A Bayesian semi-parametric scalar-on-function regression with measurement error using instrumental variables.

Wearable devices such as the ActiGraph are now commonly used in research to monitor or track physical activity. This trend corresponds with the growing need to assess the relationships between physical activity and health outcomes, such as obesity, accurately. Device-based physical activity measures are best treated as functions when assessing their associations with scalar-valued outcomes such as body mass index. Scalar-on-function regression (SoFR) is a suitable regression model in this setting. Most estimation approaches in SoFR assume that the measurement error in functional covariates is white noise. Violating this assumption can lead to underestimating model parameters. There are limited approaches to correcting measurement errors for frequentist methods and none for Bayesian methods in this area. We present a non-parametric Bayesian measurement error-corrected SoFR model that relaxes all the constraining assumptions often involved with these models. Our estimation relies on an instrumental variable allowing a time-varying biasing factor, a significant departure from the current generalized method of moment (GMM) approach. Our proposed method also permits model-based grouping of the functional covariate following measurement error correction. This grouping of the measurement error-corrected functional covariate allows additional ease of interpretation of how the different groups differ. Our method is easy to implement, and we demonstrate its finite sample properties in extensive simulations. Finally, we applied our method to data from the National Health and Examination Survey to assess the relationship between wearable device-based measures of physical activity and body mass index in adults in the United States.

Predicting plant disease epidemics using boosted regression trees.

Plant epidemics are often associated with weather-related variables. It is difficult to identify weather-related predictors for models predicting plant epidemics. In the article by Shah et al., to predict Fusarium head blight (FHB) epidemics of wheat, they explored a functional approach using scalar-on-function regression to model a binary outcome (FHB epidemic or non-epidemic) with respect to weather time series spanning 140 days relative to anthesis. The scalar-on-function models fit the data better than previously described logistic regression models. In this work, given the same dataset and models, we attempt to reproduce the article by Shah et al. using a different approach, boosted regression trees. After fitting, the classification accuracy and model statistics are surprisingly good.

Functional support vector machine.

Linear and generalized linear scalar-on-function modeling have been commonly used to understand the relationship between a scalar response variable (e.g. continuous, binary outcomes) and functional predictors. Such techniques are sensitive to model misspecification when the relationship between the response variable and the functional predictors is complex. On the other hand, support vector machines (SVMs) are among the most robust prediction models but do not take account of the high correlations between repeated measurements and cannot be used for irregular data. In this work, we propose a novel method to integrate functional principal component analysis with SVM techniques for classification and regression to account for the continuous nature of functional data and the nonlinear relationship between the scalar response variable and the functional predictors. We demonstrate the performance of our method through extensive simulation experiments and two real data applications: the classification of alcoholics using electroencephalography signals and the prediction of glucobrassicin concentration using near-infrared reflectance spectroscopy. Our methods especially have more advantages when the measurement errors in functional predictors are relatively large.

Compositional functional regression and isotemporal substitution analysis: Methods and application in time-use epidemiology.

The distribution of time that people spend in physical activity of various intensities has important health implications. Physical activity (commonly categorised by the intensity into light, moderate and vigorous physical activity), sedentary behaviour and sleep, should not be analysed separately, because they are parts of a time-use composition with a natural constraint of 24 h/day. To find out how are relative reallocations of time between physical activity of various intensities associated with health, herewith we describe compositional scalar-on-function regression and a newly developed compositional functional isotemporal substitution analysis. Physical activity intensity data can be considered as probability density functions, which better reflects the continuous character of their measurement using accelerometers. These probability density functions are characterised by specific properties, such as scale invariance and relative scale, and they are geometrically represented using Bayes spaces with the Hilbert space structure. This makes possible to process them using standard methods of functional data analysis in the L2 space, via centred logratio (clr) transformation. The scalar-on-function regression with clr transformation of the explanatory probability density functions and compositional functional isotemporal substitution analysis were applied to a dataset from a cross-sectional study on adiposity conducted among school-aged children in the Czech Republic. Theoretical reallocations of time to physical activity of higher intensities were found to be associated with larger and more progressive expected decreases in adiposity. We obtained a detailed insight into the dose-response relationship between physical activity intensity and adiposity, which was enabled by using the compositional functional approach.

An integrative latent class model of heterogeneous data modalities for diagnosing kidney obstruction.

Radionuclide imaging plays a critical role in the diagnosis and management of kidney obstruction. However, most practicing radiologists in US hospitals have insufficient time and resources to acquire training and experience needed to interpret radionuclide images, leading to increased diagnostic errors. To tackle this problem, Emory University embarked on a study that aims to develop a computer-assisted diagnostic (CAD) tool for kidney obstruction by mining and analyzing patient data comprised of renogram curves, ordinal expert ratings on the obstruction status, pharmacokinetic variables, and demographic information. The major challenges here are the heterogeneity in data modes and the lack of gold standard for determining kidney obstruction. In this article, we develop a statistically principled CAD tool based on an integrative latent class model that leverages heterogeneous data modalities available for each patient to provide accurate prediction of kidney obstruction. Our integrative model consists of three sub-models (multilevel functional latent factor regression model, probit scalar-on-function regression model, and Gaussian mixture model), each of which is tailored to the specific data mode and depends on the unknown obstruction status (latent class). An efficient MCMC algorithm is developed to train the model and predict kidney obstruction with associated uncertainty. Extensive simulations are conducted to evaluate the performance of the proposed method. An application to an Emory renal study demonstrates the usefulness of our model as a CAD tool for kidney obstruction.

Multiple exposure distributed lag models with variable selection.

Distributed lag models are useful in environmental epidemiology as they allow the user to investigate critical windows of exposure, defined as the time periods during which exposure to a pollutant adversely affects health outcomes. Recent studies have focused on estimating the health effects of a large number of environmental exposures, or an environmental mixture, on health outcomes. In such settings, it is important to understand which environmental exposures affect a particular outcome, while acknowledging the possibility that different exposures have different critical windows. Further, in studies of environmental mixtures, it is important to identify interactions among exposures and to account for the fact that this interaction may occur between two exposures having different critical windows. Exposure to one exposure early in time could cause an individual to be more or less susceptible to another exposure later in time. We propose a Bayesian model to estimate the temporal effects of a large number of exposures on an outcome. We use spike-and-slab priors and semiparametric distributed lag curves to identify important exposures and exposure interactions and discuss extensions with improved power to detect harmful exposures. We then apply these methods to estimate the effects of exposure to multiple air pollutants during pregnancy on birthweight from vital records in Colorado.

Developing Multimodal Dynamic Functional Connectivity as a Neuroimaging Biomarker.

Background: In spite of increasing evidence highlighting the role of dynamic functional connectivity (FC) in characterizing mental disorders, there is a lack of (a) reliable statistical methods to compute dynamic connectivity and (b) rigorous dynamic FC-based approaches for predicting mental health outcomes in heterogeneous disorders such as post-traumatic stress disorder (PTSD). Methods: In one of the first such efforts, we develop a reliable and accurate approach for estimating dynamic FC guided by brain structural connectivity (SC) computed using diffusion tensor imaging data and investigate the potential of the proposed multimodal dynamic FC to predict continuous mental health outcomes. We develop concrete measures of temporal network variability that are predictive of PTSD resilience, and identify regions whose temporal connectivity fluctuations are significantly related to resilience. Results: Our results illustrate that the multimodal approach is more sensitive to connectivity change points, it can clearly detect localized brain regions with the dynamic network features such as small-worldedness, clustering coefficients, and efficiency associated with resilience, and that it has superior predictive performance compared with existing static and dynamic network models when modeling PTSD resilience. Discussion: While the majority of resting-state network modeling in psychiatry has focused on static FC, our novel multimodal dynamic network analyses that are sensitive to network fluctuations allowed us to provide a model of neural correlates of resilience with high accuracy compared with existing static connectivity approaches or those that do not use brain SC information, and provided us with an expanded understanding of the neurobiological causes for PTSD. Impact statement The methods developed in this article provide reliable and accurate dynamic functional connectivity (FC) approaches by fusing multimodal imaging data that are highly predictive of continuous clinical phenotypes in heterogeneous mental disorders. Currently, there is very little theoretical work to explain how network dynamics might contribute to individual differences in behavior or psychiatric symptoms. Our analysis conclusively discovers localized brain resting-state networks, regions, and connections where variations in dynamic FC (that is estimated after incorporating brain structural connectivity information) are associated with post-traumatic stress disorder resilience, which could potentially provide valuable tools for the development of neural circuit modeling in psychiatry in the future.

Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density.

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously estimate the bandwidths in the regression function and kernel error density by minimizing the Kullback-Leibler divergence. For estimating the regression function and error density, a series of simulation studies demonstrate that the functional partial linear model gives improved estimation and forecast accuracies compared with the functional principal component regression and functional nonparametric regression. Using a spectroscopy dataset, the functional partial linear model yields better forecast accuracy than some commonly used functional regression models. As a by-product of the Bayesian method, a pointwise prediction interval can be obtained, and marginal likelihood can be used to select the optimal semi-metric.

Scalar-on-function regression for predicting distal outcomes from intensively gathered longitudinal data: Interpretability for applied scientists.

Researchers are sometimes interested in predicting a distal or external outcome (such as smoking cessation at follow-up) from the trajectory of an intensively recorded longitudinal variable (such as urge to smoke). This can be done in a semiparametric way via scalar-on-function regression. However, the resulting fitted coefficient regression function requires special care for correct interpretation, as it represents the joint relationship of time points to the outcome, rather than a marginal or cross-sectional relationship. We provide practical guidelines, based on experience with scientific applications, for helping practitioners interpret their results and illustrate these ideas using data from a smoking cessation study.

Predicting plant disease epidemics from functionally represented weather series.

Epidemics are often triggered by specific weather patterns favouring the pathogen on susceptible hosts. For plant diseases, models predicting epidemics have therefore often emphasized the identification of early season weather patterns that are correlated with a disease outcome at some later point. Toward that end, window-pane analysis is an exhaustive search algorithm traditionally used in plant pathology for mining correlations in a weather series with respect to a disease endpoint. Here we show, with reference to Fusarium head blight (FHB) of wheat, that a functional approach is a more principled analytical method for understanding the relationship between disease epidemics and environmental conditions over an extended time series. We used scalar-on-function regression to model a binary outcome (FHB epidemic or non-epidemic) relative to weather time series spanning 140 days relative to flowering (when FHB infection primarily occurs). The functional models overall fit the data better than previously described standard logistic regression (lr) models. Periods much earlier than heretofore realized were associated with FHB epidemics. The findings were used to create novel weather summary variables which, when incorporated into lr models, yielded a new set of models that performed as well as existing lr models for real-time predictions of disease risk. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Variable-Domain Functional Regression for Modeling ICU Data.

We introduce a class of scalar-on-function regression models with subject-specific functional predictor domains. The fundamental idea is to consider a bivariate functional parameter that depends both on the functional argument and on the width of the functional predictor domain. Both parametric and nonparametric models are introduced to fit the functional coefficient. The nonparametric model is theoretically and practically invariant to functional support transformation, or support registration. Methods were motivated by and applied to a study of association between daily measures of the Intensive Care Unit (ICU) Sequential Organ Failure Assessment (SOFA) score and two outcomes: in-hospital mortality, and physical impairment at hospital discharge among survivors. Methods are generally applicable to a large number of new studies that record a continuous variables over unequal domains.