Multivariate spatiotemporal functional principal component analysis for modeling hospitalization and mortality rates in the dialysis population.

Dialysis patients experience frequent hospitalizations and a higher mortality rate compared to other Medicare populations, in whom hospitalizations are a major contributor to morbidity, mortality, and healthcare costs. Patients also typically remain on dialysis for the duration of their lives or until kidney transplantation. Hence, there is growing interest in studying the spatiotemporal trends in the correlated outcomes of hospitalization and mortality among dialysis patients as a function of time starting from transition to dialysis across the United States Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multivariate spatiotemporal functional principal component analysis model to study the joint spatiotemporal patterns of hospitalization and mortality rates among dialysis patients. The proposal is based on a multivariate Karhunen-Loéve expansion that describes leading directions of variation across time and induces spatial correlations among region-specific scores. An efficient estimation procedure is proposed using only univariate principal components decompositions and a Markov Chain Monte Carlo framework for targeting the spatial correlations. The finite sample performance of the proposed method is studied through simulations. Novel applications to the USRDS data highlight hot spots across the United States with higher hospitalization and/or mortality rates and time periods of elevated risk.

Modeling intra-individual inter-trial EEG response variability in autism.

Autism spectrum disorder (autism) is a prevalent neurodevelopmental condition characterized by early emerging impairments in social behavior and communication. EEG represents a powerful and non-invasive tool for examining functional brain differences in autism. Recent EEG evidence suggests that greater intra-individual trial-to-trial variability across EEG responses in stimulus-related tasks may characterize brain differences in autism. Traditional analysis of EEG data largely focuses on mean trends of the trial-averaged data, where trial-level analysis is rarely performed due to low neural signal to noise ratio. We propose to use nonlinear (shape-invariant) mixed effects (NLME) models to study intra-individual inter-trial EEG response variability using trial-level EEG data. By providing more precise metrics of response variability, this approach could enrich our understanding of neural disparities in autism and potentially aid the identification of objective markers. The proposed multilevel NLME models quantify variability in the signal's interpretable and widely recognized features (e.g., latency and amplitude) while also regularizing estimation based on noisy trial-level data. Even though NLME models have been studied for more than three decades, existing methods cannot scale up to large data sets. We propose computationally feasible estimation and inference methods via the use of a novel minorization-maximization (MM) algorithm. Extensive simulations are conducted to show the efficacy of the proposed procedures. Applications to data from a large national consortium find that children with autism have larger intra-individual inter-trial variability in P1 latency in a visual evoked potential (VEP) task, compared to their neurotypical peers.

The impact of psychological strengths on Veteran populations' mental health trajectories during the COVID-19 pandemic.

PURPOSE: Mental health trajectories during the COVID-19 pandemic have been examined in Veterans with tenuous social connections, i.e., those with recent homelessness (RHV) or a psychotic disorder (PSY), and in control Veterans (CTL). We test potential moderating effects on these trajectories by psychological factors that may help individuals weather the socio-emotional challenges associated with the pandemic (i.e., 'psychological strengths'). METHODS: We assessed 81 PSY, 76 RHV, and 74 CTL over 5 periods between 05/2020 and 07/2021. Mental health outcomes (i.e., symptoms of depression, anxiety, contamination concerns, loneliness) were assessed at each period, and psychological strengths (i.e., a composite score based on tolerance of uncertainty, performance beliefs, coping style, resilience, perceived stress) were assessed at the initial assessment. Generalized models tested fixed and time-varying effects of a composite psychological strengths score on clinical trajectories across samples and within each group. RESULTS: Psychological strengths had a significant effect on trajectories for each outcome (ps < 0.05), serving to ameliorate changes in mental health symptoms. The timing of this effect varied across outcomes, with early effects for depression and anxiety, later effects for loneliness, and sustained effects for contamination concerns. A significant time-varying effect of psychological strengths on depressive symptoms was evident in RHV and CTL, anxious symptoms in RHV, contamination concerns in PSY and CTL, and loneliness in CTL (ps < 0.05). CONCLUSION: Across vulnerable and non-vulnerable Veterans, presence of psychological strengths buffered against exacerbations in clinical symptoms. The timing of the effect varied across outcomes and by group.

Bayesian analysis of longitudinal and multidimensional functional data.

Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this article, we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a longitudinal functional framework we aim to capture low dimensional interpretable features. We propose a computationally efficient nonparametric Bayesian method to simultaneously smooth observed data, estimate conditional functional means and functional covariance surfaces. Statistical inference is based on Monte Carlo samples from the posterior measure through adaptive blocked Gibbs sampling. Several operative characteristics associated with the proposed modeling framework are assessed comparatively in a simulated environment. We illustrate the application of our work in two case studies. The first case study involves age-specific fertility collected over time for various countries. The second case study is an implicit learning experiment in children with autism spectrum disorder.

A Bayesian multilevel time-varying framework for joint modeling of hospitalization and survival in patients on dialysis.

Over 782 000 individuals in the United States have end-stage kidney disease with about 72% of patients on dialysis, a life-sustaining treatment. Dialysis patients experience high mortality and frequent hospitalizations, at about twice per year. These poor outcomes are exacerbated at key time periods, such as the fragile period after transition to dialysis. In order to study the time-varying effects of modifiable patient and dialysis facility risk factors on hospitalization and mortality, we propose a novel Bayesian multilevel time-varying joint model. Efficient estimation and inference is achieved within the Bayesian framework using Markov chain Monte Carlo, where multilevel (patient- and dialysis facility-level) varying coefficient functions are targeted via Bayesian P-splines. Applications to the United States Renal Data System, a national database which contains data on nearly all patients on dialysis in the United States, highlight significant time-varying effects of patient- and facility-level risk factors on hospitalization risk and mortality. Finite sample performance of the proposed methodology is studied through simulations.

Multilevel hybrid principal components analysis for region-referenced functional electroencephalography data.

Electroencephalography experiments produce region-referenced functional data representing brain signals in the time or the frequency domain collected across the scalp. The data typically also have a multilevel structure with high-dimensional observations collected across multiple experimental conditions or visits. Common analysis approaches reduce the data complexity by collapsing the functional and regional dimensions, where event-related potential (ERP) features or band power are targeted in a pre-specified scalp region. This practice can fail to portray more comprehensive differences in the entire ERP signal or the power spectral density (PSD) across the scalp. Building on the weak separability of the high-dimensional covariance process, the proposed multilevel hybrid principal components analysis (M-HPCA) utilizes dimension reduction tools from both vector and functional principal components analysis to decompose the total variation into between- and within-subject variance. The resulting model components are estimated in a mixed effects modeling framework via a computationally efficient minorization-maximization algorithm coupled with bootstrap. The diverse array of applications of M-HPCA is showcased with two studies of individuals with autism. While ERP responses to match vs mismatch conditions are compared in an audio odd-ball paradigm in the first study, short-term reliability of the PSD across visits is compared in the second. Finite sample properties of the proposed methodology are studied in extensive simulations.

A study of longitudinal trends in time-frequency transformations of EEG data during a learning experiment.

EEG experiments yield high-dimensional event-related potential (ERP) data in response to repeatedly presented stimuli throughout the experiment. Changes in the high-dimensional ERP signal throughout the duration of an experiment (longitudinally) is the main quantity of interest in learning paradigms, where they represent the learning dynamics. Typical analysis, which can be performed in the time or the frequency domain, average the ERP waveform across all trials, leading to the loss of the potentially valuable longitudinal information in the data. Longitudinal time-frequency transformation of ERP (LTFT-ERP) is proposed to retain information from both the time and frequency domains, offering distinct but complementary information on the underlying cognitive processes evoked, while still retaining the longitudinal dynamics in the ERP waveforms. LTFT-ERP begins by time-frequency transformations of the ERP data, collected across subjects, electrodes, conditions and trials throughout the duration of the experiment, followed by a data driven multidimensional principal components analysis (PCA) approach for dimension reduction. Following projection of the data onto leading directions of variation in the time and frequency domains, longitudinal learning dynamics are modeled within a mixed effects modeling framework. Applications to a learning paradigm in autism depict distinct learning patterns throughout the experiment among children diagnosed with Autism Spectrum Disorder and their typically developing peers. LTFT-ERP time-frequency joint transformations are shown to bring an additional level of specificity to interpretations of the longitudinal learning patterns related to underlying cognitive processes, which is lacking in single domain analysis (in the time or the frequency domain only). Simulation studies show the efficacy of the proposed methodology.

Functional connectivity during language processing in 3-month-old infants at familial risk for autism spectrum disorder.

Auditory statistical learning (ASL) plays a role in language development and may lay a foundation for later social communication impairment. As part of a longitudinal study of infant siblings, we asked whether electroencephalography (EEG) measures of connectivity during ASL at 3 months of age-differentiated infants who showed signs of autism spectrum disorder (ASD) at age 18 months. We measured spectral power and phase coherence in the theta (4-6 Hz) and alpha (6-12 Hz) frequency bands within putative language networks. Infants were divided into ASD-concern (n = 14) and No-ASD-concern (n = 49) outcome groups based on their ASD symptoms at 18 months, measured using the Autism Diagnostic Observation Scale Toddler Module. Using permutation testing, we identified a trend toward reduced left fronto-central phase coherence at the electrode pair F9-C3 in both theta and alpha frequency bands in infants who later showed ASD symptoms at 18 months. Across outcome groups, alpha coherence at 3 months correlated with greater word production at 18 months on the MacArthur-Bates Communicative Development Inventory. This study introduces signal processing and analytic tools that account for the challenges inherent in infant EEG studies, such as short duration of recordings, considerable movement artifact, and variable volume conduction. Our results indicate that connectivity, as measured by phase coherence during 2.5 min of ASL, can be quantified as early as 3 months and suggest that early alternations in connectivity may serve as markers of resilience for neurodevelopmental impairments.

Hybrid principal components analysis for region-referenced longitudinal functional EEG data.

Electroencephalography (EEG) data possess a complex structure that includes regional, functional, and longitudinal dimensions. Our motivating example is a word segmentation paradigm in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. For each subject, continuous EEG signals recorded at each electrode were divided into one-second segments and projected into the frequency domain via fast Fourier transform. Following a spectral principal components analysis, the resulting data consist of region-referenced principal power indexed regionally by scalp location, functionally across frequencies, and longitudinally by one-second segments. Standard EEG power analyses often collapse information across the longitudinal and functional dimensions by averaging power across segments and concentrating on specific frequency bands. We propose a hybrid principal components analysis for region-referenced longitudinal functional EEG data, which utilizes both vector and functional principal components analyses and does not collapse information along any of the three dimensions of the data. The proposed decomposition only assumes weak separability of the higher-dimensional covariance process and utilizes a product of one dimensional eigenvectors and eigenfunctions, obtained from the regional, functional, and longitudinal marginal covariances, to represent the observed data, providing a computationally feasible non-parametric approach. A mixed effects framework is proposed to estimate the model components coupled with a bootstrap test for group level inference, both geared towards sparse data applications. Analysis of the data from the word segmentation paradigm leads to valuable insights about group-region differences among the TD and verbal and minimally verbal children with ASD. Finite sample properties of the proposed estimation framework and bootstrap inference procedure are further studied via extensive simulations.

Multilevel modeling of spatially nested functional data: Spatiotemporal patterns of hospitalization rates in the US dialysis population.

End-stage renal disease patients on dialysis experience frequent hospitalizations. In addition to known temporal patterns of hospitalizations over the life span on dialysis, where poor outcomes are typically exacerbated during the first year on dialysis, variations in hospitalizations among dialysis facilities across the US contribute to spatial variation. Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multilevel spatiotemporal functional model to study spatiotemporal patterns of hospitalization rates among dialysis facilities. Hospitalization rates of dialysis facilities are considered as spatially nested functional data (FD) with longitudinal hospitalizations nested in dialysis facilities and dialysis facilities nested in geographic regions. A multilevel Karhunen-Loéve expansion is utilized to model the two-level (facility and region) FD, where spatial correlations are induced among region-specific principal component scores accounting for regional variation. A new efficient algorithm based on functional principal component analysis and Markov Chain Monte Carlo is proposed for estimation and inference. We report a novel application using USRDS data to characterize spatiotemporal patterns of hospitalization rates for over 400 health service areas across the US and over the posttransition time on dialysis. Finite sample performance of the proposed method is studied through simulations.

Early concerns in parents of infants at risk for autism.

AIM: To examine parental concerns about children at increased familial risk (i.e. high risk) of developing autism spectrum disorder (ASD) in early infancy. METHOD: ASD-related and general parental concerns were prospectively collected for 76 infants at ages 1.5, 3, 6, 9, 12, and 18 months. Outcome classification was determined at 36 months. Analyses included generalized linear mixed models and qualitative evaluation of parental concerns in relation to risk status (high vs low risk) and outcome classification within the high-risk group (atypically developing vs typically developing) over time. RESULTS: Most parents had no concerns at 1.5 (high risk 71%, low risk 87%) and 3 months (high risk 77%, low risk 86%). Beginning at 6 months, parents of high-risk infants reported more ASD-related (p<0.001) and general concerns (p=0.003) than parents of low-risk infants. Beginning at 12 months, parents of high-risk atypically developing infants reported more ASD-related concerns than parents of high-risk typically developing infants (p=0.013). INTERPRETATION: Clinicians should elicit parental concerns and provide support, as parents are worried about their high-risk infants by age 6 months. Additionally, parents' abilities to identify concerns that are suggestive of ASD by age 12 months may aid in earlier screening and intervention. What this paper adds Most parents did not report concerns during early infancy. By 6 months, parents of high-risk infants reported autism spectrum disorder (ASD)-related and general concerns. By 12 months, parents of high-risk atypically developing infants identified ASD-related concerns.

Infants' identification of gender in biological motion displays.

Infants' knowledge of social categories, including gender-typed characteristics, is a vital aspect of social cognitive development. In the current study, we examined 9- to 12-month-old infants' understanding of the categories "male" and "female" by testing for gender matching in voices or faces with biological motion depicted in point light displays (PLDs). Infants did not show voice-PLD gender matching spontaneously (Experiment 1) or after "training" with gender-matching voice-PLD pairs (Experiment 2). In Experiment 3, however, infants were trained with gender-matching face-PLD pairs and we found that patterns of visual attention to top regions of PLD stimuli during training predicted gender matching of female faces and PLDs. Prior to the end of the first postnatal year, therefore, infants may begin to identify gender in human walk motions, and perhaps form social categories from biological motion.

Principle ERP reduction and analysis: Estimating and using principle ERP waveforms underlying ERPs across tasks, subjects and electrodes.

Event-related potentials (ERP) waveforms are the summation of many overlapping signals. Changes in the peak or mean amplitude of a waveform over a given time period, therefore, cannot reliably be attributed to a particular ERP component of ex ante interest, as is the standard approach to ERP analysis. Though this problem is widely recognized, it is not well addressed in practice. Our approach begins by presuming that any observed ERP waveform - at any electrode, for any trial type, and for any participant - is approximately a weighted combination of signals from an underlying set of what we refer to as principle ERPs, or pERPs. We propose an accessible approach to analyzing complete ERP waveforms in terms of their underlying pERPs. First, we propose the principle ERP reduction (pERP-RED) algorithm for investigators to estimate a suitable set of pERPs from their data, which may span multiple tasks. Next, we provide tools and illustrations of pERP-space analysis, whereby observed ERPs are decomposed into the amplitudes of the contributing pERPs, which can be contrasted across conditions or groups to reveal which pERPs differ (substantively and/or significantly) between conditions/groups. Differences on all pERPs can be reported together rather than selectively, providing complete information on all components in the waveform, thereby avoiding selective reporting or user discretion regarding the choice of which components or windows to use. The scalp distribution of each pERP can also be plotted for any group/condition. We demonstrate this suite of tools through simulations and on real data collected from multiple experiments on participants diagnosed with Autism Spectrum Disorder and Attention Deficit Hyperactivity Disorder. Software for conducting these analyses is provided in the pERPred package for R.

A multilevel mixed effects varying coefficient model with multilevel predictors and random effects for modeling hospitalization risk in patients on dialysis.

For patients on dialysis, hospitalizations remain a major risk factor for mortality and morbidity. We use data from a large national database, United States Renal Data System, to model time-varying effects of hospitalization risk factors as functions of time since initiation of dialysis. To account for the three-level hierarchical structure in the data where hospitalizations are nested in patients and patients are nested in dialysis facilities, we propose a multilevel mixed effects varying coefficient model (MME-VCM) where multilevel (patient- and facility-level) random effects are used to model the dependence structure of the data. The proposed MME-VCM also includes multilevel covariates, where baseline demographics and comorbidities are among the patient-level factors, and staffing composition and facility size are among the facility-level risk factors. To address the challenge of high-dimensional integrals due to the hierarchical structure of the random effects, we propose a novel two-step approximate EM algorithm based on the fully exponential Laplace approximation. Inference for the varying coefficient functions and variance components is achieved via derivation of the standard errors using score contributions. The finite sample performance of the proposed estimation procedure is studied through simulations.

Profiling dialysis facilities for adverse recurrent events.

Profiling analysis aims to evaluate health care providers, such as hospitals, nursing homes, or dialysis facilities, with respect to a patient outcome. Previous profiling methods have considered binary outcomes, such as 30-day hospital readmission or mortality. For the unique population of dialysis patients, regular blood works are required to evaluate effectiveness of treatment and avoid adverse events, including dialysis inadequacy, imbalance mineral levels, and anemia among others. For example, anemic events (when hemoglobin levels exceed normative range) are recurrent and common for patients on dialysis. Thus, we propose high-dimensional Poisson and negative binomial regression models for rate/count outcomes and introduce a standardized event ratio measure to compare the event rate at a specific facility relative to a chosen normative standard, typically defined as an "average" national rate across all facilities. Our proposed estimation and inference procedures overcome the challenge of high-dimensional parameters for thousands of dialysis facilities. Also, we investigate how overdispersion affects inference in the context of profiling analysis. The proposed methods are illustrated with profiling dialysis facilities for recurrent anemia events.

Covariate-adjusted region-referenced generalized functional linear model for EEG data.

Electroencephalography (EEG) studies produce region-referenced functional data in the form of EEG signals recorded across electrodes on the scalp. It is of clinical interest to relate the highly structured EEG data to scalar outcomes such as diagnostic status. In our motivating study, resting-state EEG is collected on both typically developing (TD) children and children with autism spectrum disorder (ASD) aged 2 to 12 years old. The peak alpha frequency (PAF), defined as the location of a prominent peak in the alpha frequency band of the spectral density, is an important biomarker linked to neurodevelopment and is known to shift from lower to higher frequencies as children age. To retain the most amount of information from the data, we consider the oscillations in the spectral density within the alpha band, rather than just the peak location, as a functional predictor of diagnostic status (TD vs ASD), adjusted for chronological age. A covariate-adjusted region-referenced generalized functional linear model is proposed for modeling scalar outcomes from region-referenced functional predictors, which utilizes a tensor basis formed from one-dimensional discrete and continuous bases to estimate functional effects across a discrete regional domain while simultaneously adjusting for additional nonfunctional covariates, such as age. The proposed methodology provides novel insights into differences in neural development of TD and ASD children. The efficacy of the proposed methodology is investigated through extensive simulation studies.

Peak alpha frequency is a neural marker of cognitive function across the autism spectrum.

Cognitive function varies substantially and serves as a key predictor of outcome and response to intervention in autism spectrum disorder (ASD), yet we know little about the neurobiological mechanisms that underlie cognitive function in children with ASD. The dynamics of neuronal oscillations in the alpha range (6-12 Hz) are associated with cognition in typical development. Peak alpha frequency is also highly sensitive to developmental changes in neural networks, which underlie cognitive function, and therefore, it holds promise as a developmentally sensitive neural marker of cognitive function in ASD. Here, we measured peak alpha band frequency under a task-free condition in a heterogeneous sample of children with ASD (N = 59) and age-matched typically developing (TD) children (N = 38). At a group level, peak alpha frequency was decreased in ASD compared to TD children. Moreover, within the ASD group, peak alpha frequency correlated strongly with non-verbal cognition. As peak alpha frequency reflects the integrity of neural networks, our results suggest that deviations in network development may underlie cognitive function in individuals with ASD. By shedding light on the neurobiological correlates of cognitive function in ASD, our findings lay the groundwork for considering peak alpha frequency as a useful biomarker of cognitive function within this population which, in turn, will facilitate investigations of early markers of cognitive impairment and predictors of outcome in high risk infants.

Time-dynamic profiling with application to hospital readmission among patients on dialysis.

Standard profiling analysis aims to evaluate medical providers, such as hospitals, nursing homes, or dialysis facilities, with respect to a patient outcome. The outcome, for instance, may be mortality, medical complications, or 30-day (unplanned) hospital readmission. Profiling analysis involves regression modeling of a patient outcome, adjusting for patient health status at baseline, and comparing each provider's outcome rate (e.g., 30-day readmission rate) to a normative standard (e.g., national "average"). Profiling methods exist mostly for non time-varying patient outcomes. However, for patients on dialysis, a unique population which requires continuous medical care, methodologies to monitor patient outcomes continuously over time are particularly relevant. Thus, we introduce a novel time-dynamic profiling (TDP) approach to assess the time-varying 30-day readmission rate. TDP is used to estimate, for the first time, the risk-standardized time-dynamic 30-day hospital readmission rate, throughout the time period that patients are on dialysis. We develop the framework for TDP by introducing the standardized dynamic readmission ratio as a function of time and a multilevel varying coefficient model with facility-specific time-varying effects. We propose estimation and inference procedures tailored to the problem of TDP and to overcome the challenge of high-dimensional parameters when examining thousands of dialysis facilities.

Modeling time-varying effects of multilevel risk factors of hospitalizations in patients on dialysis.

For chronic dialysis patients, a unique population requiring continuous medical care, methodologies to monitor patient outcomes, such as hospitalizations, over time, after initiation of dialysis, are of particular interest. Contributing to patient hospitalizations is a number of multilevel covariates such as demographics and comorbidities at the patient level and staffing composition at the dialysis facility level. We propose a varying coefficient model for multilevel risk factors (VCM-MR) to study the time-varying effects of covariates on patient hospitalization risk as a function of time on dialysis. The proposed VCM-MR also includes subject-specific random effects to account for within-subject correlation and dialysis facility-specific fixed effect varying coefficient functions to allow for the modeling of flexible time-varying facility-specific risk trajectories. An approximate EM algorithm and an iterative Newton-Raphson approach are proposed to address the challenge of estimation of high-dimensional parameters (varying coefficient functions) for thousands of dialysis facilities in the United States. The proposed modeling allows for comparisons between time-varying effects of multilevel risk factors as well as testing of facility-specific fixed effects. The method is applied to model hospitalization risk using the rich hierarchical data available on dialysis patients initiating dialysis between January 1, 2006 and December 31, 2008 from the United States Renal Data System, a large national database, where 331 443 hospitalizations over time are nested within patients, and 89 889 patients are nested within 2201 dialysis facilities. Patients are followed-up until December 31, 2013, where the follow-up time is truncated five years after the initiation of dialysis. Finite sample properties are studied through extensive simulations.

Robust functional clustering of ERP data with application to a study of implicit learning in autism.

Motivated by a study on visual implicit learning in young children with Autism Spectrum Disorder (ASD), we propose a robust functional clustering (RFC) algorithm to identify subgroups within electroencephalography (EEG) data. The proposed RFC is an iterative algorithm based on functional principal component analysis, where cluster membership is updated via predictions of the functional trajectories obtained through a non-parametric random effects model. We consider functional data resulting from event-related potential (ERP) waveforms representing EEG time-locked to stimuli over the course of an implicit learning experiment, after applying a previously proposed meta-preprocessing step. This meta-preprocessing is designed to increase the low signal-to-noise ratio in the raw data and to mitigate the longitudinal changes in the ERP waveforms which characterize the nature and speed of learning. The resulting functional ERP components (peak amplitudes and latencies) inherently exhibit covariance heterogeneity due to low data quality over some stimuli inducing the averaging of different numbers of waveforms in sliding windows of the meta-preprocessing step. The proposed RFC algorithm incorporates this known covariance heterogeneity into the clustering algorithm, improving cluster quality, as illustrated in the data application and extensive simulation studies. ASD is a heterogeneous syndrome and identifying subgroups within ASD children is of interest for understanding the diverse nature of this complex disorder. Applications to the implicit learning paradigm identify subgroups within ASD and typically developing children with diverse learning patterns over the course of the experiment, which may inform clinical stratification of ASD.