Regression and Alignment for Functional Data and Network Topology

In the brain, functional connections form a network whose topological organization can be described by graph-theoretic network diagnostics. These include characterizations of the community structure, such as modularity and participation coefficient, which have been shown to change over the course of childhood and adolescence. To investigate if such changes in the functional network are associated with changes in cognitive performance during development, network studies often rely on an arbitrary choice of pre-processing parameters, in particular the proportional threshold of network edges. Because the choice of parameter can impact the value of the network diagnostic, and therefore downstream conclusions, we propose to circumvent that choice by conceptualizing the network diagnostic as a function of the parameter. As opposed to a single value, a network diagnostic curve describes the connectome topology at multiple scales-from the sparsest group of the strongest edges to the entire edge set. To relate these curves to executive function and other covariates, we use scalar-on-function regression, which is more flexible than previous functional data-based models used in network neuroscience. We then consider how systematic differences between networks can manifest in misalignment of diagnostic curves, and consequently propose a supervised curve alignment method that incorporates auxiliary information from other variables. Our algorithm performs both functional regression and alignment via an iterative, penalized, and nonlinear likelihood optimization. The illustrated method has the potential to improve the interpretability and generalizability of neuroscience studies where the goal is to study heterogeneity among a mixture of function- and scalar-valued measures.

Spectral features of resting-state EEG in Parkinson's Disease: A multicenter study using functional data analysis

OBJECTIVE

This study aims 1) To analyse differences in resting-state electroencephalogram (rs-EEG) spectral features of Parkinson's Disease (PD) and healthy subjects (non-PD) using Functional Data Analysis (FDA) and 2) To explore, in four independent cohorts, the external validity and reproducibility of the findings using both epoch-to-epoch FDA and averaged-epochs approach.

METHODS

We included 169 subjects (85 non-PD; 84 PD) from four centres. Rs-EEG signals were preprocessed with a combination of automated pipelines. Sensor-level relative power spectral density (PSD), dominant frequency (DF), and DF variability (DFV) features were extracted. Differences in each feature were compared between PD and non-PD on averaged epochs and using FDA to model the epoch-to-epoch change of each feature.

RESULTS

For averaged epochs, significantly higher theta relative PSD in PD was found across all datasets. Also, higher pre-alpha relative PSD was observed in three of four datasets in PD patients. For FDA, similar findings were achieved in theta, but all datasets showed consistently significant posterior pre-alpha differences across multiple epochs.

CONCLUSIONS

Increased generalised theta, with posterior pre-alpha relative PSD, was the most reproducible finding in PD.

SIGNIFICANCE

Rs-EEG theta and pre-alpha findings are generalisable in PD. FDA constitutes a reliable and powerful tool to analyse epoch-to-epoch the rs-EEG.

Constructing a polygenic risk score for childhood obesity using functional data analysis

Obesity is a highly heritable condition that affects increasing numbers of adults and, concerningly, of children. However, only a small fraction of its heritability has been attributed to specific genetic variants. These variants are traditionally ascertained from genome-wide association studies (GWAS), which utilize samples with tens or hundreds of thousands of individuals for whom a single summary measurement (e.g., BMI) is collected. An alternative approach is to focus on a smaller, more deeply characterized sample in conjunction with advanced statistical models that leverage longitudinal phenotypes. Novel functional data analysis (FDA) techniques are used to capitalize on longitudinal growth information from a cohort of children between birth and three years of age. In an ultra-high dimensional setting, hundreds of thousands of single nucleotide polymorphisms (SNPs) are screened, and selected SNPs are used to construct two polygenic risk scores (PRS) for childhood obesity using a weighting approach that incorporates the dynamic and joint nature of SNP effects. These scores are significantly higher in children with (vs. without) rapid infant weight gain-a predictor of obesity later in life. Using two independent cohorts, it is shown that the genetic variants identified in very young children are also informative in older children and in adults, consistent with early childhood obesity being predictive of obesity later in life. In contrast, PRSs based on SNPs identified by adult obesity GWAS are not predictive of weight gain in the cohort of young children. This provides an example of a successful application of FDA to GWAS. This application is complemented with simulations establishing that a deeply characterized sample can be just as, if not more, effective than a comparable study with a cross-sectional response. Overall, it is demonstrated that a deep, statistically sophisticated characterization of a longitudinal phenotype can provide increased statistical power to studies with relatively small sample sizes; and shows how FDA approaches can be used as an alternative to the traditional GWAS.

Exploration of the impact of political ideology disparity on COVID-19 transmission in the United States

BACKGROUND

Based on individual-level studies, previous literature suggested that conservatives and liberals in the United States had different perceptions and behaviors when facing the COVID-19 threat. From a state-level perspective, this study further explored the impact of personal political ideology disparity on COVID-19 transmission before and after the emergence of Omicron.

METHODS

A new index was established, which depended on the daily cumulative number of confirmed cases in each state and the corresponding population size. Then, by using the 2020 United States presidential election results, the values of the built index were further divided into two groups concerning the political party affiliation of the winner in each state. In addition, each group was further separated into two parts, corresponding to the time before and after Omicron predominated. Three methods, i.e., functional principal component analysis, functional analysis of variance, and function-on-scalar linear regression, were implemented to statistically analyze and quantify the impact.

RESULTS

Findings reveal that the disparity of personal political ideology has caused a significant discrepancy in the COVID-19 crisis in the United States. Specifically, the findings show that at the very early stage before the emergence of Omicron, Democratic-leaning states suffered from a much greater severity of the COVID-19 threat but, after July 2020, the severity of COVID-19 transmission in Republican-leaning states was much higher than that in Democratic-leaning states. Situations were reversed when the Omicron predominated. Most of the time, states with Democrat preferences were more vulnerable to the threat of COVID-19 than those with Republican preferences, even though the differences decreased over time.

CONCLUSIONS

The individual-level disparity of political ideology has impacted the nationwide COVID-19 transmission and such findings are meaningful for the government and policymakers when taking action against the COVID-19 crisis in the United States.

Ultra-Fast Approximate Inference Using Variational Functional Mixed Models

While Bayesian functional mixed models have been shown effective to model functional data with various complex structures, their application to extremely high-dimensional data is limited due to computational challenges involved in posterior sampling. We introduce a new computational framework that enables ultra-fast approximate inference for high-dimensional data in functional form. This framework adopts parsimonious basis to represent functional observations, which facilitates efficient compression and parallel computing in basis space. Instead of performing expensive Markov chain Monte Carlo sampling, we approximate the posterior distribution using variational Bayes and adopt a fast iterative algorithm to estimate parameters of the approximate distribution. Our approach facilitates a fast multiple testing procedure in basis space, which can be used to identify significant local regions that reflect differences across groups of samples. We perform two simulation studies to assess the performance of approximate inference, and demonstrate applications of the proposed approach by using a proteomic mass spectrometry dataset and a brain imaging dataset. Supplementary materials are available online.

Breathing patterns recognition: A functional data analysis approach

BACKGROUND AND OBJECTIVE

The ongoing pandemic proved fundamental is to assess a subject's respiratory functionality and breathing pattern measurement during quiet breathing is feasible in almost all patients, even those uncooperative. Breathing pattern consists of tidal volume and respiratory rate in an individual assessed by data tracks of lung or chest wall volume over time. State-of-art analysis of these data requires operator-dependent choices such as individuation of local minima in the track, elimination of anomalous breaths and individuation of breath clusters corresponding to different breathing patterns.

METHODS

A semi-automatic, robust and reproducible procedure was proposed to pre-process and analyse respiratory tracks, based on Functional Data Analysis (FDA) techniques, to identify representative breath curve and the corresponding breathing patterns. This was achieved through three steps: 1) breath separation through precise localization of the minima of the volume trace; 2) functional outlier breaths detection according to time-duration, magnitude and shape; 3) breath clustering to identify different pattern of interest, through K-medoids with Alignment. The method was firstly validated on simulated tracks and then applied to real data in conditions of clinical interest: operational volume change, exercise, mechanical ventilation, paradoxical breathing and age.

RESULTS

The total error in the accuracy of minima detection and in was less than 5%; with the artificial outliers being almost completely removed with an accuracy of 99%. During incremental exercise and independently on the bike resistance level, five clusters were identified (quiet breathing; recovery phase; onset of exercise; maximal and intermediate levels of exercise). During mechanical ventilation, the procedure was able to separate the non-ventilated from the ventilatory-supported breathing and to identify the worsening of paradoxical breathing due to the disease progression and the breathing pattern changes in healthy subjects due to age.

CONCLUSIONS

We proposed a robust validated automatic breathing patterns identification algorithm that extracted representative curves that could be implemented in clinical practice for objective comparison of the breathing patterns within and between subjects. In all case studies the identified patterns proved to be coherent with the clinical conditions and the physiopathology of the subjects, therefore enforcing the potential clinical translational value of the method.

A functional approach for characterizing safety risk of signalized intersections at the movement level: An exploratory analysis

Safety evaluation of signalized intersections is often conducted by developing statistical and data-driven methods based on data aggregated at certain temporal and spatial levels (e.g., yearly, hourly, or per signal cycle; intersection or approach leg). However, such aggregations are subject to a major simplification that masks the underlying spatio-temporal safety risk patterns within the data aggregation levels. Consequently, high-resolution analysis such as safety risk within signal cycles and at traffic movement level cannot be performed. This study contributes to the literature by proposing a new functional data analysis (FDA) approach for a novel characterization of safety risk patterns of signalized intersections. Functional data smoothing methods that can mitigate overfitting and account for the nonnegative characteristics of safety risk are proposed to model the time series of safety risk within signal cycles at the traffic movement level. Functional analysis of variance method (FANOVA) that can compare the group level differences of functional curves is used to test differences of safety risk functions among different traffic movements. A typical signalized intersection with representative signal types and channelizations is selected as the study location and approximately 1-hour traffic video data recorded by an unmanned aerial vehicle are used to extract traffic conflicts. New movement-level safety risk patterns are characterized based on the safety risk functions that can reveal the temporal distribution of risk within signal cycles. Most of the tested traffic movements have significantly distinct functional risk patterns according to the FANOVA results while risk patterns for most of the traffic movements cannot be differentiated based on the data aggregated at the cycle and approach levels. The proposed functional approach has the potential to be used for facilitating proactive safety management, calibrating microsimulation models for safety evaluation, and optimizing signal timing while considering traffic safety at more disaggregated levels.

Empirical Bayes Derivative Estimates

A dynamic system is a set of interacting elements characterized by changes occurring over time. The estimation of derivatives is a mainstay for exploring dynamics of constructs, particularly when the dynamics are complicated or unknown. The presence of measurement error in many social science constructs frequently results in poor estimates of derivatives, as even modest proportions of measurement error can compound when estimating derivatives. Given the overlap in the specification of latent differential equation models and latent growth curve models, and the equivalence of latent growth curve models and mixed models under some conditions, derivatives could be estimated from estimates of random effects. This article proposes a new method for estimating derivatives based on calculating the Empirical Bayes estimates of derivatives from a mixed model. Two simulations compare four derivative estimation methods: Generalized Local Linear Approximation, Generalized Orthogonal Derivative Estimates, Functional Data Analysis, and the proposed Empirical Bayes Derivative Estimates. The simulations consider two data collection scenarios: short time series (≤10 observations) from many individuals or occasions, and long individual time series (25-500 observations). A substantive example visualizing the dynamics of intraindividual positive affect time series is also presented.

Trajectories of the heart rate characteristics index, a physiomarker of sepsis in premature infants, predict Neonatal ICU mortality

OBJECTIVE

Trajectories of physiomarkers over time can be useful to define phenotypes of disease progression and as predictors of clinical outcomes. The aim of this study was to identify phenotypes of the time course of late-onset sepsis in premature infants in Neonatal Intensive Care Units.

METHODS

We examined the trajectories of a validated continuous physiomarker, abnormal heart rate characteristics, using functional data analysis and clustering techniques.

PARTICIPANTS

We analyzed continuous heart rate characteristics data from 2989 very low birth weight infants (<1500 grams) from nine NICUs from 2004-2010.

RESULT

Despite the relative homogeneity of the patients, we found extreme variability in the physiomarker trajectories. We identified phenotypes that were indicative of seven and 30 day mortality beyond that predicted by individual heart rate characteristics values or baseline demographic information.

CONCLUSION

Time courses of a heart rate characteristics physiomarker reveal snapshots of illness patterns, some of which were more deadly than others.

A Study of Mexican Free-Tailed Bat Chirp Syllables: Bayesian Functional Mixed Models for Nonstationary Acoustic Time Series

We describe a new approach to analyze chirp syllables of free-tailed bats from two regions of Texas in which they are predominant: Austin and College Station. Our goal is to characterize any systematic regional differences in the mating chirps and assess whether individual bats have signature chirps. The data are analyzed by modeling spectrograms of the chirps as responses in a Bayesian functional mixed model. Given the variable chirp lengths, we compute the spectrograms on a relative time scale interpretable as the relative chirp position, using a variable window overlap based on chirp length. We use 2D wavelet transforms to capture correlation within the spectrogram in our modeling and obtain adaptive regularization of the estimates and inference for the regions-specific spectrograms. Our model includes random effect spectrograms at the bat level to account for correlation among chirps from the same bat, and to assess relative variability in chirp spectrograms within and between bats. The modeling of spectrograms using functional mixed models is a general approach for the analysis of replicated nonstationary time series, such as our acoustical signals, to relate aspects of the signals to various predictors, while accounting for between-signal structure. This can be done on raw spectrograms when all signals are of the same length, and can be done using spectrograms defined on a relative time scale for signals of variable length in settings where the idea of defining correspondence across signals based on relative position is sensible.

Statistical Methods for Proteomic Biomarker Discovery based on Feature Extraction or Functional Modeling Approaches

In recent years, developments in molecular biotechnology have led to the increased promise of detecting and validating biomarkers, or molecular markers that relate to various biological or medical outcomes. Proteomics, the direct study of proteins in biological samples, plays an important role in the biomarker discovery process. These technologies produce complex, high dimensional functional and image data that present many analytical challenges that must be addressed properly for effective comparative proteomics studies that can yield potential biomarkers. Specific challenges include experimental design, preprocessing, feature extraction, and statistical analysis accounting for the inherent multiple testing issues. This paper reviews various computational aspects of comparative proteomic studies, and summarizes contributions I along with numerous collaborators have made. First, there is an overview of comparative proteomics technologies, followed by a discussion of important experimental design and preprocessing issues that must be considered before statistical analysis can be done. Next, the two key approaches to analyzing proteomics data, feature extraction and functional modeling, are described. Feature extraction involves detection and quantification of discrete features like peaks or spots that theoretically correspond to different proteins in the sample. After an overview of the feature extraction approach, specific methods for mass spectrometry (Cromwell) and 2D gel electrophoresis (Pinnacle) are described. The functional modeling approach involves modeling the proteomic data in their entirety as functions or images. A general discussion of the approach is followed by the presentation of a specific method that can be applied, wavelet-based functional mixed models, and its extensions. All methods are illustrated by application to two example proteomic data sets, one from mass spectrometry and one from 2D gel electrophoresis. While the specific methods presented are applied to two specific proteomic technologies, MALDI-TOF and 2D gel electrophoresis, these methods and the other principles discussed in the paper apply much more broadly to other expression proteomics technologies.