# cGWAS: Genomewide Association Study In cpgen: Parallelized Genomic Prediction and GWAS

## Description

This function runs GWAS for continuous traits. Population structure that can lead to false positive association signals can be accounted for by passing a Variance-covariance matrix of the phenotype vector (Kang et al., 2010). The GLS-solution for fixed effects is computed as:

\hat{\boldsymbol{β}} = (\mathbf{X'V}^{-1}\mathbf{X})^{-1}\mathbf{X'V}^{-1}\mathbf{y}

Equivalent solutions are obtained by premultiplying the design matrix \mathbf{X} for fixed effects and the phenotype vector \mathbf{y} by \mathbf{V}^{-1/2} :

\hat{\boldsymbol{β}} = (\mathbf{X}^{\ast\prime}\mathbf{X}^{\ast})^{-1}\mathbf{X}^{\ast\prime}\mathbf{y}^{\ast}

with

\mathbf{X}^{\ast} =\mathbf{V}^{-1/2}\mathbf{X}

\mathbf{y}^{\ast} =\mathbf{V}^{-1/2}\mathbf{y}

## Usage

 1 cGWAS(y,M,X=NULL,V=NULL,dom=FALSE, verbose=TRUE) 

## Arguments

 y vector of phenotypes M Marker matrix X Optional Design Matrix for additional fixed effects. If omitted a column-vector of ones will be assigned V Inverse square root of the Variance-covariance matrix for the phenotype vector of type: matrix or dgCMatrix. Used for computing the GLS-solution of fixed effects. If omitted an identity-matrix will be assigned dom Defines whether to include an additional dominance coefficient for every marker. Note: only useful if the genotype-coding in M follows {-1,0,1} The dominance coefficient is computed as: 1-abs(M) verbose prints progress to the screen

...

## Value

List of 3 vectors or matrices. If dom=TRUE every element of the list will be a matrix with two columns. First column additive, second dominance:

 p-value Vector of p-values for every marker beta GLS solution for fixed marker effects se Standard Errors for values in beta

Claas Heuer

## References

Kang, Hyun Min, Jae Hoon Sul, Susan K Service, Noah A Zaitlen, Sit-yee Kong, Nelson B Freimer, Chiara Sabatti, and Eleazar Eskin. "Variance Component Model to Account for Sample Structure in Genome-Wide Association Studies." Nature Genetics 42, no. 4 (April 2010): 348-54. doi:10.1038/ng.548.

cGWAS.emmax
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ## Not run: # generate random data rand_data(500,5000) ### GWAS without accounting for population structure mod <- cGWAS(y,M) ### GWAS - accounting for population structure ## Estimate variance covariance matrix of y G <- cgrm.A(M,lambda=0.01) fit <- cGBLUP(y,G,verbose=FALSE) ### construct V V <- G*fit$var_a + diag(length(y))*fit$var_e ### get the inverse square root of V V2inv <- V %**% -0.5 ### run GWAS again mod2 <- cGWAS(y,M,V=V2inv,verbose=TRUE) ## End(Not run)