grpCox {grpCox}

Fit a penalized Cox model.

Description

Fit the regularization paths for Cox models with grouped covariates.

Usage

grpCox(X, y, g, m, penalty=c("glasso", "gSCAD", "gMCP"), lambda=NULL, 
nlambda=100, rlambda=NULL, gamma=switch(penalty, gSCAD = 3.7, 3), 
standardize=TRUE, thresh=1e-3, maxit=1e+4)

Arguments

X

The design matrix.

y

The response vector includes time corresponding to failure/censor times, and status indicating failure (1) or censoring (0).

g

A vector indicating the group structure of the covariates. It can be unordered groups.

m

Group multipliers. Default is the square root of group size.

penalty

The penalty to be applied to the model. It is one of glasso, gSCAD, or gMCP.

lambda

A user supplied sequence of lambda values. If it is left unspecified, and the function automatically computes a grid of lambda values.

nlambda

The number of lambda values to use in the regularization path. Default is 100.

rlambda

Smallest value for lambda, as a fraction of the maximum lambda, the data derived entry value, i.e. the smallest value for which all coefficients are zero. The default depends on the sample size relative to the number of covariates. If sample size>#covariates, the default is 0.001, close to zero. If sample size>#covariates, the default is 0.05.

gamma

Tuning parameter of the group SCAD/MCP penalty. Default is 3.7 for SCAD and 3 for MCP.

standardize

Logical flag for variable standardization prior to fitting the model.

thresh

Convergence threshold for one-step coordinate descent. Defaults value is 1E-7.

maxit

Maximum number of passes over the data for all lambda values; default is 1E+5.

Details

The the group SCAD (gSCAD) and group MCP (gMCP) formulations have been presented in Wang et. al 2007, Huang et. al 2012.

Value

aBetaSTD

A standardized coefficient matrix whose columns correspond to nlambda values of lambda.

aBetaO

A coefficient matrix (without standardization) whose columns correspond to nlambda values of lambda.

lambda

The lambda values used.

ll

The log likelihood values.

g

A vector indicating the group structure of the covariates.

Author(s)

Xuan Dang <[e-mail]>

References

Wang, L., Chen, G., and Li, H. Group SCAD regression analysis for microarray time course gene expression data. Bioinformatics 23.12 (2007), pp. 1486-1494.

Huang, J., Breheny, P., and Ma, S. A selective review of group selection in high-dimensional models. Statistical Science 27.4 (2012), pp. 481-499.

Examples

set.seed(200)
N <- 50
p <- 9
x <- matrix(rnorm(N * p), nrow = N)
beta <- c(.65,.65,0,0,.65,.65,0,.65,0)
hx <- exp(x %*% beta) 
ty <- rexp(N,hx) 
tcens <- 1 - rbinom(n=N, prob = 0.2, size = 1)
y <- data.frame(illt=ty, ills=tcens)
names(y) <- c("time", "status")

g <- c(1,1,2,2,3,3,2,3,2)
m <- c(sqrt(2),sqrt(4),sqrt(3))

fit <- grpCox(x,y,g,m,penalty="glasso")
plot.gCoef(fit$aBetaO, fit$g, fit$lambda)