In Acute Severe Ulcerative Colitis Patients Who Receive Rescue Therapy, Prior Maintenance Therapy and Day 3 C-Reactive Protein After Rescue Therapy Are Associated With 12-Month Colectomy Risk.

In steroid-refractory patients with acute severe ulcerative colitis, the number of advanced therapies prior to admission and day 3 C-reactive protein post­rescue therapy is associated with a higher risk of colectomy within 12 months.

A nonparametric test of group distributional differences for hierarchically clustered functional data.

Biological sex and gender are critical variables in biomedical research, but are complicated by the presence of sex-specific natural hormone cycles, such as the estrous cycle in female rodents, typically divided into phases. A common feature of these cycles are fluctuating hormone levels that induce sex differences in many behaviors controlled by the electrophysiology of neurons, such as neuronal membrane potential in response to electrical stimulus, typically summarized using a priori defined metrics. In this paper, we propose a method to test for differences in the electrophysiological properties across estrous cycle phase without first defining a metric of interest. We do this by modeling membrane potential data in the frequency domain as realizations of a bivariate process, also depending on the electrical stimulus, by adopting existing methods for longitudinal functional data. We are then able to extract the main features of the bivariate signals through a set of basis function coefficients. We use these coefficients for testing, adapting methods for multivariate data to account for an induced hierarchical structure that is a product of the experimental design. We illustrate the performance of the proposed approach in simulations and then apply the method to experimental data.

Inference in Functional Linear Quantile Regression.

In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from functional principal component analysis and quantile regression. An adjusted Wald testing procedure is proposed for this hypothesis of interest, and its chi-square asymptotic null distribution is derived. The testing procedure is investigated numerically in simulations involving sparse and noisy functional covariates and in a capital bike share data application. The proposed approach is easy to implement and the R code is published online at https://github.com/xylimeng/fQR-testing.

Novel approach to modeling high-frequency activity data to assess therapeutic effects of analgesics in chronic pain conditions.

Osteoarthritis (OA) is a chronic condition often associated with pain, affecting approximately fourteen percent of the population, and increasing in prevalence. A globally aging population have made treating OA-associated pain as well as maintaining mobility and activity a public health priority. OA affects all mammals, and the use of spontaneous animal models is one promising approach for improving translational pain research and the development of effective treatment strategies. Accelerometers are a common tool for collecting high-frequency activity data on animals to study the effects of treatment on pain related activity patterns. There has recently been increasing interest in their use to understand treatment effects in human pain conditions. However, activity patterns vary widely across subjects; furthermore, the effects of treatment may manifest in higher or lower activity counts or in subtler ways like changes in the frequency of certain types of activities. We use a zero inflated Poisson hidden semi-Markov model to characterize activity patterns and subsequently derive estimators of the treatment effect in terms of changes in activity levels or frequency of activity type. We demonstrate the application of our model, and its advance over traditional analysis methods, using data from a naturally occurring feline OA-associated pain model.

Longitudinal dynamic functional regression.

The paper develops a parsimonious modelling framework to study the time-varying association between scalar outcomes and functional predictors observed at many instances, in longitudinal studies. The methods enable us to reconstruct the full trajectory of the response and are applicable to Gaussian and non-Gaussian responses. The idea is to model the time-varying functional predictors by using orthogonal basis functions and to expand the time-varying regression coefficient by using the same basis. Numerical investigation through simulation studies and data analysis show excellent performance in terms of accurate prediction and efficient computations, when compared with existing alternatives. The methods are inspired and applied to an animal science application, where of interest is to study the association between the feed intake of lactating sows and the minute-by-minute temperature throughout the 21 days of their lactation period. R code and an R illustration are provided.

A Spatio-Temporal Model for Longitudinal Image-on-Image Regression.

Neurologists and radiologists often use magnetic resonance imaging (MRI) in the management of subjects with multiple sclerosis (MS) because it is sensitive to inflammatory and demyelinative changes in the white matter of the brain and spinal cord. Two conventional modalities used for identifying lesions are T1-weighted (T1) and T2-weighted fluid-attenuated inversion recovery (FLAIR) imaging, which are used clinically and in research studies. Magnetization transfer ratio (MTR), which is available only in research settings, is an advanced MRI modality that has been used extensively for measuring disease-related demyelination both in white matter lesions as well across normal-appearing white matter. Acquiring MTR is not standard in clinical practice, due to the increased scan time and cost. Hence, prediction of MTR based on the modalities T1 and FLAIR could have great impact on the availability of these promising measures for improved patient management. We propose a spatio-temporal regression model for image response and image predictors that are acquired longitudinally, with images being co-registered within the subject but not across subjects. The model is additive, with the response at a voxel being dependent on the available covariates not only through the current voxel but also on the imaging information from the voxels within a neighboring spatial region as well as their temporal gradients. We propose a dynamic Bayesian estimation procedure that updates the parameters of the subject-specific regression model as data accummulates. To bypass the computational challenges associated with a Bayesian approach for high-dimensional imaging data, we propose an approximate Bayesian inference technique. We assess the model fitting and the prediction performance using longitudinally acquired MRI images from 46 MS patients.

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.

Additive Nonlinear Functional Concurrent Model.

We propose a flexible regression model to study the association between a functional response and multiple functional covariates that are observed on the same domain. Specifically, we relate the mean of the current response to current values of the covariates by a sum of smooth unknown bivariate functions, where each of the functions depends on the current value of the covariate and the time point itself. In this framework, we develop estimation methodology that accommodates realistic scenarios where the covariates are sampled with or without error on a sparse and irregular design, and prediction that accounts for unknown model correlation structure. We also discuss the problem of testing the null hypothesis that the covariate has no association with the response. The proposed methods are evaluated numerically through simulations and two real data applications.

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.

Additive Function-on-Function Regression.

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary Material for this article is available online.

A Functional Data Analysis of Spatiotemporal Trends and Variation in Fine Particulate Matter.

In this paper we illustrate the application of modern functional data analysis methods to study the spatiotemporal variability of particulate matter components across the United States. The approach models the pollutant annual profiles in a way that describes the dynamic behavior over time and space. This new technique allows us to predict yearly profiles for locations and years at which data are not available and also offers dimension reduction for easier visualization of the data. Additionally it allows us to study changes of pollutant levels annually or for a particular season. We apply our method to daily concentrations of two particular components of PM2.5 measured by two networks of monitoring sites across the United States from 2003 to 2015. Our analysis confirms existing findings and additionally reveals new trends in the change of the pollutants across seasons and years that may not be as easily determined from other common approaches such as Kriging.

Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process.

This work concerns spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models and develop an efficient posterior computational aigorithm. The proposed soft-thresholded Gaussian process provides large prior support over the class of piecewise-smooth, sparse, and continuous spatially-varying regression coefficient functions. In addition, under some mild regularity conditions the soft-thresholded Gaussian proess prior leads to the posterior consistency for parameter estimation and variable selection for scalar-on-image regression, even when the number of predictors is larger than the sample size. The proposed method is compared to alternatives via simulation and applied to an electroen-cephalography study of alcoholism.

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.

Fully Bayesian spectral methods for imaging data.

Medical imaging data with thousands of spatially correlated data points are common in many fields. Methods that account for spatial correlation often require cumbersome matrix evaluations which are prohibitive for data of this size, and thus current work has either used low-rank approximations or analyzed data in blocks. We propose a method that accounts for nonstationarity, functional connectivity of distant regions of interest, and local signals, and can be applied to large multi-subject datasets using spectral methods combined with Markov Chain Monte Carlo sampling. We illustrate using simulated data that properly accounting for spatial dependence improves precision of estimates and yields valid statistical inference. We apply the new approach to study associations between cortical thickness and Alzheimer's disease, and find several regions of the cortex where patients with Alzheimer's disease are thinner on average than healthy controls.

Reduced Target Facilitation and Increased Distractor Suppression During Mind Wandering.

The perceptual decoupling hypothesis suggests a general mechanism that while mind wandering, our attention is detached from our environment, resulting in diminished processing of external stimuli. This study focused on examining two possible specific mechanisms: the global suppression of all external stimuli, and a combination of reduced target facilitation and increased distractor suppression. An attentional capture task was used in which certain trials measured distractor suppression effects and others assessed target facilitation effects. The global suppression account predicts negative impacts on both types of trials, while the combined mechanisms of reduced target facilitation and increased distractor suppression suggest that only target-present trials would be affected. Results showed no cost of mind wandering on target-absent trials, but significant distractor suppression and target facilitation effects during mind wandering on target-present trials. These findings suggest that rather than perceptual decoupling globally suppressing all stimuli, it is more selective, falling in line with evidence on strong top-down modulation.

The Use of Functional Data Analysis to Evaluate Activity in a Spontaneous Model of Degenerative Joint Disease Associated Pain in Cats.

INTRODUCTION AND OBJECTIVES: Accelerometry is used as an objective measure of physical activity in humans and veterinary species. In cats, one important use of accelerometry is in the study of therapeutics designed to treat degenerative joint disease (DJD) associated pain, where it serves as the most widely applied objective outcome measure. These analyses have commonly used summary measures, calculating the mean activity per-minute over days and comparing between treatment periods. While this technique has been effective, information about the pattern of activity in cats is lost. In this study, functional data analysis was applied to activity data from client-owned cats with (n = 83) and without (n = 15) DJD. Functional data analysis retains information about the pattern of activity over the 24-hour day, providing insight into activity over time. We hypothesized that 1) cats without DJD would have higher activity counts and intensity of activity than cats with DJD; 2) that activity counts and intensity of activity in cats with DJD would be inversely correlated with total radiographic DJD burden and total orthopedic pain score; and 3) that activity counts and intensity would have a different pattern on weekends versus weekdays. RESULTS AND CONCLUSIONS: Results showed marked inter-cat variability in activity. Cats exhibited a bimodal pattern of activity with a sharp peak in the morning and broader peak in the evening. Results further showed that this pattern was different on weekends than weekdays, with the morning peak being shifted to the right (later). Cats with DJD showed different patterns of activity from cats without DJD, though activity and intensity were not always lower; instead both the peaks and troughs of activity were less extreme than those of the cats without DJD. Functional data analysis provides insight into the pattern of activity in cats, and an alternative method for analyzing accelerometry data that incorporates fluctuations in activity across the day.

Functional feature construction for individualized treatment regimes.

Evidence-based personalized medicine formalizes treatment selection as an individualized treatment regime that maps up-to-date patient information into the space of possible treatments. Available patient information may include static features such race, gender, family history, genetic and genomic information, as well as longitudinal information including the emergence of comorbidities, waxing and waning of symptoms, side-effect burden, and adherence. Dynamic information measured at multiple time points before treatment assignment should be included as input to the treatment regime. However, subject longitudinal measurements are typically sparse, irregularly spaced, noisy, and vary in number across subjects. Existing estimators for treatment regimes require equal information be measured on each subject and thus standard practice is to summarize longitudinal subject information into a scalar, ad hoc summary during data pre-processing. This reduction of the longitudinal information to a scalar feature precedes estimation of a treatment regime and is therefore not informed by subject outcomes, treatments, or covariates. Furthermore, we show that this reduction requires more stringent causal assumptions for consistent estimation than are necessary. We propose a data-driven method for constructing maximally prescriptive yet interpretable features that can be used with standard methods for estimating optimal treatment regimes. In our proposed framework, we treat the subject longitudinal information as a realization of a stochastic process observed with error at discrete time points. Functionals of this latent process are then combined with outcome models to estimate an optimal treatment regime. The proposed methodology requires weaker causal assumptions than Q-learning with an ad hoc scalar summary and is consistent for the optimal treatment regime.

A note on modeling sparse exponential-family functional response curves.

Non-Gaussian functional data are considered and modeling through functional principal components analysis (FPCA) is discussed. The direct extension of popular FPCA techniques to the generalized case incorrectly uses a marginal mean estimate for a model that has an inherently conditional interpretation, and thus leads to biased estimates of population and subject-level effects. The methods proposed address this shortcoming by using either a two-stage or joint estimation strategy. The performance of all methods is compared numerically in simulations. An application to ambulatory heart rate monitoring is used to further illustrate the distinctions between approaches.

Interactive graphics for functional data analyses.

Although there are established graphics that accompany the most common functional data analyses, generating these graphics for each dataset and analysis can be cumbersome and time consuming. Often, the barriers to visualization inhibit useful exploratory data analyses and prevent the development of intuition for a method and its application to a particular dataset. The refund.shiny package was developed to address these issues for several of the most common functional data analyses. After conducting an analysis, the plot shiny() function is used to generate an interactive visualization environment that contains several distinct graphics, many of which are updated in response to user input. These visualizations reduce the burden of exploratory analyses and can serve as a useful tool for the communication of results to non-statisticians.

A Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis.

Motivated by an imaging study, this paper develops a nonparametric testing procedure for testing the null hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. The objective is to formally compare white matter tract profiles between healthy individuals and multiple sclerosis patients, as assessed by conventional diffusion tensor imaging measures. We propose to decompose the curves using functional principal component analysis of a mixture process, which we refer to as marginal functional principal component analysis. This approach reduces the dimension of the testing problem in a way that enables the use of traditional nonparametric univariate testing procedures. The procedure is computationally efficient and accommodates different sampling designs. Numerical studies are presented to validate the size and power properties of the test in many realistic scenarios. In these cases, the proposed test has been found to be more powerful than its primary competitor. Application to the diffusion tensor imaging data reveals that all the tracts studied are associated with multiple sclerosis and the choice of the diffusion tensor image measurement is important when assessing axonal disruption.