cpgen (version 0.1)

cGWAS: Genomewide Association Study

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:

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

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

$$\hat{\boldsymbol{\beta}} = (\mathbf{X}^{\ast\prime}\mathbf{X}^{\ast})^{-1}\mathbf{X}^{\ast\prime}\mathbf{y}^{\ast}$$ with $$\mathbf{X}^{\ast} =\mathbf{V}^{-1/2}\mathbf{X}$$ $$\mathbf{y}^{\ast} =\mathbf{V}^{-1/2}\mathbf{y}$$

Usage

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

Details

...

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

# 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)