A test for the slope in the functional measurement error model

There are two measurement error models in linear regression, the structural and the functional. Theoretical investigations and applications are concentrated on the structural model with jointly normally and identically distributed observations because there is no test for the slope in the functional model so far. This gap will be closed here for the model with one independent variable. Furthermore it is stated that the functional model is a natural extension of the classical linear regression model with one independent variable if there are errors of measurement in both variables. Moreover it is not postulated in the functional model that the expectations are equal. So the functional model is more realistic than the structural

Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regression models with errors--in--variables, in the case where various data sets are merged into a single analysis and the observable variables deviate possibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possible non--normality of the data, normal--theory methods yield correct inferences for the parameters of interest and for the goodness--of--fit test. The theory described encompasses both the functional and structural model cases, and can be implemented using standard software for structural equations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.Asymptotic robustness, multivariate regression, asymptotic efficiency, normal theory methods, multi--samples, errors--in--variables

A model of impairment and functional limitation in rheumatoid arthritis

BACKGROUND: We have previously proposed a theoretical model for studying physical disability and other outcomes in rheumatoid arthritis (RA). The purpose of this paper is to test a model of impairment and functional limitation in (RA), using empirical data from a sample of RA patients. We based the model on the disablement process framework. METHODS: We posited two distinct types of impairment in RA: 1) Joint inflammation, measured by the tender, painful and swollen joint counts; and 2) Joint deformity, measured by the deformed joint count. We hypothesized direct paths from the two impairments to functional limitation, measured by the shirt-button speed, grip strength and walking velocity. We used structural equation modeling to test the hypothetical relationships, using empirical data from a sample of RA patients recruited from six rheumatology clinics. RESULTS: The RA sample was comprised of 779 RA patients. In the structural equation model, the joint inflammation impairment displayed a strong significant path toward the measured variables of joint pain, tenderness and swelling (standardized regression coefficients 0.758, 0.872 and 0.512, P ≤ 0.001 for each). The joint deformity impairment likewise displayed significant paths toward the measured upper limb, lower limb, and other deformed joint counts (standardized regression coefficients 0.849, 0.785, 0.308, P ≤ 0.001 for each). Both the joint inflammation and joint deformity impairments displayed strong direct paths toward functional limitation (standardized regression coefficients of -0.576 and -0.564, respectively, P ≤ 0.001 for each), and explained 65% of its variance. Model fit to data was fair to good, as evidenced by a comparative fit index of 0.975, and the root mean square error of approximation = 0.058. CONCLUSION: This evidence supports the occurrence of two distinct impairments in RA, joint inflammation and joint deformity, that together, contribute strongly to functional limitations in this disease. These findings may have implications for investigators aiming to measure outcome in RA

Stronger prediction of motor recovery and outcome post-stroke by cortico-spinal tract integrity than functional connectivity

<div><p>Objectives</p><p>To examine longitudinal changes in structural and functional connectivity post-stroke in patients with motor impairment, and define their importance for recovery and outcome at 12 months.</p><p>Methods</p><p>First-time stroke patients (N = 31) were studied at 1–2 weeks, 3 months, and 12 months post-injury with a validated motor battery and resting-state fMRI to measure inter-hemispheric functional connectivity (FC). Fractional anisotropy (FA) of the cortico-spinal tract (CST) was derived from diffusion tensor imaging as a measure of white matter organization. ANOVAs were used to test for changes in FC, FA, and motor performance scores over time, and regression analysis related motor outcome to clinical and neuroimaging variables.</p><p>Results</p><p>FA of the ipsilesional CST improved significantly from 3 to 12 months and was strongly correlated with motor performance. FA improved even in the absence of direct damage to the CST. Inter-hemispheric FC also improved over time, but did not correlate with motor performance at 12 months. Clinical variables (early motor score, education level, and age) predicted 80.4% of the variation of motor outcome, and FA increased the predictability to 84.6%. FC did not contribute to the prediction of motor outcome.</p><p>Conclusions</p><p>Stroke causes changes to the CST microstructure that can account for behavioral variability even in the absence of demonstrable lesion. Ipsilesional CST undergoes remodeling post-stroke, even past the three-month window when most of the motor recovery happens. FA of the CST, but not inter-hemispheric FC, can improve to the prediction of motor outcome based on early motor scores.</p></div

Detecting relevant changes in time series models

Most of the literature on change-point analysis by means of hypothesis testing considers hypotheses of the form H0 : \theta_1 = \theta_2 vs. H1 : \theta_1 != \theta_2, where \theta_1 and \theta_2 denote parameters of the process before and after a change point. This paper takes a different perspective and investigates the null hypotheses of no relevant changes, i.e. H0 : ||\theta_1 - \theta_2|| ? \leq \Delta?, where || \cdot || is an appropriate norm. This formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary, if the difference between the parameters before and after the change-point is small. A general approach to problems of this type is developed which is based on the CUSUM principle. For the asymptotic analysis weak convergence of the sequential empirical process has to be established under the alternative of non-stationarity, and it is shown that the resulting test statistic is asymptotically normal distributed. Several applications of the methodology are given including tests for relevant changes in the mean, variance, parameter in a linear regression model and distribution function among others. The finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analyzing a data example from economics.Comment: Keywords: change-point analysis, CUSUM, relevant changes, precise hypotheses, strong mixing, weak convergence under the alternative AMS Subject Classification: 62M10, 62F05, 62G1

Lagged and instantaneous dynamical influences related to brain structural connectivity

Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Different MRI acquisitions provide different brain networks at the macroscale; whilst diffusion-weighted MRI (dMRI) provides a structural connectivity (SC) coincident with the bundles of parallel fibers between brain areas, functional MRI (fMRI) accounts for the variations in the blood-oxygenation-level-dependent T2* signal, providing functional connectivity (FC).Understanding the precise relation between FC and SC, that is, between brain dynamics and structure, is still a challenge for neuroscience. To investigate this problem, we acquired data at rest and built the corresponding SC (with matrix elements corresponding to the fiber number between brain areas) to be compared with FC connectivity matrices obtained by 3 different methods: directed dependencies by an exploratory version of structural equation modeling (eSEM), linear correlations (C) and partial correlations (PC). We also considered the possibility of using lagged correlations in time series; so, we compared a lagged version of eSEM and Granger causality (GC). Our results were two-fold: firstly, eSEM performance in correlating with SC was comparable to those obtained from C and PC, but eSEM (not C nor PC) provides information about directionality of the functional interactions. Second, interactions on a time scale much smaller than the sampling time, captured by instantaneous connectivity methods, are much more related to SC than slow directed influences captured by the lagged analysis. Indeed the performance in correlating with SC was much worse for GC and for the lagged version of eSEM. We expect these results to supply further insights to the interplay between SC and functional patterns, an important issue in the study of brain physiology and function.Comment: Accepted and published in Frontiers in Psychology in its current form. 27 pages, 1 table, 5 figures, 2 suppl. figure

Functional connectivity changes and their relationship with clinical disability and white matter integrity in patients with relapsing-remitting multiple sclerosis

Background and objective: To define the pathological substrate underlying disability in multiple sclerosis by evaluating the relationship of resting-state functional connectivity with microstructural brain damage, as assessed by diffusion tensor maging, and clinical impairments. Methods: Thirty relapsing–remitting patients and 24 controls underwent 3T-MRI; motor abilities were evaluated by using measures of walking speed, hand dexterity and balance capability, while information processing speed was evaluated by a paced auditory serial addiction task. Independent component analysis and tract-based spatial statistics were applied to RS-fMRI and diffusion tensor imaging data using FSL software. Group differences, after dual regression, and clinical correlations were modelled with GeneralLinear-Model and corrected for multiple comparisons. Results: Patients showed decreased functional connectivity in 5 of 11 resting-state-networks (cerebellar, executive-control, medial-visual, basal ganglia and sensorimotor), changes in inter-network correlations and widespread white matter microstructural damage. In multiple sclerosis, corpus callosum microstructural damage positively correlated with functional connectivity in cerebellar and auditory networks. Moreover, functional connectivity within the medial-visual network inversely correlated with information processing speed. White matter widespread microstructural damage inversely correlated with both the paced auditory serial addiction task and hand dexterity. Conclusions: Despite the within-network functional connectivity decrease and the widespread microstructural damage, the inter-network functional connectivity changes suggest a global brain functional rearrangement in multiple sclerosis. The correlation between functional connectivity alterations and callosal damage uncovers a link between functional and structural connectivity. Finally, functional connectivity abnormalities affect information processing speed rather than motor abilities