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Abstract Magnetic resonance imaging (MRI) is a technique that scans the anatomical structure of the brain, whereas functional magnetic resonance imaging (fMRI) uses the same basic principles of atomic physics as MRI scans but image metabolic function. A major goal of MRI and fMRI study is to precisely delineate various types of tissues, anatomical structure, pathologies, and detect the brain regions that react to outer stimuli (e.g., viewing an image). As a key feature of these MRI‐based neuroimaging data, voxels (cubic pixels of the brain volume) are highly correlated. However, the associations between voxels are often overlooked in the statistical analysis. We adapt a recently proposed dimension reduction method called the envelope method to analyze neuoimaging data taking into account correlation among voxels. We refer to the modified procedure the envelope chain procedure. Because the envelope chain procedure has not been employed before, we demonstrate in simulations the empirical performance of estimator, and examine its sensitivity when our assumptions are violated. We use the estimator to analyze the MRI data from ADHD‐200 study. Data analyses demonstrate that leveraging the correlations among voxels can significantly increase the efficiency of the regression analysis, thus achieving higher detection power with small sample sizes.
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Simultaneous confidence corridors for mean functions in functional data analysis of imaging data
Abstract Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle an irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two‐sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyze brain positron emission tomography data in two different studies. One data set used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.
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- Award ID(s):
- 1916204
- PAR ID:
- 10123443
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 76
- Issue:
- 2
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 427-437
- Size(s):
- p. 427-437
- Sponsoring Org:
- National Science Foundation
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