Genome-wide association study for subclinical atherosclerosis in major arterial territories in the NHLBI's Framingham Heart Study

INTRODUCTION:Subclinical atherosclerosis (SCA) measures in multiple arterial beds are heritable phenotypes that are associated with increased incidence of cardiovascular disease. We conducted a genome-wide association study (GWAS) for SCA measurements in the community-based Framingham Heart Study.METHODS:Over 100,000 single nucleotide polymorphisms (SNPs) were genotyped (Human 100K GeneChip, Affymetrix) in 1345 subjects from 310 families. We calculated sex-specific age-adjusted and multivariable-adjusted residuals in subjects tested for quantitative SCA phenotypes, including ankle-brachial index, coronary artery calcification and abdominal aortic calcification using multi-detector computed tomography, and carotid intimal medial thickness (IMT) using carotid ultrasonography. We evaluated associations of these phenotypes with 70,987 autosomal SNPs with minor allele frequency [greater than or equal to] 0.10, call rate [greater than or equal to] 80%, and Hardy-Weinberg p-value [greater than or equal to] 0.001 in samples ranging from 673 to 984 subjects, using linear regression with generalized estimating equations (GEE) methodology and family-based association testing (FBAT). Variance components LOD scores were also calculated.RESULTS:There was no association result meeting criteria for genome-wide significance, but our methods identified 11 SNPs with p < 10-5 by GEE and five SNPs with p < 10-5 by FBAT for multivariable-adjusted phenotypes. Among the associated variants were SNPs in or near genes that may be considered candidates for further study, such as rs1376877 (GEE p < 0.000001, located in ABI2) for maximum internal carotid artery IMT and rs4814615 (FBAT p = 0.000003, located in PCSK2) for maximum common carotid artery IMT. Modest significant associations were noted with various SCA phenotypes for variants in previously reported atherosclerosis candidate genes, including NOS3 and ESR1. Associations were also noted of a region on chromosome 9p21 with CAC phenotypes that confirm associations with coronary heart disease and CAC in two recently reported genome-wide association studies. In linkage analyses, several regions of genome-wide linkage were noted, confirming previously reported linkage of internal carotid artery IMT on chromosome 12. All GEE, FBAT and linkage results are provided as an open-access results resource at http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007.CONCLUSION:The results from this GWAS generate hypotheses regarding several SNPs that may be associated with SCA phenotypes in multiple arterial beds. Given the number of tests conducted, subsequent independent replication in a staged approach is essential to identify genetic variants that may be implicated in atherosclerosis.

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Efficient Support for Common Relations in Lightweight Formal Reasoning Systems

In work that involves mathematical rigor, there are numerous benefits to adopting a representation of models and arguments that can be supplied to a formal reasoning or verification system: reusability, automatic evaluation of examples, and verification of consistency and correctness. However, accessibility has not been a priority in the design of formal verification tools that can provide these benefits. In earlier work [Lap09a], we attempt to address this broad problem by proposing several specific design criteria organized around the notion of a natural context: the sphere of awareness a working human user maintains of the relevant constructs, arguments, experiences, and background materials necessary to accomplish the task at hand. This work expands one aspect of the earlier work by considering more extensively an essential capability for any formal reasoning system whose design is oriented around simulating the natural context: native support for a collection of mathematical relations that deal with common constructs in arithmetic and set theory. We provide a formal definition for a context of relations that can be used to both validate and assist formal reasoning activities. We provide a proof that any algorithm that implements this formal structure faithfully will necessary converge. Finally, we consider the efficiency of an implementation of this formal structure that leverages modular implementations of well-known data structures: balanced search trees and transitive closures of hypergraphs.