Multiple comparison procedures for neuroimaging genomewide association studies.

Recent research in neuroimaging has focused on assessing associations between genetic variants that are measured on a genomewide scale and brain imaging phenotypes. A large number of works in the area apply massively univariate analyses on a genomewide basis to find single nucleotide polymorphisms that influence brain structure. In this paper, we propose using various dimensionality reduction methods on both brain structural MRI scans and genomic data, motivated by the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. We also consider a new multiple testing adjustment method and compare it with two existing false discovery rate (FDR) adjustment methods. The simulation results suggest an increase in power for the proposed method. The real-data analysis suggests that the proposed procedure is able to find associations between genetic variants and brain volume differences that offer potentially new biological insights.

Equivalence of kernel machine regression and kernel distance covariance for multidimensional phenotype association studies.

Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance (KDC). KMR is a semiparametric regression framework that models covariate effects parametrically and genetic markers non-parametrically, while KDC represents a class of methods that include distance covariance (DC) and Hilbert-Schmidt independence criterion (HSIC), which are nonparametric tests of independence. We show that the equivalence between the score test of KMR and the KDC statistic under certain conditions can lead to a novel generalization of the KDC test that incorporates covariates. Our contributions are 3-fold: (1) establishing the equivalence between KMR and KDC; (2) showing that the principles of KMR can be applied to the interpretation of KDC; (3) the development of a broader class of KDC statistics, where the class members are statistics corresponding to different kernel combinations. Finally, we perform simulation studies and an analysis of real data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. The ADNI study suggest that SNPs of FLJ16124 exhibit pairwise interaction effects that are strongly correlated to the changes of brain region volumes.

Penalized nonparametric scalar-on-function regression via principal coordinates.

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model.