Description Usage Arguments Details Value Author(s) References See Also Examples
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}
1 |
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: |
dom |
Defines whether to include an additional dominance coefficient for every marker. Note: only useful if the genotype-coding in |
verbose |
prints progress to the screen |
...
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 |
Claas Heuer
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.
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)
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