Applying compressed sensing to genome-wide association studies.

Shashaank Vattikuti,James J Lee,Stephen D H Hsu,Carson C Chow,Christopher C Chang

doi:10.1186/2047-217x-3-10

Abstract

BackgroundThe aim of a genome-wide association study (GWAS) is to isolate DNA markers for variants affecting phenotypes of interest. This is constrained by the fact that the number of markers often far exceeds the number of samples. Compressed sensing (CS) is a body of theory regarding signal recovery when the number of predictor variables (i.e., genotyped markers) exceeds the sample size. Its applicability to GWAS has not been investigated.ResultsUsing CS theory, we show that all markers with nonzero coefficients can be identified (selected) using an efficient algorithm, provided that they are sufficiently few in number (sparse) relative to sample size. For heritability equal to one (h 2 = 1), there is a sharp phase transition from poor performance to complete selection as the sample size is increased. For heritability below one, complete selection still occurs, but the transition is smoothed. We find for h 2 ∼ 0.5 that a sample size of approximately thirty times the number of markers with nonzero coefficients is sufficient for full selection. This boundary is only weakly dependent on the number of genotyped markers.ConclusionPractical measures of signal recovery are robust to linkage disequilibrium between a true causal variant and markers residing in the same genomic region. Given a limited sample size, it is possible to discover a phase transition by increasing the penalization; in this case a subset of the support may be recovered. Applying this approach to the GWAS analysis of height, we show that 70-100% of the selected markers are strongly correlated with height-associated markers identified by the GIANT Consortium.

Highlights

The aim of a genome-wide association study (GWAS) is to isolate DNA markers for variants affecting phenotypes of interest
Methods relying on the assumption of sparsity have been adopted by workers in the field of genomic selection (GS), which uses genetic information to guide the artificial selection of livestock and crops [12,13,14,15]
Using more than 12,000 subjects from the Atherosclerosis Risk in Communities Study (ARIC) European American and Gene-Environment Association Studies (GENEVA) cohorts and nearly 700,000 single-nucleotide polymorphisms (SNPs), we show that the matrix of genotypes acquired in GWAS obeys properties suitable for the application of Compressed sensing (CS) theory

Summary

Introduction

The aim of a genome-wide association study (GWAS) is to isolate DNA markers for variants affecting phenotypes of interest. This is constrained by the fact that the number of markers often far exceeds the number of samples. The search for genetic variants associated with a given phenotype in a genome-wide association study (GWAS) is a classic example of what has been called a p ≫ n problem, where n is the sample size (number of subjects) and p is the number of predictor variables (genotyped markers) [1]. Estimating the partial regression coefficients of the predictor variables by ordinary least squares (OLS) requires that the sample size exceed the number of coefficients, which in the GWAS context, may be of order 105 or even 106. The lasso is one of the methods studied by GS investigators [16,17], Bayesian methods that regularize the coefficients with strong priors tend to be favored [18,19]

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