MARM: Multiscale Adaptive Regression Model, a DTI-Statistics Toolkit
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 estimates and the asymptotic distribution of the adaptive test statistics.
Citation: Yimei Li, Hongtu Zhu, Dinggang Shen, Weili Lin, John H. Gilmore and Joseph G Ibrahim. Multiscale Adaptive Regression Models for Neuroimaging Data. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2011.