title: Applying compressed sensing to genome-wide association studies.
abstract: BACKGROUND
  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. 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.
  
  
  RESULTS
  Using 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.
  
  
  CONCLUSIONS
  Practical 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.
authors.affiliation: Mathematical Biology Section, Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, South Drive, Bethesda, MD 20814, USA.
authors.forename: Shashaank
authors.initials: S
authors.lastname: Vattikuti
authors.affiliation: Mathematical Biology Section, Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, South Drive, Bethesda, MD 20814, USA ; Department of Psychology, University of Minnesota Twin Cities, 75 East River Parkway, Minneapolis, MN 55455, USA ; Cognitive Genomics Lab, BGI Shenzhen, Yantian District, Shenzhen, China.
authors.forename: James J
authors.initials: JJ
authors.lastname: Lee
authors.affiliation: BGI Hong Kong, 16 Dai Fu Street, Tai Po Industrial Estate, Tai Po, Hong Kong ; Cognitive Genomics Lab, BGI Shenzhen, Yantian District, Shenzhen, China.
authors.forename: Christopher C
authors.initials: CC
authors.lastname: Chang
authors.affiliation: Department of Physics and Office of the Vice President for Research and Graduate Studies, Michigan State University, 426 Auditorium Road, East Lansing, MI 48824, USA ; Cognitive Genomics Lab, BGI Shenzhen, Yantian District, Shenzhen, China.
authors.forename: Stephen D H
authors.initials: SD
authors.lastname: Hsu
authors.affiliation: Mathematical Biology Section, Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, South Drive, Bethesda, MD 20814, USA.
authors.forename: Carson C
authors.initials: CC
authors.lastname: Chow
keywords: Compressed sensing; GWAS; Genomic selection; Lasso; Phase transition; Sparsity; Underdetermined system