383 research outputs found
Regression Trees for Longitudinal Data
While studying response trajectory, often the population of interest may be
diverse enough to exist distinct subgroups within it and the longitudinal
change in response may not be uniform in these subgroups. That is, the
timeslope and/or influence of covariates in longitudinal profile may vary among
these different subgroups. For example, Raudenbush (2001) used depression as an
example to argue that it is incorrect to assume that all the people in a given
population would be experiencing either increasing or decreasing levels of
depression. In such cases, traditional linear mixed effects model (assuming
common parametric form for covariates and time) is not directly applicable for
the entire population as a group-averaged trajectory can mask important
subgroup differences. Our aim is to identify and characterize longitudinally
homogeneous subgroups based on the combination of baseline covariates in the
most parsimonious way. This goal can be achieved via constructing regression
tree for longitudinal data using baseline covariates as partitioning variables.
We have proposed LongCART algorithm to construct regression tree for the
longitudinal data. In each node, the proposed LongCART algorithm determines the
need for further splitting (i.e. whether parameter(s) of longitudinal profile
is influenced by any baseline attributes) via parameter instability tests and
thus the decision of further splitting is type-I error controlled. We have
obtained the asymptotic results for the proposed instability test and examined
finite sample behavior of the whole algorithm through simulation studies.
Finally, we have applied the LongCART algorithm to study the longitudinal
changes in choline level among HIV patients
Structured penalties for functional linear models---partially empirical eigenvectors for regression
One of the challenges with functional data is incorporating spatial
structure, or local correlation, into the analysis. This structure is inherent
in the output from an increasing number of biomedical technologies, and a
functional linear model is often used to estimate the relationship between the
predictor functions and scalar responses. Common approaches to the ill-posed
problem of estimating a coefficient function typically involve two stages:
regularization and estimation. Regularization is usually done via dimension
reduction, projecting onto a predefined span of basis functions or a reduced
set of eigenvectors (principal components). In contrast, we present a unified
approach that directly incorporates spatial structure into the estimation
process by exploiting the joint eigenproperties of the predictors and a linear
penalty operator. In this sense, the components in the regression are
`partially empirical' and the framework is provided by the generalized singular
value decomposition (GSVD). The GSVD clarifies the penalized estimation process
and informs the choice of penalty by making explicit the joint influence of the
penalty and predictors on the bias, variance, and performance of the estimated
coefficient function. Laboratory spectroscopy data and simulations are used to
illustrate the concepts.Comment: 29 pages, 3 figures, 5 tables; typo/notational errors edited and
intro revised per journal review proces
Filters and plant trait strategies:What steers vegetation dynamics in floodplains of regulated lowland rivers?
Gaze Self-Similarity Plot - A New Visualization Technique
Eye tracking has become a valuable way for extending knowledge of human behavior based on visual patterns. One of the most important elements of such an analysis is the presentation of obtained results, which proves to be a challenging task. Traditional visualization techniques such as scan-paths or heat maps may reveal interesting information, nonetheless many useful features are still not visible, especially when temporal characteristics of eye movement is taken into account. This paper introduces a technique called gaze self-similarity plot (GSSP) that may be applied to visualize both spatial and temporal eye movement features on the single two-dimensional plot. The technique is an extension of the idea of recurrence plots, commonly used in time series analysis. The paper presents the basic concepts of the proposed approach (two types of GSSP) complemented with some examples of what kind of information may be disclosed and finally showing areas of the GSSP possible applications
LONGITUDINAL FUNCTIONAL MODELS WITH STRUCTURED PENALTIES
Collection of functional data is becoming increasingly common including longitudinal observations in many studies. For example, we use magnetic resonance (MR) spectra collected over a period of time from late stage HIV patients. MR spectroscopy (MRS) produces a spectrum which is a mixture of metabolite spectra, instrument noise and baseline profile. Analysis of such data typically proceeds in two separate steps: feature extraction and regression modeling. In contrast, a recently-proposed approach, called partially empirical eigenvectors for regression (PEER) (Randolph, Harezlak and Feng, 2012), for functional linear models incorporates a priori knowledge via a scientifically-informed penalty operator in the regression function estimation process. We extend the scope of PEER to the longitudinal setting with continuous outcomes and longitudinal functional covariates. The method presented in this paper: 1) takes into account external information; and 2) allows for a time-varying regression function. In the proposed approach, we express the time-varying regression function as linear combination of several time-invariant component functions; the time dependence enters into the regression function through their coefficients. The estimation procedure is easy to implement due to its mixed model equivalence. We derive the precision and accuracy of the estimates and discuss their connection with the generalized singular value decomposition. Real MRS data and simulations are used to illustrate the concepts
Model-free estimation of time-varying correlation coefficients and their confidence intervals with an application to fMRI data
poster abstractOne of main interests in fMRI (functional magnetic resonance imaging) research is the study of associations between time series from different brain regions, so called functional connectivity (FC). Recently, it has become increasingly important to assess dynamic changes in FC, both during resting state and task-based fMRI experiments, as this is thought to provide the information needed to better understand the brain’s inner workings. Currently, the most common approach to estimate these dynamic changes is by computing the correlation coefficient between time series within a sliding-window. However, one of the disadvantages of this method is that it tends to overestimate the association between the time series obtained from different brain regions (Lindquist et al. 2014). Here we propose a new approach for estimating time-varying FC using the correlation between two time series and provide valid confidence bands for this estimator. We propose an algorithm based on the sliding-window approach which utilizes the multivariate linear process bootstrap. Both numerical results and an application to fMRI study will be presented
Assessing uncertainty in dynamic functional connectivity
Functional connectivity (FC) - the study of the statistical association between time series from anatomically distinct regions (Friston, 1994, 2011) - has become one of the primary areas of research in the field surrounding resting state functional magnetic resonance imaging (rs-fMRI). Although for many years researchers have implicitly assumed that FC was stationary across time in rs-fMRI, it has recently become increasingly clear that this is not the case and the ability to assess dynamic changes in FC is critical for better understanding of the inner workings of the human brain (Hutchison et al., 2013; Chang and Glover, 2010). Currently, the most common strategy for estimating these dynamic changes is to use the sliding-window technique. However, its greatest shortcoming is the inherent variation present in the estimate, even for null data, which is easily confused with true time-varying changes in connectivity (Lindquist et al., 2014). This can have serious consequences as even spurious fluctuations caused by noise can easily be confused with an important signal. For these reasons, assessment of uncertainty in the sliding-window correlation estimates is of critical importance. Here we propose a new approach that combines the multivariate linear process bootstrap (MLPB) method and a sliding-window technique to assess the uncertainty in a dynamic FC estimate by providing its confidence bands. Both numerical results and an application to rs-fMRI study are presented, showing the efficacy of the proposed method
Semiparametric Estimation of Task-Based Dynamic Functional Connectivity on the Population Level
Dynamic functional connectivity (dFC) estimates time-dependent associations between pairs of brain region time series as typically acquired during functional MRI. dFC changes are most commonly quantified by pairwise correlation coefficients between the time series within a sliding window. Here, we applied a recently developed bootstrap-based technique (Kudela et al., 2017) to robustly estimate subject-level dFC and its confidence intervals in a task-based fMRI study (24 subjects who tasted their most frequently consumed beer and Gatorade as an appetitive control). We then combined information across subjects and scans utilizing semiparametric mixed models to obtain a group-level dFC estimate for each pair of brain regions, flavor, and the difference between flavors. The proposed approach relies on the estimated group-level dFC accounting for complex correlation structures of the fMRI data, multiple repeated observations per subject, experimental design, and subject-specific variability. It also provides condition-specific dFC and confidence intervals for the whole brain at the group level. As a summary dFC metric, we used the proportion of time when the estimated associations were either significantly positive or negative. For both flavors, our fully-data driven approach yielded regional associations that reflected known, biologically meaningful brain organization as shown in prior work, as well as closely resembled resting state networks (RSNs). Specifically, beer flavor-potentiated associations were detected between several reward-related regions, including the right ventral striatum (VST), lateral orbitofrontal cortex, and ventral anterior insular cortex (vAIC). The enhancement of right VST-vAIC association by a taste of beer independently validated the main activation-based finding (Oberlin et al., 2016). Most notably, our novel dFC methodology uncovered numerous associations undetected by the traditional static FC analysis. The data-driven, novel dFC methodology presented here can be used for a wide range of task-based fMRI designs to estimate the dFC at multiple levels-group-, individual-, and task-specific, utilizing a combination of well-established statistical methods
Study of sexual partner accrual patterns among adolescent women via Generalized Additive Mixed Models
poster abstractThe number of lifetime partners is a consistently identified epidemiological risk factor for sexually transmitted infections (STIs). Higher rate of partner accrual during adolescence has been associated with increased STI rates among adolescent women. To study sexual partner accrual pattern among adolescent females, we applied generalized additive mixed models (GAMM) to the data obtained from a longitudinal STI study. GAMM regression components included a bivariate function enabling separation of cohort (“age at study entry”) and longitudinal (“follow-up years”) effects on partner accrual while the correlation was accounted for by the subject-specific random components. Longitudinal effect partial derivative was used to estimate within-subject rates of partner accrual and their standard errors. The results show that slowing of partner accrual depends more on the prior sexual experience and less on the females’ chronological age. Our modeling approach combining the GAMM flexibility and the time covariates’ of interest definition enabled clear differentiation between the cohort (chronological age) and longitudinal (follow-up time) effects, thus providing the estimates of both between-subject differences and within-subject trajectories of partner accrual
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