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. 2012 Nov 1;63(2):858-73.
doi: 10.1016/j.neuroimage.2012.07.012. Epub 2012 Jul 16.

Increasing Power for Voxel-Wise Genome-Wide Association Studies: The Random Field Theory, Least Square Kernel Machines and Fast Permutation Procedures

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Free PMC article

Increasing Power for Voxel-Wise Genome-Wide Association Studies: The Random Field Theory, Least Square Kernel Machines and Fast Permutation Procedures

Tian Ge et al. Neuroimage. .
Free PMC article

Abstract

Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer's disease neuroimaging initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-d-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer's disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains.

Figures

Fig. 1
Fig. 1
Gaussian null simulations to evaluate validity of brain-wise FWE-corrected p-values. Q–Q plots of pFWEbrain for the four combinations of voxel vs. cluster and single-locus T vs. multi-locus χ2 tests, showing that voxel-wise inferences are valid, while cluster size inferences are also valid but somewhat conservative. For each case 10,000 simulations were carried out, with SNPs randomly selected and their subject IDs shuffled; cluster forming threshold was set at 0.001. Gray region shows 95% confidence bands (see text for details).
Fig. 2
Fig. 2
Real data null simulations to evaluate LSKM uncorrected p-values. Q–Q plot (main figure) and histogram (inset) of puc from the LSKM multi-locus model, showing that approximate χ2 distribution appears accurate. 10,000 realizations were created from randomly selected voxels and 1–20 randomly selected SNPs with their IDs shuffled.
Fig. 3
Fig. 3
Real data null simulations to evaluate validity of brain-wise FWE-corrected p-values. Q–Q plots of pFWEbrain for the four combinations of voxel vs. cluster and single-locus T vs. multi-locus χ2 tests, showing that voxel-wise inferences appear to be valid, while cluster size inferences are dramatically anti-conservative and invalid. For each case 10,000 simulations were carried out, with SNPs randomly selected and their subject IDs shuffled; cluster forming threshold was set at 0.001. Gray region shows 95% confidence bands (see text for details).
Fig. 4
Fig. 4
Validation of the “small effect” assumption for FWHM estimation. Histograms of the FWHM in voxels estimated in three directions, for 1000 randomly selected SNPs (blue) and the FWHM from the no-SNP model marked in red. The FWHM from the no-SNP model appears to be an excellent surrogate for individual SNP models, rarely differing by more than 0.005 in any direction.
Fig. 5
Fig. 5
Validation of parametric tail approximation to nonparametric permutation distribution. The “gold standard” distribution from 1 million permutations (blue), and the GPD fit based on one independent sample of 100,000 permutations (black line) shows excellent agreement. The shaded region shows the 95% confidence band (gray) based on 2.5 and 97.5 percentiles of the 1000 repeated GPD fits (each based on 100,000 permutations). The tails were truncated and 250 of the most extreme permutation values were used in all parametric fittings.
Fig. 6
Fig. 6
Multi-locus LSKM results for gene GRIN2B. The parietal (upper panels) and temporal (lower panels) foci that the most associated gene GRIN2B affects in the brain. Brain-wide genome-wide significant voxels are in yellow; brain-wide (post hoc gene-wise) significant voxels are in dark blue; and 0.001 uncorrected significant voxels are in light blue. Both parietal and temporal lobes are known to be affected in Alzheimer's disease.
Fig. 7
Fig. 7
Intrinsic correlation between the cluster size and the corresponding RPV image. Clusters observed in Model-A were measured by RPV-A and an alternative RPV image, RPV-B, estimated from a different model. Three scatter plots are presented where the difference in cluster size measured in RESELs, RPV-A–RPV-B, is plotted against the true cluster size measured by RPV-A. The left panel is for all one-voxel clusters. The right panel is for the top 5% largest clusters. All moderate size clusters are shown in the middle panel.
Fig. 8
Fig. 8
Nonstationarity of the volumetric tissue difference image. A histogram of the FWHM in voxels. The embedded panel is a zoom-in of the right tail behavior.

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