Single-index models with functional connectivity network predictors.

Functional connectivity is defined as the undirected association between two or more functional magnetic resonance imaging (fMRI) time series. Increasingly, subject-level functional connectivity data have been used to predict and classify clinical outcomes and subject attributes. We propose a single-index model wherein response variables and sparse functional connectivity network valued predictors are linked by an unspecified smooth function in order to accommodate potentially nonlinear relationships. We exploit the network structure of functional connectivity by imposing meaningful sparsity constraints, which lead not only to the identification of association of interactions between regions with the response but also the assessment of whether or not the functional connectivity associated with a brain region is related to the response variable. We demonstrate the effectiveness of the proposed model in simulation studies and in an application to a resting-state fMRI data set from the Human Connectome Project to model fluid intelligence and sex and to identify predictive links between brain regions.

Two-stage linked component analysis for joint decomposition of multiple biologically related data sets.

Integrative analysis of multiple data sets has the potential of fully leveraging the vast amount of high throughput biological data being generated. In particular such analysis will be powerful in making inference from publicly available collections of genetic, transcriptomic and epigenetic data sets which are designed to study shared biological processes, but which vary in their target measurements, biological variation, unwanted noise, and batch variation. Thus, methods that enable the joint analysis of multiple data sets are needed to gain insights into shared biological processes that would otherwise be hidden by unwanted intra-data set variation. Here, we propose a method called two-stage linked component analysis (2s-LCA) to jointly decompose multiple biologically related experimental data sets with biological and technological relationships that can be structured into the decomposition. The consistency of the proposed method is established and its empirical performance is evaluated via simulation studies. We apply 2s-LCA to jointly analyze four data sets focused on human brain development and identify meaningful patterns of gene expression in human neurogenesis that have shared structure across these data sets.

Latent factor model for multivariate functional data.

For multivariate functional data, a functional latent factor model is proposed, extending the traditional latent factor model for multivariate data. The proposed model uses unobserved stochastic processes to induce the dependence among the different functions, and thus, for a large number of functions, may provide a more parsimonious and interpretable characterization of the otherwise complex dependencies between the functions. Sufficient conditions are provided to establish the identifiability of the proposed model. The performance of the proposed model is assessed through simulation studies and an application to electroencephalography data.

Functional data analysis for longitudinal data with informative observation times.

In functional data analysis for longitudinal data, the observation process is typically assumed to be noninformative, which is often violated in real applications. Thus, methods that fail to account for the dependence between observation times and longitudinal outcomes may result in biased estimation. For longitudinal data with informative observation times, we find that under a general class of shared random effect models, a commonly used functional data method may lead to inconsistent model estimation while another functional data method results in consistent and even rate-optimal estimation. Indeed, we show that the mean function can be estimated appropriately via penalized splines and that the covariance function can be estimated appropriately via penalized tensor-product splines, both with specific choices of parameters. For the proposed method, theoretical results are provided, and simulation studies and a real data analysis are conducted to demonstrate its performance.

Multivariate functional mixed model with MRI data: An application to Alzheimer's disease.

Alzheimer's Disease (AD) is the leading cause of dementia and impairment in various domains. Recent AD studies, (ie, Alzheimer's Disease Neuroimaging Initiative (ADNI) study), collect multimodal data, including longitudinal neurological assessments and magnetic resonance imaging (MRI) data, to better study the disease progression. Adopting early interventions is essential to slow AD progression for subjects with mild cognitive impairment (MCI). It is of particular interest to develop an AD predictive model that leverages multimodal data and provides accurate personalized predictions. In this article, we propose a multivariate functional mixed model with MRI data (MFMM-MRI) that simultaneously models longitudinal neurological assessments, baseline MRI data, and the survival outcome (ie, dementia onset) for subjects with MCI at baseline. Two functional forms (the random-effects model and instantaneous model) linking the longitudinal and survival process are investigated. We use Markov Chain Monte Carlo (MCMC) method based on No-U-Turn Sampling (NUTS) algorithm to obtain posterior samples. We develop a dynamic prediction framework that provides accurate personalized predictions of longitudinal trajectories and survival probability. We apply MFMM-MRI to the ADNI study and identify significant associations among longitudinal outcomes, MRI data, and the risk of dementia onset. The instantaneous model with voxels from the whole brain has the best prediction performance among all candidate models. The simulation study supports the validity of the estimation and dynamic prediction method.

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.

Joint model for survival and multivariate sparse functional data with application to a study of Alzheimer's Disease.

Studies of Alzheimer's disease (AD) often collect multiple longitudinal clinical outcomes, which are correlated and predictive of AD progression. It is of great scientific interest to investigate the association between the outcomes and time to AD onset. We model the multiple longitudinal outcomes as multivariate sparse functional data and propose a functional joint model linking multivariate functional data to event time data. In particular, we propose a multivariate functional mixed model to identify the shared progression pattern and outcome-specific progression patterns of the outcomes, which enables more interpretable modeling of associations between outcomes and AD onset. The proposed method is applied to the Alzheimer's Disease Neuroimaging Initiative study (ADNI) and the functional joint model sheds new light on inference of five longitudinal outcomes and their associations with AD onset. Simulation studies also confirm the validity of the proposed model. Data used in preparation of this article were obtained from the ADNI database.

Fixed-effects inference and tests of correlation for longitudinal functional data.

We propose an inferential framework for fixed effects in longitudinal functional models and introduce tests for the correlation structures induced by the longitudinal sampling procedure. The framework provides a natural extension of standard longitudinal correlation models for scalar observations to functional observations. Using simulation studies, we compare fixed effects estimation under correctly and incorrectly specified correlation structures and also test the longitudinal correlation structure. Finally, we apply the proposed methods to a longitudinal functional dataset on physical activity. The computer code for the proposed method is available at https://github.com/rli20ST758/FILF.

Fetal growth velocity standards from the Fetal Growth Longitudinal Study of the INTERGROWTH-21st Project.

BACKGROUND: Human growth is susceptible to damage from insults, particularly during periods of rapid growth. Identifying those periods and the normative limits that are compatible with adequate growth and development are the first key steps toward preventing impaired growth. OBJECTIVE: This study aimed to construct international fetal growth velocity increment and conditional velocity standards from 14 to 40 weeks' gestation based on the same cohort that contributed to the INTERGROWTH-21st Fetal Growth Standards. STUDY DESIGN: This study was a prospective, longitudinal study of 4321 low-risk pregnancies from 8 geographically diverse populations in the INTERGROWTH-21st Project with rigorous standardization of all study procedures, equipment, and measurements that were performed by trained ultrasonographers. Gestational age was accurately determined clinically and confirmed by ultrasound measurement of crown-rump length at <14 weeks' gestation. Thereafter, the ultrasonographers, who were masked to the values, measured the fetal head circumference, biparietal diameter, occipitofrontal diameter, abdominal circumference, and femur length in triplicate every 5 weeks (within 1 week either side) using identical ultrasound equipment at each site (4-7 scans per pregnancy). Velocity increments across a range of intervals between measures were modeled using fractional polynomial regression. RESULTS: Peak velocity was observed at a similar gestational age: 16 and 17 weeks' gestation for head circumference (12.2 mm/wk), and 16 weeks' gestation for abdominal circumference (11.8 mm/wk) and femur length (3.2 mm/wk). However, velocity growth slowed down rapidly for head circumference, biparietal diameter, occipitofrontal diameter, and femur length, with an almost linear reduction toward term that was more marked for femur length. Conversely, abdominal circumference velocity remained relatively steady throughout pregnancy. The change in velocity with gestational age was more evident for head circumference, biparietal diameter, occipitofrontal diameter, and femur length than for abdominal circumference when the change was expressed as a percentage of fetal size at 40 weeks' gestation. We have also shown how to obtain accurate conditional fetal velocity based on our previous methodological work. CONCLUSION: The fetal skeleton and abdomen have different velocity growth patterns during intrauterine life. Accordingly, we have produced international Fetal Growth Velocity Increment Standards to complement the INTERGROWTH-21st Fetal Growth Standards so as to monitor fetal well-being comprehensively worldwide. Fetal growth velocity curves may be valuable if one wants to study the pathophysiology of fetal growth. We provide an application that can be used easily in clinical practice to evaluate changes in fetal size as conditional velocity for a more refined assessment of fetal growth than is possible at present (https://lxiao5.shinyapps.io/fetal_growth/). The application is freely available with the other INTERGROWTH-21st tools at https://intergrowth21.tghn.org/standards-tools/.

Cycloartane-type triterpenoids from the root of Astragalus membranaceus var. mongholicus.

Three new (1-3) and 11 known (4-14) cycloartane-type triterpenoids were isolated from the root of Astragalus membranaceus var. mongholicus. Their structures were determined by spectroscopic analyses and chemical methods. Cycloartane-type triterpenoids are a class of major bioactive constituents in the root of A. membranaceus var. mongholicus, and the discovery of compounds 1-3 added new members of this kind of natural product. [Formula: see text].

Reservoir water stratification and mixing affects microbial community structure and functional community composition in a stratified drinking reservoir.

To investigate how the aquatic bacterial community of a stratified reservoir drives the evolution of water parameters, the microbial community structure and network characteristics of bacteria in a stratified reservoir were investigated using Illumina MiSeq sequencing technology. A total of 42 phyla and 689 distinct genera were identified, which showed significant seasonal variation. Additionally, stratified variations in the bacterial community strongly reflected the vertical gradient and seasonal changes in water temperature, dissolved oxygen, and nutrition concentration. Furthermore, principal coordinate analysis indicated that most microorganisms were likely influenced by changes in water stratification conditions, exhibiting significant differences during the stratification period and mixing period based on Adonis, MRPP, and Anosim. Compared to the stratification period, 123 enhanced operational taxonomic units (OTUs; 29%) and 226 depleted OTUs (52%) were identified during the mixing period. Linear discriminant analysis effect size results showed that 15 major genera were enriched in the mixing period and 10 major genera were enriched in the stratification period. Importantly, network analysis revealed that the keystone species belonged to hgcI_clade, CL500-29, Acidibacter, Paucimonas, Flavobacterium, Prochlorothrix, Xanthomonadales, Chloroflexia, Burkholderiales, OPB56, KI89A_clade, Synechococcus, Caulobacter or were unclassified. Redundancy analysis showed that temperature, dissolved oxygen, pH, chlorophyll-α, total phosphorus, nitrate, and ammonia were important factors influencing the water bacterial community and function composition, which were consistent with the results of the Mantel test analysis. Furthermore, random forest analysis showed that temperature, dissolved oxygen, ammonia, and total dissolved phosphorous were the most important variables predicting water bacterial community and function community α- and ß-diversity (P < 0.05). Overall, these results provide insight into the interactions between the microbial community and water quality evolution mechanism in Zhoucun reservoir.

Simple fixed-effects inference for complex functional models.

We propose simple inferential approaches for the fixed effects in complex functional mixed effects models. We estimate the fixed effects under the independence of functional residuals assumption and then bootstrap independent units (e.g. subjects) to conduct inference on the fixed effects parameters. Simulations show excellent coverage probability of the confidence intervals and size of tests for the fixed effects model parameters. Methods are motivated by and applied to the Baltimore Longitudinal Study of Aging, though they are applicable to other studies that collect correlated functional data.

Relay optical function and pre-construction results of a Giant Steerable Science Mirror for a thirty meter telescope.

The Giant Steerable Science Mirror (GSSM) is the tertiary mirror system of the Thirty Meter Telescope (TMT) that relays optical beams from the secondary mirror to active instruments on Nasmyth platforms. One of the key technologies involved in GSSM functions is the error budget allocation from the system engineering of TMT. A novel approach of error analysis and allocation with strong adaptability, which is based on normalized Point Source Sensitivity (PSSn), is proposed. The relay optical function including the quality of the wavefront, the rationality of the mechanism, and the stability of the light were achieved based on the proposed method. The experiments validate the proposed method.

A smoothing-based goodness-of-fit test of covariance for functional data.

Functional data methods are often applied to longitudinal data as they provide a more flexible way to capture dependence across repeated observations. However, there is no formal testing procedure to determine if functional methods are actually necessary. We propose a goodness-of-fit test for comparing parametric covariance functions against general nonparametric alternatives for both irregularly observed longitudinal data and densely observed functional data. We consider a smoothing-based test statistic and approximate its null distribution using a bootstrap procedure. We focus on testing a quadratic polynomial covariance induced by a linear mixed effects model and the method can be used to test any smooth parametric covariance function. Performance and versatility of the proposed test is illustrated through a simulation study and three data applications.

Using data from multiple studies to develop a child growth correlation matrix.

In many countries, the monitoring of child growth does not occur in a regular manner, and instead, we may have to rely on sporadic observations that are subject to substantial measurement error. In these countries, it can be difficult to identify patterns of poor growth, and faltering children may miss out on essential health interventions. The contribution of this paper is to provide a framework for pooling together multiple datasets, thus allowing us to overcome the issue of sparse data and provide improved estimates of growth. We use data from multiple longitudinal growth studies to construct a common correlation matrix that can be used in estimation and prediction of child growth. We propose a novel 2-stage approach: In stage 1, we construct a raw matrix via a set of univariate meta-analyses, and in stage 2, we smooth this raw matrix to obtain a more realistic correlation matrix. The methodology is illustrated using data from 16 child growth studies from the Bill and Melinda Gates Foundation's Healthy Birth Growth and Development knowledge integration project and identifies strong correlation for both height and weight between the ages of 4 and 12 years. We use a case study to provide an example of how this matrix can be used to help compute growth measures.

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

Many modern neuroimaging studies acquire large spatial images of the brain observed sequentially over time. Such data are often stored in the forms of matrices. To model these matrix-variate data we introduce a class of separable processes using explicit latent process modeling. To account for the size and two-way structure of the data, we extend principal component analysis to achieve dimensionality reduction at the individual level. We introduce necessary identifiability conditions for each model and develop scalable estimation procedures. The method is motivated by and applied to a functional magnetic resonance imaging study designed to analyze the relationship between pain and brain activity.

Dynamic prediction in functional concurrent regression with an application to child growth.

In many studies, it is of interest to predict the future trajectory of subjects based on their historical data, referred to as dynamic prediction. Mixed effects models have traditionally been used for dynamic prediction. However, the commonly used random intercept and slope model is often not sufficiently flexible for modeling subject-specific trajectories. In addition, there may be useful exposures/predictors of interest that are measured concurrently with the outcome, complicating dynamic prediction. To address these problems, we propose a dynamic functional concurrent regression model to handle the case where both the functional response and the functional predictors are irregularly measured. Currently, such a model cannot be fit by existing software. We apply the model to dynamically predict children's length conditional on prior length, weight, and baseline covariates. Inference on model parameters and subject-specific trajectories is conducted using the mixed effects representation of the proposed model. An extensive simulation study shows that the dynamic functional regression model provides more accurate estimation and inference than existing methods. Methods are supported by fast, flexible, open source software that uses heavily tested smoothing techniques.

Novel metrics for growth model selection.

BACKGROUND: Literature surrounding the statistical modeling of childhood growth data involves a diverse set of potential models from which investigators can choose. However, the lack of a comprehensive framework for comparing non-nested models leads to difficulty in assessing model performance. This paper proposes a framework for comparing non-nested growth models using novel metrics of predictive accuracy based on modifications of the mean squared error criteria. METHODS: Three metrics were created: normalized, age-adjusted, and weighted mean squared error (MSE). Predictive performance metrics were used to compare linear mixed effects models and functional regression models. Prediction accuracy was assessed by partitioning the observed data into training and test datasets. This partitioning was constructed to assess prediction accuracy for backward (i.e., early growth), forward (i.e., late growth), in-range, and on new-individuals. Analyses were done with height measurements from 215 Peruvian children with data spanning from near birth to 2 years of age. RESULTS: Functional models outperformed linear mixed effects models in all scenarios tested. In particular, prediction errors for functional concurrent regression (FCR) and functional principal component analysis models were approximately 6% lower when compared to linear mixed effects models. When we weighted subject-specific MSEs according to subject-specific growth rates during infancy, we found that FCR was the best performer in all scenarios. CONCLUSION: With this novel approach, we can quantitatively compare non-nested models and weight subgroups of interest to select the best performing growth model for a particular application or problem at hand.

A joint design for functional data with application to scheduling ultrasound scans.

A joint design for sampling functional data is proposed to achieve optimal prediction of both functional data and a scalar outcome. The motivating application is fetal growth, where the objective is to determine the optimal times to collect ultrasound measurements in order to recover fetal growth trajectories and to predict child birth outcomes. The joint design is formulated using an optimization criterion and implemented in a pilot study. Performance of the proposed design is evaluated via simulation study and application to fetal ultrasound data.

Re-evaluating the effect of age on physical activity over the lifespan.

Advancements in accelerometer analytic and visualization techniques allow researchers to more precisely identify and compare critical periods of physical activity (PA) decline by age across the lifespan, and describe how daily PA patterns may vary across age groups. We used accelerometer data from the 2003-2006 cohorts of the National Health and Nutrition Examination Survey (NHANES) (n=12,529) to quantify total PA as well as PA by intensity across the lifespan using sex-stratified, age specific percentile curves constructed using generalized additive models. We additionally estimated minute-to-minute diurnal PA using smoothed bivariate surfaces. We found that from childhood to adolescence (ages 6-19) across sex, PA is sharply lower by age partially due to a later initiation of morning PA. Total PA levels, at age 19 are comparable to levels at age 60. Contrary to prior evidence, during young adulthood (ages 20-30) total and light intensity PA increases by age and then stabilizes during midlife (ages 31-59) partially due to an earlier initiation of morning PA. We additionally found that males compared to females have an earlier lowering in PA by age at midlife and lower total PA, higher sedentary behavior, and lower light intensity PA in older adulthood; these trends seem to be driven by lower PA in the afternoon compared to females. Our results suggest a re-evaluation of how emerging adulthood may affect PA levels and the importance of considering time of day and sex differences when developing PA interventions.