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.
Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such longitudinal Riemannian data is challenging, because of both the sparsity of the observations and the nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for longitudinal Riemannian data. Information is pooled across subjects by estimating the mean curve with local Fréchet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean. Dimension reduction and imputation of the manifold‐valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction. We show that the proposed mean and covariance function estimates achieve state‐of‐the‐art convergence rates. For illustration, we study the development of brain connectivity in a longitudinal cohort of Alzheimer's disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine‐invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.
more » « less- Award ID(s):
- 2014626
- PAR ID:
- 10448123
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 77
- Issue:
- 4
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 1328-1341
- Size(s):
- p. 1328-1341
- Sponsoring Org:
- National Science Foundation
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