TwinMARM: Two-Stage Multiscale Adaptive Regression Methods for Twin Neuroimaging Data

Twin imaging studies have been valuable for understanding the relative contribution of the environment and genes on brain structures and their functions. Conventional analyses of twin imaging data include three sequential steps: spatially smoothing imaging data, independently fitting a structural equation model at each voxel, and finally correcting for multiple comparisons. However, conventional analyses are limited due to the same amount of smoothing throughout the whole image, the arbitrary choice of smoothing extent, and the decreased power in detecting environmental and genetic effects introduced by smoothing raw images. The goal of this article is to develop a two-stage multiscale adaptive regression method (TwinMARM) for spatial and adaptive analysis of twin neuroimaging and behavioral data. The first stage is to establish the relationship between twin imaging data and a set of covariates of interest, such as age and gender. The second stage is to disentangle the environmental and genetic influences on brain structures and their functions. In each stage, TwinMARM employs hierarchically nested spheres with increasing radii at each location and then captures spatial dependence among imaging observations via consecutively connected spheres across all voxels. Simulation studies show that our TwinMARM significantly outperforms conventional analyses of twin imaging data. Finally, we use our method to detect statistically significant effects of genetic and environmental variations on white matter structures in a neonatal twin study

Multiscale adaptive generalized estimating equations for longitudinal neuroimaging data

Many large-scale longitudinal imaging studies have been or are being widely conducted to better understand the progress of neuropsychiatric and neurodegenerative disorders and normal brain development. The goal of this article is to develop a multiscale adaptive generalized estimation equation (MAGEE) method for spatial and adaptive analysis of neuroimaging data from longitudinal studies. MAGEE is applicable to making statistical inference on regression coefficients in both balanced and unbalanced longitudinal designs and even twin and familial studies, whereas standard software platforms have several major limitations in handling these complex studies. Specifically, conventional voxel-based analyses in these software platforms involve Gaussian smoothing imaging data and then independently fitting a statistical model at each voxel. However, the conventional smoothing methods suffer from the lack of spatial adaptivity to the shape and spatial extent of region of interest and the arbitrary choice of smoothing extent, while independently fitting statistical models across voxels does not account for the spatial properties of imaging observations and noise distribution. To address such drawbacks, we adapt a powerful propagation–separation (PS) procedure to sequentially incorporate the neighboring information of each voxel and develop a new novel strategy to solely update a set of parameters of interest, while fixing other nuisance parameters at their initial estimators. Simulation studies and real data analysis show that MAGEE significantly outperforms voxel-based analysis

FSEM: Functional Structural Equation Models for Twin Functional Data

The aim of this article is to develop a novel class of functional structural equation models (FSEMs) for dissecting functional genetic and environmental effects on twin functional data, while characterizing the varying association between functional data and covariates of interest. We propose a three-stage estimation procedure to estimate varying coefficient functions for various covariates (e.g., gender) as well as three covariance operators for the genetic and environmental effects. We develop an inference procedure based on weighted likelihood ratio statistics to test the genetic/environmental effect at either a fixed location or a compact region. We also systematically carry out the theoretical analysis of the estimated varying functions, the weighted likelihood ratio statistics, and the estimated covariance operators. We conduct extensive Monte Carlo simulations to examine the finite-sample performance of the estimation and inference procedures. We apply the proposed FSEM to quantify the degree of genetic and environmental effects on twin white matter tracts obtained from the UNC early brain development study. Supplementary materials for this article are available online

SGPP: spatial Gaussian predictive process models for neuroimaging data

The aim of this paper is to develop a spatial Gaussian predictive process (SGPP) framework for accurately predicting neuroimaging data by using a set of covariates of interest, such as age and diagnostic status, and an existing neuroimaging data set. To achieve better prediction, we not only delineate spatial association between neuroimaging data and covariates, but also explicitly model spatial dependence in neuroimaging data. The SGPP model uses a functional principal component model to capture medium-to-long-range (or global) spatial dependence, while SGPP uses a multivariate simultaneous autoregressive model to capture short-range (or local) spatial dependence as well as cross-correlations of different imaging modalities. We propose a three-stage estimation procedure to simultaneously estimate varying regression coefficients across voxels and the global and local spatial dependence structures. Furthermore, we develop a predictive method to use the spatial correlations as well as the cross-correlations by employing a cokriging technique, which can be useful for the imputation of missing imaging data. Simulation studies and real data analysis are used to evaluate the prediction accuracy of SGPP and show that SGPP significantly outperforms several competing methods, such as voxel-wise linear model, in prediction. Although we focus on the morphometric variation of lateral ventricle surfaces in a clinical study of neurodevelopment, it is expected that SGPP is applicable to other imaging modalities and features

A new perspective on the Propagation-Separation approach: Taking advantage of the propagation condition

The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven weights. Within homogeneous regions it ensures a similar behavior as non-adaptive smoothing (propagation), while avoiding smoothing among distinct regions (separation). In order to enable a proof of stability of estimates, the authors of the original study introduced an additional memory step aggregating the estimators of the successive iteration steps. Here, we study theoretical properties of the simplified algorithm, where the memory step is omitted. In particular, we introduce a new strategy for the choice of the adaptation parameter yielding propagation and stability for local constant functions with sharp discontinuities.Comment: 28 pages, 5 figure

Patch-Wise Adaptive Weights Smoothing in R

Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patchwise adaptive smoothing, that extends the propagation-separation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes for an improved balance of reduced variability and bias in the reconstruction result. We present the implementation of the new method in an R package aws and demonstrate its properties on a number of examples in comparison with other state-of-the art image reconstruction methods

Patch-wise adaptive weights smoothing

Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patch-wise adaptive smoothing, that extends the Propagation-Separation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes for an improved balance of reduced variability and bias in the reconstruction result. We present the implementation of the new method in an R package aws and demonstrate its properties on a number of examples in comparison with other state-of-the art image reconstruction methods

Functional-Mixed Effects Models for Candidate Genetic Mapping in Imaging Genetic Studies

The aim of this paper is to develop a functional mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for effciently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function

FVGWAS: Fast voxelwise genome wide association analysis of large-scale imaging genetic data

More and more large-scale imaging genetic studies are being widely conducted to collect a rich set of imaging, genetic, and clinical data to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders. Several major big-data challenges arise from testing genome-wide (NC > 12 million known variants) associations with signals at millions of locations (NV ~ 106) in the brain from thousands of subjects (n ~ 103). The aim of this paper is to develop a Fast Voxelwise Genome Wide Association analysiS (FVGWAS) framework to e ciently carry out whole-genome analyses of whole-brain data. FVGWAS consists of three components including a heteroscedastic linear model, a global sure independence screening (G-SIS) procedure, and a detection procedure based on wild bootstrap methods. Specifically, for standard linear association, the computational complexity is O(nNV NC) for voxelwise genome wide association analysis (VGWAS) method compared with O((NC + NV)n2) for FVGWAS. Simulation studies show that FVGWAS is an effcient method of searching sparse signals in an extremely large search space, while controlling for the family-wise error rate. Finally, we have successfully applied FVGWAS to a large-scale imaging genetic data analysis of ADNI data with 708 subjects, 193,275 voxels in RAVENS maps, and 501,584 SNPs, and the total processing time was 203,645 seconds for a single CPU. Our FVG-WAS may be a valuable statistical toolbox for large-scale imaging genetic analysis as the field is rapidly advancing with ultra-high-resolution imaging and whole-genome sequencing