cGWAS: Genomewide Association Study

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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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

Details

...

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

Author(s)

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.

See Also

cGWAS.emmax

Examples

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## 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)


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