smoothedLasso (version 1.6)

prsLasso: Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the Lasso for polygenic risk scores (prs).

Description

Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the Lasso for polygenic risk scores (prs).

Usage

prsLasso(X, y, s, lambda)

Arguments

X

The design matrix.

y

The response vector.

s

The shrinkage parameter used to regularize the design matrix.

lambda

The regularization parameter of the prs Lasso.

Value

A list with six functions, precisely the objective \(u\), penalty \(v\), and dependence structure \(w\), as well as their derivatives \(du\), \(dv\), and \(dw\).

References

Mak, T.S., Porsch, R.M., Choi, S.W., Zhou, X., and Sham, P.C. (2017). Polygenic scores via penalized regression on summary statistics. Genet Epidemiol, 41(6):469-480.

Mak, T.S. and Porsch, R.M. (2020). lassosum: LASSO with summary statistics and a reference panel. R package version 0.4.5.

Hahn, G., Lutz, S., Laha, N., and Lange, C. (2020). A framework to efficiently smooth L1 penalties for linear regression. bioRxiv:2020.09.17.301788.

Examples

# NOT RUN {
library(smoothedLasso)
n <- 100
p <- 500
betavector <- runif(p)
X <- matrix(runif(n*p),nrow=n,ncol=p)
y <- X %*% betavector
s <- 0.5
lambda <- 1
temp <- prsLasso(X,y,s,lambda)

# }