grpCoxOverlap {grpCox}

Fit a penalized regression path with overlapping grouped covariates.

Description

Fit the regularization paths for Cox's models with overlapping grouped covariates.

Usage

grpCoxOverlap(X0, y, group, 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, returnLatent=TRUE)

Arguments

X0

The design matrix.

y

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

group

A list of groups, each includes indices of covariates in the group.

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.

returnLatent

Return the coefficient matrix in latent space. Default is TRUE.

Details

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

The method based on the latent group approach (Jacob et al. 2009, Obozinski et al. 2011.)

Value

aBetaLatent

A coefficient matrix whose columns correspond to nlambda values of lambda in latent space.

aBetaOri

A coefficient matrix whose columns correspond to nlambda values of lambda in original space.

lambda

The lambda values used.

ll

The log likelihood values.

group

A list of groups, each includes indices of covariates in the group.

glatent

A vector indicating the group structure of the covariates in latent space.

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.

Jacob, L., Obozinski, G., and Vert, J. P. (2009, June). Group lasso with overlap and graph lasso. In Proceedings of the 26th annual international conference on machine learning, ACM: 433-440.

Obozinski, G., Jacob, L., and Vert, J. P. (2011). Group lasso with overlaps: the latent group lasso approach.

Examples

set.seed(100001)
N <- 50
p <- 6
times <- 1:p
rho <- 0.5
H <- abs(outer(times, times, "-"))
C <- 1 * rho^H
C[cbind(1:p, 1:p)] <- C[cbind(1:p, 1:p)] 
sigma <- matrix(C,p,p)
mu <- rep(0,p)
x <- mvrnorm(n=N, mu, sigma)

beta <- c(0, .8, 1, 2, 1, 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")

group <- list(g1 = c(1,2,3,4), g2 = c(1,2,6), g3 = c(2,3), g4 = c(4,5), g5 = c(5))
fit <- grpCoxOverlap(x, y, group, penalty="glasso", nlambda=50)
# plot the coefficient values in latent space
plot.gCoef(fit$aBetaLatent, fit$glatent, fit$lambda)
# plot the coefficient values in original space
plot.Coef(fit$aBetaOri, fit$lambda)