5,820 research outputs found
Joint analysis of SNP and gene expression data in genetic association studies of complex diseases
Genetic association studies have been a popular approach for assessing the
association between common Single Nucleotide Polymorphisms (SNPs) and complex
diseases. However, other genomic data involved in the mechanism from SNPs to
disease, for example, gene expressions, are usually neglected in these
association studies. In this paper, we propose to exploit gene expression
information to more powerfully test the association between SNPs and diseases
by jointly modeling the relations among SNPs, gene expressions and diseases. We
propose a variance component test for the total effect of SNPs and a gene
expression on disease risk. We cast the test within the causal mediation
analysis framework with the gene expression as a potential mediator. For eQTL
SNPs, the use of gene expression information can enhance power to test for the
total effect of a SNP-set, which is the combined direct and indirect effects of
the SNPs mediated through the gene expression, on disease risk. We show that
the test statistic under the null hypothesis follows a mixture of
distributions, which can be evaluated analytically or empirically using the
resampling-based perturbation method. We construct tests for each of three
disease models that are determined by SNPs only, SNPs and gene expression, or
include also their interactions. As the true disease model is unknown in
practice, we further propose an omnibus test to accommodate different
underlying disease models. We evaluate the finite sample performance of the
proposed methods using simulation studies, and show that our proposed test
performs well and the omnibus test can almost reach the optimal power where the
disease model is known and correctly specified. We apply our method to
reanalyze the overall effect of the SNP-set and expression of the ORMDL3 gene
on the risk of asthma.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS690 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
We show the fundamental theorems of curves and surfaces in the 3-dimensional
Heisenberg group and find a complete set of invariants for curves and surfaces
respectively. The proofs are based on Cartan's method of moving frames and Lie
group theory. As an application of the main theorems, a Crofton-type formula is
proved in terms of p-area which naturally arises from the variation of volume.
The application makes a connection between CR geometry and integral geometry
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