Generalized functional linear model with a point process predictor.

Point process data have become increasingly popular these days. For example, many of the data captured in electronic health records (EHR) are in the format of point process data. It is of great interest to study the association between a point process predictor and a scalar response using generalized functional linear regression models. Various generalized functional linear regression models have been developed under different settings in the past decades. However, existing methods can only deal with functional or longitudinal predictors, not point process predictors. In this article, we propose a novel generalized functional linear regression model for a point process predictor. Our proposed model is based on the joint modeling framework, where we adopt a log-Gaussian Cox process model for the point process predictor and a generalized linear regression model for the outcome. We also develop a new algorithm for fast model estimation based on the Gaussian variational approximation method. We conduct extensive simulation studies to evaluate the performance of our proposed method and compare it to competing methods. The performance of our proposed method is further demonstrated on an EHR dataset of patients admitted into the intensive care units of the Beth Israel Deaconess Medical Center between 2001 and 2008.

A functional-model-adjusted spatial scan statistic.

This paper introduces a new spatial scan statistic designed to adjust cluster detection for longitudinal confounding factors indexed in space. The functional-model-adjusted statistic was developed using generalized functional linear models in which longitudinal confounding factors were considered to be functional covariates. A general framework was developed for application to various probability models. Application to a Poisson model showed that the new method is equivalent to a conventional spatial scan statistic that adjusts the underlying population for covariates. In a simulation study with single and multiple covariate models, we found that our new method adjusts the cluster detection procedure more accurately than other methods. Use of the new spatial scan statistic was illustrated by analyzing data on premature mortality in France over the period from 1998 to 2013, with the quarterly unemployment rate as a longitudinal confounding factor.

Use of Functional Linear Models to Detect Associations between Characteristics of Walking and Continuous Responses Using Accelerometry Data.

Various methods exist to measure physical activity. Subjective methods, such as diaries and surveys, are relatively inexpensive ways of measuring one's physical activity; however, they are prone to measurement error and bias due to self-reporting. Wearable accelerometers offer a non-invasive and objective measure of one's physical activity and are now widely used in observational studies. Accelerometers record high frequency data and each produce an unlabeled time series at the sub-second level. An important activity to identify from the data collected is walking, since it is often the only form of activity for certain populations. Currently, most methods use an activity summary which ignores the nuances of walking data. We propose methodology to model specific continuous responses with a functional linear model utilizing spectra obtained from the local fast Fourier transform (FFT) of walking as a predictor. Utilizing prior knowledge of the mechanics of walking, we incorporate this as additional information for the structure of our transformed walking spectra. The methods were applied to the in-the-laboratory data obtained from the Developmental Epidemiologic Cohort Study (DECOS).

Cumulative weather effects can impact across the whole life cycle.

Predicting how species will be affected by future climatic change requires the underlying environmental drivers to be identified. As vital rates vary over the lifecycle, structured population models derived from statistical environment-demography relationships are often used to inform such predictions. Environmental drivers are typically identified independently for different vital rates and demographic classes. However, these rates often exhibit positive temporal covariance, suggesting that vital rates respond to common environmental drivers. Additionally, models often only incorporate average weather conditions during a single, a priori chosen time window (e.g. monthly means). Mismatches between these windows and the period when the vital rates are sensitive to variation in climate decrease the predictive performance of such approaches. We used a demographic structural equation model (SEM) to demonstrate that a single axis of environmental variation drives the majority of the (co)variation in survival, reproduction, and twinning across six age-sex classes in a Soay sheep population. This axis provides a simple target for the complex task of identifying the drivers of vital rate variation. We used functional linear models (FLMs) to determine the critical windows of three local climatic drivers, allowing the magnitude and direction of the climate effects to differ over time. Previously unidentified lagged climatic effects were detected in this well-studied population. The FLMs had a better predictive performance than selecting a critical window a priori, but not than a large-scale climate index. Positive covariance amongst vital rates and temporal variation in the effects of environmental drivers are common, suggesting our SEM-FLM approach is a widely applicable tool for exploring the joint responses of vital rates to environmental change.

Methods for scalar-on-function regression.

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

Quantifying the effect of body mass index, age, and depression severity on 24-h activity patterns in persons with a lifetime history of affective disorders.

BACKGROUND: Patients with affective disorders of different ages have been found to present weight changes and different circadian activity patterns. This study assessed the effects of age, Body Mass Index (BMI) and depression severity on the activity-rest cycle in persons with affective disorders using a novel multifactorial 24-h analysis method. METHODS: Two hundred and thirty-six participants aged between 14 and 85 years underwent 5 to 22 days of actigraphy monitoring (mean duration = 14 days). BMI was also recorded and symptom severity was assessed with the Hamilton Depression Rating Scale (HDRS). Participants were divided into two groups: healthy controls (n = 68) and participants with a lifetime diagnosis of affective disorders (n = 168). First, the multiple regression method was employed to formulate the circadian activity pattern in term of the factors age, BMI and HDRS. For each group, the functional linear analysis method was applied to assess the relative effects of the factors. Finally, Wald-tests were used to assess the contribution of each factor on the circadian activity pattern. RESULTS: In the affective disorders group, higher BMI was associated with higher activity levels from 3 am until 5.30 am and with lower activity levels from 10 am until 10.30 pm. Older age was associated with less activity across the day, evening, and night - from 11 am until 5.30 am. Higher HDRS scores were associated with higher activity around 1:30 am. In healthy controls, the effects of BMI and age on activity patterns were less pronounced and affected a narrower portion of the 24-h period. CONCLUSION: These findings suggest that older age and higher BMI are linked to lower daytime activity levels. Higher BMI and worse symptom severity were also associated with nocturnal activity patterns suggestive of sleep disturbances. The influence of age and BMI on 24-h activity profiles appear to be especially pronounced in people with affective disorders.

Classical Testing in Functional Linear Models.

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

A variational Bayes spatiotemporal model for electromagnetic brain mapping.

In this article, we present a new variational Bayes approach for solving the neuroelectromagnetic inverse problem arising in studies involving electroencephalography (EEG) and magnetoencephalography (MEG). This high-dimensional spatiotemporal estimation problem involves the recovery of time-varying neural activity at a large number of locations within the brain, from electromagnetic signals recorded at a relatively small number of external locations on or near the scalp. Framing this problem within the context of spatial variable selection for an underdetermined functional linear model, we propose a spatial mixture formulation where the profile of electrical activity within the brain is represented through location-specific spike-and-slab priors based on a spatial logistic specification. The prior specification accommodates spatial clustering in brain activation, while also allowing for the inclusion of auxiliary information derived from alternative imaging modalities, such as functional magnetic resonance imaging (fMRI). We develop a variational Bayes approach for computing estimates of neural source activity, and incorporate a nonparametric bootstrap for interval estimation. The proposed methodology is compared with several alternative approaches through simulation studies, and is applied to the analysis of a multimodal neuroimaging study examining the neural response to face perception using EEG, MEG, and fMRI.

Functional data analysis of the relationship between electricity consumption and climate change drivers.

Climate change has become increasingly important in recent years. It is the outcome of the burning of fossil fuels that increased the concentration of atmospheric carbon dioxide (CO2), over the last century. Mitigating the impacts of climate change requires a better understanding and assessment of the countries' economic decisions on the amount of CO2 emissions. This paper assesses the variability between the different countries in the trends of CO2 emissions and electricity consumption from 1975 to 2014, while identifying clusters of countries of similar trends over time. The novel methodology applied in this paper enables us to assess long-debated issues in climate literature. The temporal dynamic effects of electricity consumption and economic growth on CO2 emissions across countries are studied using functional data analysis (FDA) methods. The latter have proven to be useful tools for visualising similarities and differences in the non-linear trends of CO2 emissions without forcing linear trends and stationary relationships which can be unrealistic and misleading. The results indicate the possibility of identifying changes in the trends of CO2 emissions and electricity consumption for a wide range of heterogeneous countries over the study period. The findings also reveal that economic growth puts a strain on the environment, where many high-income countries are still away from attaining economic-energy sustainability.

Simulation Research on the Methods of Multi-Gene Region Association Analysis Based on a Functional Linear Model.

Genome-wide association analysis is an important approach to identify genetic variants associated with complex traits. Complex traits are not only affected by single gene loci, but also by the interaction of multiple gene loci. Studies of association between gene regions and quantitative traits are of great significance in revealing the genetic mechanism of biological development. There have been a lot of studies on single-gene region association analysis, but the application of functional linear models in multi-gene region association analysis is still less. In this paper, a functional multi-gene region association analysis test method is proposed based on the functional linear model. From the three directions of common multi-gene region method, multi-gene region weighted method and multi-gene region loci weighted method, that test method is studied combined with computer simulation. The following conclusions are obtained through computer simulation: (a) The functional multi-gene region association analysis test method has higher power than the functional single gene region association analysis test method; (b) The functional multi-gene region weighted method performs better than the common functional multi-gene region method; (c) the functional multi-gene region loci weighted method is the best method for association analysis on three directions of the common multi-gene region method; (d) the performance of the Step method and Multi-gene region loci weighted Step for multi-gene regions is the best in general. Functional multi-gene region association analysis test method can theoretically provide a feasible method for the study of complex traits affected by multiple genes.

Quantifying and Visualizing Intraregional Connectivity in Resting-State Functional Magnetic Resonance Imaging with Correlation Densities.

The use of correlation densities is introduced to quantify and provide visual interpretation for intraregional functional connectivity in the brain. For each brain region, pairwise correlations are computed between a seed voxel and other gray matter voxels within the region, and the distribution of the ensemble of these correlation values is represented as a probability density, the correlation density. The correlation density can be estimated by kernel smoothing. It provides an intuitive and comprehensive representation of subject-specific functional connectivity strength at the local level for each region. To address the challenge of interpreting and utilizing this rich connectivity information when multiple regions are considered, methods from functional data analysis are implemented, including a recently developed method of dimensionality reduction specifically tailored to the analysis of probability distributions. To illustrate the utility of these methods in neuroimaging, experiments were carried out to identify the associations between local functional connectivity and a battery of neurocognitive scores. These experiments demonstrate that correlation densities facilitate the discovery and interpretation of specific region-score associations.

A LAG FUNCTIONAL LINEAR MODEL FOR PREDICTION OF MAGNETIZATION TRANSFER RATIO IN MULTIPLE SCLEROSIS LESIONS.

We propose a lag functional linear model to predict a response using multiple functional predictors observed at discrete grids with noise. Two procedures are proposed to estimate the regression parameter functions: (1) an approach that ensures smoothness for each value of time using generalized cross-validation; and (2) a global smoothing approach using a restricted maximum likelihood framework. Numerical studies are presented to analyze predictive accuracy in many realistic scenarios. The methods are employed to estimate a magnetic resonance imaging (MRI)-based measure of tissue damage (the magnetization transfer ratio, or MTR) in multiple sclerosis (MS) lesions, a disease that causes damage to the myelin sheaths around axons in the central nervous system. Our method of estimation of MTR within lesions is useful retrospectively in research applications where MTR was not acquired, as well as in clinical practice settings where acquiring MTR is not currently part of the standard of care. The model facilitates the use of commonly acquired imaging modalities to estimate MTR within lesions, and outperforms cross-sectional models that do not account for temporal patterns of lesion development and repair.

FEATURE SCREENING FOR TIME-VARYING COEFFICIENT MODELS WITH ULTRAHIGH DIMENSIONAL LONGITUDINAL DATA.

Motivated by an empirical analysis of the Childhood Asthma Management Project, CAMP, we introduce a new screening procedure for varying coefficient models with ultrahigh dimensional longitudinal predictor variables. The performance of the proposed procedure is investigated via Monte Carlo simulation. Numerical comparisons indicate that it outperforms existing ones substantially, resulting in significant improvements in explained variability and prediction error. Applying these methods to CAMP, we are able to find a number of potentially important genetic mutations related to lung function, several of which exhibit interesting nonlinear patterns around puberty.

Simultaneous detection of multiple bioactive pollutants using a multiparametric biochip for water quality monitoring.

Water is a renewable resource but yet finite. Its sustainable usage and the maintenance of a good quality are essential for an intact environment, human life and a stable economy. Emerging technologies aim for a continuous monitoring of water quality, overcoming periodic analytical sampling, and providing information on the current state of inshore waters in real time. So does the here presented cell-based sensor system which uses RLC-18 cells (rat liver cells) as the detection layer for the detection of water pollutants. The electrical read-out of the system, cellular metabolism, oxygen consumption and morphological integrity detects small changes in the water quality and indicates a possible physiological damage caused. A generalized functional linear model was implemented in order to regress the chemicals present in the sample on the electrical read-out. The chosen environmental pollutants to test the system were chlorpyrifos, an organophosphate pesticide, and tetrabromobisphenol A, a flame retardant. Each chemical gives a very characteristic response, but the toxicity is mitigated if both chemicals are present at once. This will focus our attention on the statistical approach which is able to discriminate between these pollutants.

Multiple functional linear model for association analysis of RNA-seq with imaging.

Emerging integrative analysis of genomic and anatomical imaging data which has not been well developed, provides invaluable information for the holistic discovery of the genomic structure of disease and has the potential to open a new avenue for discovering novel disease susceptibility genes which cannot be identified if they are analyzed separately. A key issue to the success of imaging and genomic data analysis is how to reduce their dimensions. Most previous methods for imaging information extraction and RNA-seq data reduction do not explore imaging spatial information and often ignore gene expression variation at the genomic positional level. To overcome these limitations, we extend functional principle component analysis from one dimension to two dimensions (2DFPCA) for representing imaging data and develop a multiple functional linear model (MFLM) in which functional principal scores of images are taken as multiple quantitative traits and RNA-seq profile across a gene is taken as a function predictor for assessing the association of gene expression with images. The developed method has been applied to image and RNA-seq data of ovarian cancer and kidney renal clear cell carcinoma (KIRC) studies. We identified 24 and 84 genes whose expressions were associated with imaging variations in ovarian cancer and KIRC studies, respectively. Our results showed that many significantly associated genes with images were not differentially expressed, but revealed their morphological and metabolic functions. The results also demonstrated that the peaks of the estimated regression coefficient function in the MFLM often allowed the discovery of splicing sites and multiple isoforms of gene expressions.

Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.

We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint functional and exposure models, and give a method for efficient computation. We contrast our approach with existing state-of-the-art methods for regression with functional predictors, and show that our method is more effective and efficient for data that include features occurring at varying locations. We apply our methodology to a large and complex dataset from the Sleep Heart Health Study, to quantify the association between sleep characteristics and health outcomes. Software and technical appendices are provided in online supplemental materials.