sbl (version 0.1.0)

sblgwas: Sparse Bayesian Learning for QTL Mapping and Genome-Wide Association Studies

Description

The sparse Bayesian learning (SBL) method for quantitative trait locus (QTL) mapping and genome-wide association studies (GWAS) deals with a linear mixed model. This is also a multiple locus model that includes all markers (random effects) in a single model and detect significant markers simultaneously. SBL method adopts coordinate descent algorithm to update parameters by estimating one parameter at a time conditional on the posterior modes of all other parameters. The parameter estimation process requires multiple iterations and the final estimated parameters take the values when the entire program converges.

Usage

sblgwas(x, y, z, t = -1, max.iter = 200, min.err = 1e-06)

Arguments

x

a design matrix for fixed effects

y

a vector of response variables

z

a design matrix for random effects

t

a number between [-2,0] to control sparseness of the model, default is -1.

max.iter

maximum number of iterations set by user to stop the program, default is 200.

min.err

minimum threshold of mean squared error of random effects estimated from the current and the previous iteration to stop the program, default is 1e-6.

Value

iteration

a matrix storing intermediate results of each iteration before the entire program converges, including

"iter" iteration indicator

"error" mean squared error of random effects estimated from the current and the previous iteration

"s2" estimated variance of residual error

"\(beta[1]\dots beta[p]\)" estimates of fixed effects

"\(gamma[1]\dots gamma[m]\)" estimates of random effects

parm

a vector containing 5 elements: "iter", "error", "s2", "beta" and "df"

"iter" the number of iterations required by program to stop

"error" mean square error of random effect estimated from the last iteration before the program stops

"s2" estimated variance of residual error

"beta" estimate of fixed effect

"df" the effective degree of freedom from total random effects

blup

a matrix containing 4 columns: "gamma", "vg", "wald" and "p_wald"

"gamma" estimate of random effect

"vg" estimated variance of random effect

"wald" Wald statistic calculated as \(\gamma^2\)/\(\Phi\)

"p_wald" the p-value of Wald statistic following Chi-squared distribution with 1 degree of freedom

Details

The multiple locus hierarchical linear mixed model of SBL is $$y=X\beta+Z\gamma+\epsilon$$ where y is an \(n*1\) vector of response variables (observations of the trait); X is an \(n*p\) design matrix for fixed effects; \(\beta\) is a \(p*1\) vector of fixed effect; Z is an \(n*m\) genotype indicator matrix; \(\gamma\) is an \(m*1\) vector of marker effects and \(\epsilon\) is an \(n*1\) vector of residual errors with an aassumed \(\epsilon~N(0,\Sigma)\) distribution. Each marker effect, \(\gamma[k]\) for marker k, is treated as a random variable following \(N(0,\Phi[k])\) distribution, where \(\Phi[k]\) is the prior variance. The estimate of \(\gamma[k]\) is best linear unbiased prediciton (BLUP). The estimate of \(\Phi[k]\) is miximum likelihood estimate (MLE).

Examples

# NOT RUN {
# Load example data from sbl package
data(gen)
data(phe)
data(intercept)

# Run sblgwas() to perform association study of example data
# setting t = 0 leads to the most sparse model
fit<-sblgwas(x=intercept, y=phe, z=gen, t=0)
my.blup<-fit$blup

# setting t = -2 leads to the least sparse model
fit<-sblgwas(x=intercept, y=phe, z=gen, t=-2)
my.blup<-fit$blup
# }