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. 2011 Sep;73(4):559-578.
doi: 10.1111/j.1467-9868.2010.00767.x.

Multiscale Adaptive Regression Models for Neuroimaging Data

Yimei Li  1 , Hongtu Zhu, Dinggang Shen, Weili Lin, John H Gilmore, Joseph G Ibrahim
Affiliations

Multiscale Adaptive Regression Models for Neuroimaging Data

Yimei Li et al. J R Stat Soc Series B Stat Methodol. 2011 Sep.

Abstract

Neuroimaging studies aim to analyze imaging data with complex spatial patterns in a large number of locations (called voxels) on a two-dimensional (2D) surface or in a 3D volume. Conventional analyses of imaging data include two sequential steps: spatially smoothing imaging data and then independently fitting a statistical model at each voxel. However, conventional analyses suffer from the same amount of smoothing throughout the whole image, the arbitrary choice of smoothing extent, and low statistical power in detecting spatial patterns. We propose a multiscale adaptive regression model (MARM) to integrate the propagation-separation (PS) approach (Polzehl and Spokoiny, 2000, 2006) with statistical modeling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects. MARM has three features: being spatial, being hierarchical, and being adaptive. We use a multiscale adaptive estimation and testing procedure (MAET) to utilize imaging observations from the neighboring voxels of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish consistency and asymptotic normality of the adaptive parameter estimates and the asymptotic distribution of the adaptive test statistics. Our simulation studies and real data analysis confirm that MARM significantly outperforms conventional analyses of imaging data.

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Figures

Fig. 1
Fig. 1
Illustration of the key features in the multiscale adaptive regression model. For a relatively large radius r0, panel (a) shows the overlapping spherical neighborhoods B(d, r0) of multiple points (or voxels) d on the cortical surface. Panel (b) shows the spherical neighborhoods with four different bandwidths h of the six selected points d on the cortical surface. Panel (c) shows the spherical neighborhoods B(d, r0) of three selected voxels in a 3D volume, in which voxels A and C are inside the activated regions, whereas voxel B is on the boundary of an activated region.
Fig. 2
Fig. 2
Results from a simulation study of comparing the voxel-wise method and MARM based on 1,000 N(0, 1) distributed data with n = 60. Panel (k) is the ground truth image of five ROIs with black, blue, red, yellow, and white color representing β2(d)=0, 0.2, 0.4, 0.6, and 0.8, respectively. The first row contains the results from the voxel-wise method: (a) a selected image of β̂2(d, h0) obtained from a simulated data set; (b) bias image of β̂2(d, h0); (c) RMS image of β̂2(d, h0); (d) SD image of β̂2(d, h0); and (e) RE image of β̂2(d, h0). The second row contains the results obtained from MAET as S = 10 and ch = 1.1: (f) a selected image of β̂2(d, h10) obtained from a simulated data set; (g) bias image of β̂2(d, h10); (h) RMS image of β̂2(d, h10); (i) SD image of β̂2(d, h10); and (j) RE image of β̂2(d, h10). Panels (l) and (m) are the scatter plots of biases and REs of β̂2(d, h0) versus β̂2(d, h10), respectively.
Fig. 3
Fig. 3
Results from the neonatal project on brain development. Panel (a): the Bonferroni corrected −log10(p) values of Wμ(d, h0) from a selected slice and a selected voxel in the red circle in the ventricle; panel (b): the Bonferroni corrected −log10(p) values of Wμ(d, h10) from the same selected slice; panel (c): the Bonferroni corrected −log10(p) values of the Wald test statistics obtained from the Gaussian kernel smoothed FA images for the same selected slice; panel (d): longitudinal trajectories of unsmoothed FA values in the red voxel identified in panel (a); panel (h): longitudinal trajectories of the Gaussian kernel smoothed FA values in the red voxel identified in panel (a); panels (e), (f), and (g): estimated β̂1(d, h10), β̂2(d, h10), and β̂3(d, h10) for the same selected slice; panels (i), (j), and (k): anatomical images with eight labeled regions of interest including the genu, splenium (Sple), internal capsule (IC), external capsule (EC), ventricle, grey matter (GM), white matter (WM), cerebrospinal fluid (CSF), and corpus callosum body (Body); panel (l): the growth patterns from the ROIs located in the splenium (Sple), genu (Genu) and body (Body) of corpus callosum, internal capsule (IC), and external capsule (EC) for FA.
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