Number Of Time Points Research Articles

WE-FG-206-02: Brief Variations of BOLD Signal in Resting State FMRI Leading to Functional Connectivity Pattern Identification

Purpose: To assess the role of spontaneous brain activity in identifying functional connectivity patterns in the brain during resting-state using both high and low blood-oxygen level dependent (BOLD) signals from functional magnetic resonance imaging (fMRI). Methods: fMRI BOLD signals within seed regions from known functional connectivity networks were extracted to find an average seed-region time profile. A threshold was applied to the BOLD signal and and time points were selected where the BOLD signal satisfied the threshold requirements. The same threshold was also applied to the time profile of each voxel in the brain, i.e., including voxels outside of the seed region. The signal profile of seed region time points above the threshold was compared to the signal profile of whole brain voxel time points over the threshold. Any time point that occurred on both signal profiles was considered a match. We then evaluated whether or not a voxel was part of the functional connectivity network based on the percentage of matching time points. Results: These findings suggest that functional connectivity patterns can be identified only using a small number of time points. Using only 10% of the time points during a functional MRI functional connectivity patterns can be reproduced with varying degrees of accuracy. Using this same method, with a 33% threshold a histogram of numbers of matches per matches possible within the region where we expect to see the functional connectivity pattern, shows no significant separation between using the top third, the middle third, or the bottom third of data. Conclusion: This work indicates that functional connectivity patterns can be reproduced not only with spontaneous activity of high signals, but also from brief instances of low BOLD signal. As the potential role of resting-state fMRI for clinical diagnosis evolves, understanding the fundamentals of functional connectivity patterns is critical. NIH R01-NS074045

An LM-type test for idiosyncratic unit roots in the exact factor model with integrated factors

ABSTRACTWe consider an exact factor model with integrated factors and propose an LM-type test for unit roots in the idiosyncratic component. We show that, for a fixed number of panel individuals (N) and when the number of time points (T) tends to infinity, the limiting distribution of the LM-type statistic is a weighted sum of independent Chi-square variables with one degree of freedom, and when T tends to infinity followed by N tending to infinity, the limiting distribution is standard normal. The results should contribute to the challenging task of deriving likelihood-based unit-root tests in dynamic factor models.

Handling high-dimensional data in air pollution forecasting tasks

In the paper methods aimed at handling high-dimensional weather forecasts data used to predict the concentrations of PM10, PM2.5, SO2, NO, CO and O3 are being proposed. The procedure employed to predict pollution normally requires historical data samples for a large number of points in time — particularly weather forecast data, actual weather data and pollution data. Likewise, it typically involves using numerous features related to atmospheric conditions. Consequently the analysis of such datasets to generate accurate forecasts becomes very cumbersome task. The paper examines a variety of unsupervised dimensionality reduction methods aimed at obtaining compact yet informative set of features. As an alternative, approach using fractional distances for data analysis tasks is being considered as well. Both strategies were evaluated on real-world data obtained from the Institute of Meteorology and Water Management in Katowice (Poland), with extended Air Pollution Forecast Model (e-APFM) being used as underlying prediction tool. It was found that employing fractional distance as a dissimilarity measure ensures the best accuracy of forecasting. Satisfactory results can be also obtained with Isomap, Landmark Isomap and Factor Analysis as dimensionality reduction techniques. These methods can be also used to formulate universal mapping, ready-to-use for data gathered at different geographical areas.

Longitudinal Assessment Design and Statistical Power for Detecting an Intervention Impact.

In evaluating randomized control trials (RCTs), statistical power analyses are necessary to choose a sample size which strikes the balance between an insufficient and an excessive design, with the latter leading to misspent resources. With the growing popularity of using longitudinal data to evaluate RCTs, statistical power calculations have become more complex. Specifically, with repeated measures, the number and frequency of measurements per person additionally influence statistical power by determining the precision with which intra-individual change can be measured as well as the reliability with which inter-individual differences in change can be assessed. The application of growth mixture models has shown that the impact of universal interventions is often concentrated among a small group of individuals at the highest level of risk. General sample size calculations were consequently not sufficient to determine whether statistical power is adequate to detect the desired effect. Currently, little guidance exists to recommend a sufficient assessment design to evaluating intervention impact. To this end, Monte Carlo simulations are conducted to assess the statistical power and precision when manipulating study duration and assessment frequency. Estimates were extracted from a published evaluation of the proximal of the Good Behavior Game (GBG) on the developmental course of aggressive behavior. Results indicated that the number of time points and the frequency of assessments influence statistical power and precision. Recommendations for the assessment design of longitudinal studies are discussed.

Dynamic ticket pricing and the impact of time – an analysis of price paths of the English soccer club Derby County

ABSTRACTResearch question: Empirical studies about dynamic ticket pricing (DTP) in sports to date have focused exclusively on the Major League Baseball and on analyzing dynamic ticket prices based on a limited number of points in time. The current study extends the literature by examining the impact of time over the whole selling period. Furthermore, the presented study is the first to analyze a dynamic pricing system of a football club in Europe.Research methods: Ticket prices for selected games of the English football club Derby County were collected daily during the 2013/2014 season. A data set of 5862 price points was analyzed by means of a hedonic pricing regression.Results and findings: The model suggests that time has a significant effect on dynamic ticket prices. Ticket prices increased monotonously over time. This finding is consistent with previous research on dynamic pricing in sports. However, the pricing system can be differentiated from models applied in the airline or the hotel industry.Implications: The current study extends the existing literature by analyzing the effect of time in the context of DTP. Sport managers can apply these findings concerning the specification of a more sophisticated pricing approach.

Detecting Appropriate Trajectories of Growth in Latent Growth Models: The Performance of Information-Based Criteria

ABSTRACTLatent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact educational policy decisions. A Monte Carlo simulation study was conducted to examine the accuracy of six information-based criteria (i.e., AIC, CAIC, AICC, BIC, nBIC, and HQIC) when selecting among various growth trajectories modeled using LGM under different sample size, number of time points, and growth trajectory scenarios. The accuracy of the information criteria generally improved as sample size increased. The cubic and linear growth models were distinguished most accurately by the information criteria. All of the nonlinear models were more easily distinguished as the number of time points increased. The comparative performance of the six information criteria was dependent upon the manipulated conditions. Implications of the findings are discussed.

Indirect enantioseparation of fluoxetine in mouse serum by derivatization with 1R-(-)-menthyl chloroformate followed by ultra high performance liquid chromatography and quadrupole time-of-flight mass spectrometry.

Here we describe a simple and sensitive analytical method for the enantioselective quantification of fluoxetine in mouse serum using ultra high performance liquid chromatography with quadrupole time-of-flight mass spectrometry. The sample preparation method included a simple deproteinization with acetonitrile in 50 μL of serum, followed by derivatization of the extracts in 50 μL of 2 mM 1R-(-)-menthyl chloroformate at 45ºC for 55 min. These conditions were statistically optimized through response surface methodology using a central composite design. Under the optimized conditions, neither racemization nor kinetic resolution occurred. The derivatized diastereomers were readily resolved on a conventional sub-2 μm C18 column under a simple gradient elution of aqueous methanol containing 0.1% formic acid. The established method was validated and found to be linear, precise, and accurate over the concentration range of 5.0-1000.0 ng/mL for both R and S enantiomers (r(2) > 0.993). Stability tests of the prepared samples at three different concentration levels showed that the R- and S-fluoxetine derivatives were relatively stable for 48 h. No significant matrix effects were observed. Last, the developed method was successfully used for enantiomeric analysis of real serum samples collected at a number of time points from mice administered with racemic fluoxetine.

D‐optimal designs for a continuous predictor in longitudinal trials with discrete‐time survival endpoints

In designing an experiment with one single, continuous predictor, the questions are composed of what is the optimal number of the predictor's values, what are these values, and how many subjects should be assigned to each of these values. In this study, locally D‐optimal designs for such experiments with discrete‐time event occurrence data are studied by using a sequential construction algorithm. Using the Weibull survival function for modeling the underlying time to event function, it is shown that the optimal designs for a linear effect of the predictor have two points that coincide with the design region's boundaries, but the design weights highly depend on the predictor effect size and its direction, the survival pattern, and the number of time points. For a quadratic effect of the predictor, three or four design points are needed.

Accounting for Time Series Errors in Partially Linear Model With Single- or Multiple-Runs

This article concerns statistical estimation of the partially linear model (PLM) for time course measurements, which are temporally correlated and allow multiple-runs for repeated measurements to enhance experimental accuracy without extending the number of time points within each trial. Such features arise naturally from biomedical data, for example, in brain fMRI, and call for special treatment beyond classical methods in either a purely nonparametric regression model or a PLM with independent errors. We develop a stepwise procedure for estimating the parametric and nonparametric components of the multiple-run PLM and making inference for parameters of interest, adaptive to either single- or multiple-run, in the presence of error temporal dependence. Simulation study and real fMRI data applications illustrate the computational simplicity and effectiveness of the proposed methods. Supplementary material for this article is available online.

Validation of Structural Equation Modeling Methods for Functional MRI Data Acquired in the Human Brainstem and Spinal Cord.

Structural equation modeling (SEM) provides a means of investigating relationships between blood oxygenation level-dependent (BOLD) signal changes in functional MRI data across neuroanatomical regions. The objectives of this study were to demonstrate adapted SEM methods for the brainstem and spinal cord, validate statistical methods and appropriate statistical thresholds, and test the methods with existing data. SEM methods were applied using an anatomical model of regions of the thalamus, brainstem, and spinal cord that are involved with pain processing. Statistical distributions (Z-scores), significance thresholds, and corrections for multiple comparisons were determined from repeated simulations using "null" data sets. SEM analyses were then applied to data from prior studies involving noxious stimulation in healthy participants. Z-score distributions were observed to vary with the number of source regions modeled, the number of time points (volumes) included in the analysis, and the time span (epoch) used for dynamic analyses. Appropriate choices of statistical thresholds and corrections for multiple comparisons were demonstrated. The results reveal consistent network features across/within studies, as well as dependences on study conditions. They show the effectiveness of a SEM method for functional MRI data from the brainstem and spinal cord.

Application of Mixed Linear Models in the Analysis of Road Surface Features

The data were collected by researchers at the Road Research Institute, in a study investigating the impact of differentfactors on road surface strength. In this statistical analysis, we apply linear mixed models (LMMs) to clustered longitudinal data, inwhich the units of analysis (points in the road) are nested within clusters (sample of four different road segments), and repeatedmeasures of road strength in these different points are collected over time with unequally spaced time intervals. The data arebalanced – each cluster has the same number of units, which are measured at the same number of time points. Because of correlateddata and different clusters in which data could be correlated, linear regression models are not appropriate here, and therefore linearmixed models are applied.

The panel-clustering method for the wave equation in two spatial dimensions

We consider the numerical solution of the wave equation in a two-dimensional domain and start from a boundary integral formulation for its discretization. We employ the convolution quadrature (CQ) for the temporal and a Galerkin boundary element method (BEM) for the spatial discretization. Our main focus is the sparse approximation of the arising sequence of boundary integral operators by panel clustering. This requires the definition of an appropriate admissibility condition such that the arising kernel functions can be efficiently approximated on admissible blocks. The resulting method has a complexity of O ( N ( N + M ) q 4 + s ) , s ? { 0 , 1 } , where N is the number of time points, M denotes the dimension of the boundary element space, and q = O ( log ? ( N M ) ) is the order of the panel-clustering expansion. Numerical experiments will illustrate the efficiency and accuracy of the proposed CQ-BEM method with panel clustering.

A time-varying effect model for studying gender differences in health behavior.

This study proposes a time-varying effect model that can be used to characterize gender-specific trajectories of health behaviors and conduct hypothesis testing for gender differences. The motivating examples demonstrate that the proposed model is applicable to not only multi-wave longitudinal studies but also short-term studies that involve intensive data collection. The simulation study shows that the accuracy of estimation of trajectory functions improves as the sample size and the number of time points increase. In terms of the performance of the hypothesis testing, the type I error rates are close to their corresponding significance levels under all combinations of sample size and number of time points. Furthermore, the power increases as the alternative hypothesis deviates more from the null hypothesis, and the rate of this increasing trend is higher when the sample size and the number of time points are larger.

Inferring Longitudinal Relationships Between Variables: Model Selection Between the Latent Change Score and Autoregressive Cross-Lagged Factor Models

This research focuses on the problem of model selection between the latent change score (LCS) model and the autoregressive cross-lagged (ARCL) model when the goal is to infer the longitudinal relationship between variables. We conducted a large-scale simulation study to (a) investigate the conditions under which these models return statistically (and substantively) different results concerning the presence of bivariate longitudinal relationships, and (b) ascertain the relative performance of an array of model selection procedures when such different results arise. The simulation results show that the primary sources of differences in parameter estimates across models are model parameters related to the slope factor scores in the LCS model (specifically, the correlation between the intercept factor and the slope factor scores) as well as the size of the data (specifically, the number of time points and sample size). Among several model selection procedures, correct selection rates were higher when using model fit indexes (i.e., comparative fit index, root mean square error of approximation) than when using a likelihood ratio test or any of several information criteria (i.e., Akaike’s information criterion, Bayesian information criterion, consistent AIC, and sample-size-adjusted BIC).

Tests for time-invariant correlation of longitudinally measured biomarkers.

Our work is motivated by a study that longitudinally measured serum biomarkers and levels of bacterial pathogens in the oral cavity with the intent of testing if the correlation between each biomarker and each pathogen is homogeneous over time. To address this question, we propose a model for the joint distribution of the serial biomarker measures and the serial pathogen measures and use the variance of this distribution to derive the asymptotic distribution of the sample correlation coefficient of a biomarker and a pathogen at each time point. We use both a Wald test based upon Fisher's Z-transformation and an F-test with an estimated degrees of freedom in order to produce a test with valid size. We examine the performance of both tests via Monte Carlo simulation in a variety of settings defined by the number of subjects, the number of time points, and the range of the true correlation coefficients.

Evaluation of the physicochemical compatibility of cyclosporin infusion and parenteral nutrition when intravenously administered via the same central line lumen

AbstractBackgroundPatients undergoing allogeneic haematopoietic stem cell transplantation require cyclosporin (CsA) infusion to be administered concurrently with parenteral nutrition (PN).AimsTo evaluate the physicochemical compatibility of parenteral CsA and PN administered via the same lumen of a central venous access device and to quantify and identify any particulate matter.MethodsThree PN formulations were tested. Standard PN solution and PN solution with glutamine manufactured by Baxter Healthcare and standard PN solution manufactured by Fresenius Kabi. CsA concentrate for intravenous infusion 250 mg/5 mL (Sandimmun, Novartis Pharmaceuticals) was used.PN solutions were mixed with CsA at different volume ratios to simulate different rates of co‐infusion in clinical practice.A real‐life simulation was also performed with CsA in glucose 5% co‐infused with the PN solution via the same lumen of a central venous access device.The size of colloidal species in the resulting samples was measured using dynamic light scattering.ResultsThe static experiments for all dilution ratios and types of PN with CsA indicated average particle diameters of less than 500 nm. Only one sample indicated a particle larger than 5 µm.The ‘real‐life’ simulation did not detect any particle with diameter greater than 5 µm. This was across all types of PN solutions and for all samples taken at a number of time points up to 24 h.ConclusionCommercially available PN formulations can be administered concurrently with CsA via the same lumen of a central venous access device. For infusions running up to 24 h, there is minimal risk of particle formation with a diameter greater than 5 µm.

Comparison of methods for analyzing binary repeated measures data: A simulation-based study (comparison of methods for binary repeated measures)

ABSTRACTIn this study, some methods suggested for binary repeated measures, namely, Weighted Least Squares (WLS), Generalized Estimating Equations (GEE), and Generalized Linear Mixed Models (GLMM) are compared with respect to power, type 1 error, and properties of estimates. The results indicate that with adequate sample size, no missing data, the only covariate being time effect, and a relatively limited number of time points, the WLS method performs well. The GEE approach performs well only for large sample sizes. The GLMM method is satisfactory with respect to type I error, but its estimates have poorer properties than the other methods.

A Multilevel AR(1) Model: Allowing for Inter-Individual Differences in Trait-Scores, Inertia, and Innovation Variance

In this article we consider a multilevel first-order autoregressive [AR(1)] model with random intercepts, random autoregression, and random innovation variance (i.e., the level 1 residual variance). Including random innovation variance is an important extension of the multilevel AR(1) model for two reasons. First, between-person differences in innovation variance are important from a substantive point of view, in that they capture differences in sensitivity and/or exposure to unmeasured internal and external factors that influence the process. Second, using simulation methods we show that modeling the innovation variance as fixed across individuals, when it should be modeled as a random effect, leads to biased parameter estimates. Additionally, we use simulation methods to compare maximum likelihood estimation to Bayesian estimation of the multilevel AR(1) model and investigate the trade-off between the number of individuals and the number of time points. We provide an empirical illustration by applying the extended multilevel AR(1) model to daily positive affect ratings from 89 married women over the course of 42 consecutive days.

A wavelet-based estimator of the degrees of freedom in denoised fMRI time series for probabilistic testing of functional connectivity and brain graphs

Connectome mapping using techniques such as functional magnetic resonance imaging (fMRI) has become a focus of systems neuroscience. There remain many statistical challenges in analysis of functional connectivity and network architecture from BOLD fMRI multivariate time series. One key statistic for any time series is its (effective) degrees of freedom, df, which will generally be less than the number of time points (or nominal degrees of freedom, N). If we know the df, then probabilistic inference on other fMRI statistics, such as the correlation between two voxel or regional time series, is feasible. However, we currently lack good estimators of df in fMRI time series, especially after the degrees of freedom of the “raw” data have been modified substantially by denoising algorithms for head movement. Here, we used a wavelet-based method both to denoise fMRI data and to estimate the (effective) df of the denoised process. We show that seed voxel correlations corrected for locally variable df could be tested for false positive connectivity with better control over Type I error and greater specificity of anatomical mapping than probabilistic connectivity maps using the nominal degrees of freedom. We also show that wavelet despiked statistics can be used to estimate all pairwise correlations between a set of regional nodes, assign a P value to each edge, and then iteratively add edges to the graph in order of increasing P. These probabilistically thresholded graphs are likely more robust to regional variation in head movement effects than comparable graphs constructed by thresholding correlations. Finally, we show that time-windowed estimates of df can be used for probabilistic connectivity testing or dynamic network analysis so that apparent changes in the functional connectome are appropriately corrected for the effects of transient noise bursts. Wavelet despiking is both an algorithm for fMRI time series denoising and an estimator of the (effective) df of denoised fMRI time series. Accurate estimation of df offers many potential advantages for probabilistically thresholding functional connectivity and network statistics tested in the context of spatially variant and non-stationary noise. Code for wavelet despiking, seed correlational testing and probabilistic graph construction is freely available to download as part of the BrainWavelet Toolbox at www.brainwavelet.org.

DCEMRI.jl: a fast, validated, open source toolkit for dynamic contrast enhanced MRI analysis.

We present a fast, validated, open-source toolkit for processing dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) data. We validate it against the Quantitative Imaging Biomarkers Alliance (QIBA) Standard and Extended Tofts-Kety phantoms and find near perfect recovery in the absence of noise, with an estimated 10–20× speedup in run time compared to existing tools. To explain the observed trends in the fitting errors, we present an argument about the conditioning of the Jacobian in the limit of small and large parameter values. We also demonstrate its use on an in vivo data set to measure performance on a realistic application. For a 192 × 192 breast image, we achieved run times of <1 s. Finally, we analyze run times scaling with problem size and find that the run time per voxel scales as O(N1.9), where N is the number of time points in the tissue concentration curve. DCEMRI.jl was much faster than any other analysis package tested and produced comparable accuracy, even in the presence of noise.