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].