@article {822, title = {An evaluation of independent component analyses with an application to resting-state fMRI.}, journal = {Biometrics}, volume = {70}, year = {2014}, month = {2014 Mar}, pages = {224-36}, abstract = {

We examine differences between independent component analyses (ICAs) arising from different assumptions, measures of dependence, and starting points of the algorithms. ICA is a popular method with diverse applications including artifact removal in electrophysiology data, feature extraction in microarray data, and identifying brain networks in functional magnetic resonance imaging (fMRI). ICA can be viewed as a generalization of principal component analysis (PCA) that takes into account higher-order cross-correlations. Whereas the PCA solution is unique, there are many ICA methods-whose solutions may differ. Infomax, FastICA, and JADE are commonly applied to fMRI studies, with FastICA being arguably the most popular. Hastie and Tibshirani (2003) demonstrated that ProDenICA outperformed FastICA in simulations with two components. We introduce the application of ProDenICA to simulations with more components and to fMRI data. ProDenICA was more accurate in simulations, and we identified differences between biologically meaningful ICs from ProDenICA versus other methods in the fMRI analysis. ICA methods require nonconvex optimization, yet current practices do not recognize the importance of, nor adequately address sensitivity to, initial values. We found that local optima led to dramatically different estimates in both simulations and group ICA of fMRI, and we provide evidence that the global optimum from ProDenICA is the best estimate. We applied a modification of the Hungarian (Kuhn-Munkres) algorithm to match ICs from multiple estimates, thereby gaining novel insights into how brain networks vary in their sensitivity to initial values and ICA method.

}, keywords = {Adolescent, Algorithms, Attention Deficit Disorder with Hyperactivity, brain mapping, Child, Child, Preschool, Computer Simulation, Humans, Magnetic Resonance Imaging, Models, Statistical, Principal Component Analysis}, issn = {1541-0420}, doi = {10.1111/biom.12111}, author = {Risk, Benjamin B and Matteson, David S and Ruppert, David and Eloyan, Ani and Caffo, Brian S} } @article {684, title = {Corrected confidence bands for functional data using principal components.}, journal = {Biometrics}, volume = {69}, year = {2013}, month = {2013 Mar}, pages = {41-51}, abstract = {

Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this article, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- and decomposition-based variability are constructed. Standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. Iterated expectation and variance formulas combine model-based conditional estimates across the distribution of decompositions. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented in the R package refund on CRAN.

}, keywords = {Brain, CD4 Lymphocyte Count, Computer Simulation, Confidence Intervals, HIV, HIV Infections, Humans, Magnetic Resonance Imaging, Models, Statistical, Multiple Sclerosis, Principal Component Analysis}, issn = {1541-0420}, doi = {10.1111/j.1541-0420.2012.01808.x}, author = {Goldsmith, J and Greven, S and Crainiceanu, C} } @article {812, title = {Likelihood-based population independent component analysis.}, journal = {Biostatistics}, volume = {14}, year = {2013}, month = {2013 Jul}, pages = {514-27}, abstract = {

Independent component analysis (ICA) is a widely used technique for blind source separation, used heavily in several scientific research areas including acoustics, electrophysiology, and functional neuroimaging. We propose a scalable two-stage iterative true group ICA methodology for analyzing population level functional magnetic resonance imaging (fMRI) data where the number of subjects is very large. The method is based on likelihood estimators of the underlying source densities and the mixing matrix. As opposed to many commonly used group ICA algorithms, the proposed method does not require significant data reduction by a 2-fold singular value decomposition. In addition, the method can be applied to a large group of subjects since the memory requirements are not restrictive. The performance of our approach is compared with a commonly used group ICA algorithm via simulation studies. Furthermore, the proposed method is applied to a large collection of resting state fMRI datasets. The results show that established brain networks are well recovered by the proposed algorithm.

}, keywords = {Adult, Algorithms, Attention Deficit Disorder with Hyperactivity, Biostatistics, Brain, Child, Computer Simulation, Databases, Factual, Humans, Imaging, Three-Dimensional, Likelihood Functions, Magnetic Resonance Imaging, Principal Component Analysis, Statistics, Nonparametric}, issn = {1468-4357}, doi = {10.1093/biostatistics/kxs055}, author = {Eloyan, Ani and Crainiceanu, Ciprian M and Caffo, Brian S} } @article {814, title = {Longitudinal scalar-on-functions regression with application to tractography data.}, journal = {Biostatistics}, volume = {14}, year = {2013}, month = {2013 Jul}, pages = {447-61}, abstract = {

We propose a class of estimation techniques for scalar-on-function regression where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging tractography study. One of the study{\textquoteright}s primary goals is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires the development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and predictor measurements per patient; (3) Gaussian or non-Gaussian outcomes; and (4) missing values within functional predictors. We propose two versions of a new method, longitudinal functional principal components regression (PCR). These methods extend the well-known functional PCR and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The new methods are compared with existing approaches, and the most promising techniques are used for analyzing the tractography data.

}, keywords = {Anisotropy, Biostatistics, Brain, Diffusion Tensor Imaging, Humans, Linear Models, Models, Statistical, Multiple Sclerosis, Principal Component Analysis, Regression Analysis}, issn = {1468-4357}, doi = {10.1093/biostatistics/kxs051}, author = {Gertheiss, Jan and Goldsmith, Jeff and Crainiceanu, Ciprian and Greven, Sonja} } @article {827, title = {Analysis of group ICA-based connectivity measures from fMRI: application to Alzheimer{\textquoteright}s disease.}, journal = {PLoS One}, volume = {7}, year = {2012}, month = {2012}, pages = {e49340}, abstract = {

Functional magnetic resonance imaging (fMRI) is a powerful tool for the in vivo study of the pathophysiology of brain disorders and disease. In this manuscript, we propose an analysis stream for fMRI functional connectivity data and apply it to a novel study of Alzheimer{\textquoteright}s disease. In the first stage, spatial independent component analysis is applied to group fMRI data to obtain common brain networks (spatial maps) and subject-specific mixing matrices (time courses). In the second stage, functional principal component analysis is utilized to decompose the mixing matrices into population-level eigenvectors and subject-specific loadings. Inference is performed using permutation-based exact logistic regression for matched pairs data. The method is applied to a novel fMRI study of Alzheimer{\textquoteright}s disease risk under a verbal paired associates task. We found empirical evidence of alternative ICA-based metrics of connectivity when comparing subjects evidencing mild cognitive impairment relative to carefully matched controls.

}, keywords = {Aged, Algorithms, Alzheimer Disease, Brain, brain mapping, Case-Control Studies, Female, Humans, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Male, Middle Aged, Mild Cognitive Impairment, Nerve Net, Principal Component Analysis, Task Performance and Analysis, Time Factors}, issn = {1932-6203}, doi = {10.1371/journal.pone.0049340}, author = {Li, Shanshan and Eloyan, Ani and Joel, Suresh and Mostofsky, Stewart and Pekar, James and Bassett, Susan Spear and Caffo, Brian} }