Variable-Domain Functional Regression for Modeling ICU Data

Functional proportional hazards mixture cure model with applications in cancer mortality in NHANES and post ICU recovery

We develop a functional proportional hazards mixture cure model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the expectation-maximization algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness penalty. Simulation studies illustrate a satisfactory performance of the proposed method in accurately estimating the model parameters and the baseline survival function. Finally, the clinical potential of the model is demonstrated in two real data examples that incorporate rich high-dimensional biomedical signals as functional covariates measured at the baseline and constitute novel domains to apply cure survival models in contemporary medical situations. In particular, we analyze (i) minute-by-minute physical activity data from the National Health And Nutrition Examination Survey 2003-2006 to study the association between diurnal patterns of physical activity at baseline and all cancer mortality through 2019 while adjusting for other biological factors; (ii) the impact of daily functional measures of disease severity collected in the intensive care unit on post intensive care unit recovery and mortality event. Our findings provide novel epidemiological insights into the association between daily patterns of physical activity and cancer mortality. Software implementation and illustration of the proposed estimation method are provided in R.

Effectiveness of Transcutaneous Neuromodulation on Abductor Muscles Electrical Activity in Subjects with Chronic Low Back Pain: A Randomized, Controlled, Crossover Clinical Trial

Introduction

Non-specific chronic low back pain (NSCLBP) is a major cause of functional impairment, resulting in consequences like job absenteeism and reduced quality of life. Risk factors such as muscle weakness and tightness have been implicated. Electromagnetic fields have therapeutic effects on human tissue, including pain relief and muscle relaxation. This study aimed to examine the impact of a tape with magnetic particles (MPT) applied to the lumbar area on abductor muscle strength and surface electromyography (sEMG) of the Gluteus Medius and Tensor of the Fascia Lata muscles in individuals with NSCLBP.

Methods

It was carried out a double-blind, randomized, controlled, crossover trial and with test retest, with 41 consecutive patients younger than 65 years who previously diagnosed with NSCLBP to assess the effect of a MPT over hip abductor muscle strength and activity. sEMG and force data were obtained during the Hip Stability Isometric Test (HipSIT). The HipSIT was used to assess the abduction strength using a hand-held dynamometer and sEMG. The HipSIT uses the maximum voluntary isometric contraction (MVIC). Four trials were recorded and the mean extracted for analysis. The tape was applied with either a MPT or a sham magnetic particle tape (SMPT) bilaterally without tension on from L1 to L5 paravertebral muscles.

Results

The significant increase in the recruitment of fibers and the significant increase in the maximum voluntary contraction by applying MPT with respect to the SMPT, correspond to the increases in the Peak Force and the decrease in the time to reach the maximum force (peak time) of both muscles.

Conclusion

Application of a MPT in patients with NSCLBP suggests an increase in muscle strength of the Gluteus Medius and Tensor Fascia Lata bilaterally during the HipSIT test. Lumbar metameric neuromodulation with MPT improves muscle activation of the hip musculature.

Robust Inference for Partially Observed Functional Response Data

Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in quantitative ultrasound signal analysis, this paper investigates a class of robust M-estimators for partially observed functional data including functional location and quantile estimators. Consistency of the estimators is established under general conditions on the partial observation process. Under smoothness conditions on the class of M-estimators, asymptotic Gaussian process approximations are established and used for large sample inference. The large sample approximations justify a bootstrap approximation for robust inferences about the functional response process. The performance is demonstrated in simulations and in the analysis of irregular functional data from quantitative ultrasound analysis.

Mean and Covariance Estimation for Functional Snippets

We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation of the covariance function for functional snippets is challenging since information for the far off-diagonal regions of the covariance structure is completely missing. We address this difficulty by decomposing the covariance function into a variance function component and a correlation function component. The variance function can be effectively estimated nonparametrically, while the correlation part is modeled parametrically, possibly with an increasing number of parameters, to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this hybrid strategy is effective. In addition, we propose a new estimator for the variance of measurement errors and analyze its asymptotic properties. This estimator is required for the estimation of the variance function from noisy measurements.

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.

Basis expansions for functional snippets

Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. We investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly, and often much, shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

Modeling continuous glucose monitoring (CGM) data during sleep

We introduce a multilevel functional Beta model to quantify the blood glucose levels measured by continuous glucose monitors for multiple days in study participants with type 2 diabetes mellitus. The model estimates the subject-specific marginal quantiles, quantifies the within- and between-subject variability, and produces interpretable parameters of blood glucose dynamics as a function of time from the actigraphy-estimated sleep onset. Results are validated via simulations and by studying the association between the estimated model parameters and hemoglobin A1c, the gold standard for assessing glucose control in diabetes.

Extrema-weighted feature extraction for functional data

Motivation

Although there is a rich literature on methods for assessing the impact of functional predictors, the focus has been on approaches for dimension reduction that do not suit certain applications. Examples of standard approaches include functional linear models, functional principal components regression and cluster-based approaches, such as latent trajectory analysis. This article is motivated by applications in which the dynamics in a predictor, across times when the value is relatively extreme, are particularly informative about the response. For example, physicians are interested in relating the dynamics of blood pressure changes during surgery to post-surgery adverse outcomes, and it is thought that the dynamics are more important when blood pressure is significantly elevated or lowered.

Results

We propose a novel class of extrema-weighted feature (XWF) extraction models. Key components in defining XWFs include the marginal density of the predictor, a function up-weighting values at extreme quantiles of this marginal, and functionals characterizing local dynamics. Algorithms are proposed for fitting of XWF-based regression and classification models, and are compared with current methods for functional predictors in simulations and a blood pressure during surgery application. XWFs find features of intraoperative blood pressure trajectories that are predictive of postoperative mortality. By their nature, most of these features cannot be found by previous methods.

Availability and implementation

The R package 'xwf' is available at the CRAN repository: https://cran.r-project.org/package=xwf.

Supplementary information

Supplementary data are available at Bioinformatics online.

Molecular imaging of autism spectrum disorder

Autism spectrum disorder (ASD) is a condition with onset in early childhood characterized by marked deficits in interpersonal interactions and communication and by a restricted and repetitive range of interests and activities. This review points out key recent findings utilizing molecular imaging including magnetic resonance spectroscopy (MRS) and nuclear neuroimaging techniques such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT). MRS indicates an excitatory/inhibitory imbalance in high-functioning autism. Dysfunction of neurotransmitter and glucose metabolism has been demonstrated by PET and SPECT. Levels of serotonin synthesis in typically developing children are approximately twice those of adults; after the age of 5 years, levels decrease to those of adults. In contrast, levels of serotonin synthesis of children with ASD increase between ages 2 and 15 to 1.5-times adult values. The dopamine transporter is increased in the orbitofrontal cortex of men with ASD. The serotonin transporter is reduced in the brains of children, adolescents, and adults with ASD. Reduced serotonin receptors in the thalamus of adults with ASD are associated with communication difficulties. Glucose metabolism is reduced in the brains of people with ASD. Molecular imaging will provide the preliminary data for promising therapeutic interventions.

Statistical modelling for precision agriculture: A case study in optimal environmental schedules for Agaricus Bisporus production via variable domain functional regression

Quantifying the effects of environmental factors over the duration of the growing process on Agaricus Bisporus (button mushroom) yields has been difficult, as common functional data analysis approaches require fixed length functional data. The data available from commercial growers, however, is of variable duration, due to commercial considerations. We employ a recently proposed regression technique termed Variable-Domain Functional Regression in order to be able to accommodate these irregular-length datasets. In this way, we are able to quantify the contribution of covariates such as temperature, humidity and water spraying volumes across the growing process, and for different lengths of growing processes. Our results indicate that optimal oxygen and temperature levels vary across the growing cycle and we propose environmental schedules for these covariates to optimise overall yields.

Flexible Bayesian additive joint models with an application to type 1 diabetes research

The joint modeling of longitudinal and time-to-event data is an important tool of growing popularity to gain insights into the association between a biomarker and an event process. We develop a general framework of flexible additive joint models that allows the specification of a variety of effects, such as smooth nonlinear, time-varying and random effects, in the longitudinal and survival parts of the models. Our extensions are motivated by the investigation of the relationship between fluctuating disease-specific markers, in this case autoantibodies, and the progression to the autoimmune disease type 1 diabetes. Using Bayesian P-splines, we are in particular able to capture highly nonlinear subject-specific marker trajectories as well as a time-varying association between the marker and event process allowing new insights into disease progression. The model is estimated within a Bayesian framework and implemented in the R-package bamlss.

A joint logistic regression and covariate-adjusted continuous-time Markov chain model

The use of longitudinal measurements to predict a categorical outcome is an increasingly common goal in research studies. Joint models are commonly used to describe two or more models simultaneously by considering the correlated nature of their outcomes and the random error present in the longitudinal measurements. However, there is limited research on joint models with longitudinal predictors and categorical cross-sectional outcomes. Perhaps the most challenging task is how to model the longitudinal predictor process such that it represents the true biological mechanism that dictates the association with the categorical response. We propose a joint logistic regression and Markov chain model to describe a binary cross-sectional response, where the unobserved transition rates of a two-state continuous-time Markov chain are included as covariates. We use the method of maximum likelihood to estimate the parameters of our model. In a simulation study, coverage probabilities of about 95%, standard deviations close to standard errors, and low biases for the parameter values show that our estimation method is adequate. We apply the proposed joint model to a dataset of patients with traumatic brain injury to describe and predict a 6-month outcome based on physiological data collected post-injury and admission characteristics. Our analysis indicates that the information provided by physiological changes over time may help improve prediction of long-term functional status of these severely ill subjects. Copyright © 2017 John Wiley & Sons, Ltd.

Autoregressive and cross-lagged model for bivariate non-commensurate outcomes

Autoregressive and cross-lagged models have been widely used to understand the relationship between bivariate commensurate outcomes in social and behavioral sciences, but not much work has been carried out in modeling bivariate non-commensurate (e.g., mixed binary and continuous) outcomes simultaneously. We develop a likelihood-based methodology combining ordinary autoregressive and cross-lagged models with a shared subject-specific random effect in the mixed-model framework to model two correlated longitudinal non-commensurate outcomes. The estimates of the cross-lagged and the autoregressive effects from our model are shown to be consistent with smaller mean-squared error than the estimates from the univariate generalized linear models. Inclusion of the subject-specific random effects in the proposed model accounts for between-subject variability arising from the omitted and/or unobservable, but possibly explanatory, subject-level predictors. Our model is not restricted to the case with equal number of events per subject, and it can be extended to different types of bivariate outcomes. We apply our model to an ecological momentary assessment study with complex dependence and sampling data structures. Specifically, we study the dependence between the condom use and sexual satisfaction based on the data reported in a longitudinal study of sexually transmitted infections. We find negative cross-lagged effect between these two outcomes and positive autoregressive effect within each outcome. Copyright © 2017 John Wiley & Sons, Ltd.

Discussion of the paper ‘A general framework for functional regression modelling’

This discussion provides our reaction to the article by Greven and Scheipl. It contains an overview of their article and a description of the many areas of research that remain open and could benefit from further methodological and computational development.

Cox Regression Models with Functional Covariates for Survival Data

We extend the Cox proportional hazards model to cases when the exposure is a densely sampled functional process, measured at baseline. The fundamental idea is to combine penalized signal regression with methods developed for mixed effects proportional hazards models. The model is fit by maximizing the penalized partial likelihood, with smoothing parameters estimated by a likelihood-based criterion such as AIC or EPIC. The model may be extended to allow for multiple functional predictors, time varying coefficients, and missing or unequally-spaced data. Methods were inspired by and applied to a study of the association between time to death after hospital discharge and daily measures of disease severity collected in the intensive care unit, among survivors of acute respiratory distress syndrome.