEC infection has a positive effect on clinical disease, intestinal mucosa, and gut microbiota in young pigs.

Diet Shapes Mortality Response to Trauma in Old Tephritid Fruit Flies.

Despite the importance of trauma in healthspan and lifespan in humans as well as in non-human species, with one important exception the literature in both gerontology and ecology contains virtually no experimental demographic studies concerned with trauma in any species. We used dietary manipulation [full diet (F) versus sugar-only (S)] to produce four levels of frailty in 55-day old tephritid fruit flies (Anastrepha ludens) that were then subject to the trauma of cage transfer stress (n = 900/sex in each of the 4 treatments). The key results included the following: (1) there is a trauma effect caused by the transfer that depends on previous diet before transfer, new diet after transfer and gender of the fly; (2) males are more vulnerable than females; (3) if initial diet was F, flies are relatively immune against the trauma, and the subsequent diet (F or S) does not matter; (4) however if initial diet was S, then the effect of the trauma depends largely on the diet after the transfer; (5) flies transferred from S to F diets do very well in terms of remaining longevity (i.e. greatest remaining longevity), while flies transferred from S to S diet do poorly (i.e. shortest remaining longevity). We discuss both the strengths and weaknesses of this study and implications of the results.

A Functional Approach to Deconvolve Dynamic Neuroimaging Data.

Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire three-dimensional volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both one-dimensional functions and 2D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.

Dynamical correlation: A new method for quantifying synchrony with multivariate intensive longitudinal data.

In this article, we introduce dynamical correlation, a new method for quantifying synchrony between 2 variables with intensive longitudinal data. Dynamical correlation is a functional data analysis technique developed to measure the similarity of 2 curves. It has advantages over existing methods for studying synchrony, such as multilevel modeling. In particular, it is a nonparametric approach that does not require a prespecified functional form, and it places no assumption on homogeneity of the sample. Dynamical correlation can be easily estimated with irregularly spaced observations and tested to draw population-level inferences. We illustrate this flexible statistical technique with a simulation example and empirical data from an experiment examining interpersonal physiological synchrony between romantic partners. We discuss the advantages and limitations of the method, and how it can be extended and applied in psychological research. We also provide a set of R code for other researchers to estimate and test for dynamical correlation. (PsycINFO Database Record

SEMIPARAMETRIC EFFICIENT ESTIMATION FOR SHARED-FRAILTY MODELS WITH DOUBLY-CENSORED CLUSTERED DATA.

In this paper, we investigate frailty models for clustered survival data that are subject to both left- and right-censoring, termed "doubly-censored data". This model extends current survival literature by broadening the application of frailty models from right-censoring to a more complicated situation with additional left censoring. Our approach is motivated by a recent Hepatitis B study where the sample consists of families. We adopt a likelihood approach that aims at the nonparametric maximum likelihood estimators (NPMLE). A new algorithm is proposed, which not only works well for clustered data but also improve over existing algorithm for independent and doubly-censored data, a special case when the frailty variable is a constant equal to one. This special case is well known to be a computational challenge due to the left censoring feature of the data. The new algorithm not only resolves this challenge but also accommodate the additional frailty variable effectively. Asymptotic properties of the NPMLE are established along with semi-parametric efficiency of the NPMLE for the finite-dimensional parameters. The consistency of Bootstrap estimators for the standard errors of the NPMLE is also discussed. We conducted some simulations to illustrate the numerical performance and robustness of the proposed algorithm, which is also applied to the Hepatitis B data.