| Type: | Package |
| Title: | Penalized Cox Model for High-Dimensional Data with Grouped Predictors |
| Version: | 1.0.2 |
| Date: | 2023-12-10 |
| Author: | Xuan Dang |
| Maintainer: | Xuan Dang <xuandang11289@gmail.com> |
| Description: | Fit the penalized Cox models with both non-overlapping and overlapping grouped penalties including the group lasso, group smoothly clipped absolute deviation, and group minimax concave penalty. The algorithms combine the MM approach and group-wise descent with some computational tricks including the screening, active set, and warm-start. Different tuning regularization parameter methods are provided. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| Imports: | Rcpp (≥ 1.0.11) |
| LinkingTo: | Rcpp, RcppEigen |
| Depends: | Matrix (≥ 1.6-1.1), MASS, colorspace |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | yes |
| Packaged: | 2023-12-11 15:42:43 UTC; xuandang |
| Repository: | CRAN |
| Date/Publication: | 2023-12-11 16:00:11 UTC |
Penalized Cox Model for High-Dimensional Data with Grouped Predictors
Description
Fit the penalized Cox models with both non-overlapping and overlapping grouped penalties including the group lasso, group smoothly clipped absolute deviation, and group minimax concave penalty. The algorithms combine the MM approach and group-wise descent with some computational tricks including the screening, active set, and warm-start. Different tuning regularization parameter methods are provided.
Package Content
Index of help topics:
cv.grpCox Cross-validation for grpCox
cv.grpCoxOverlap Cross-validation for grpCoxOverlap
grpCox Fit a penalized Cox model.
grpCox-package Penalized Cox Model for High-Dimensional Data
with Grouped Predictors
grpCoxOverlap Fit a penalized regression path with
overlapping grouped covariates.
plot.Coef Plots the coefficient paths
plot.gCoef Plots the coefficient paths with the same color
for the covariates in the same group.
plot.llCV Plot the cross-validation curve produced by
cv.grpCox or cv.grpCoxOverlap
Maintainer
Xuan Dang <xuandang11289@gmail.com>
Author(s)
Xuan Dang
Cross-validation for grpCox
Description
Does k-fold cross-validation for grpCox
Usage
cv.grpCox(X, y, g, m, penalty=c("glasso", "gSCAD", "gMCP"), lambda=NULL,
nlambda=100, rlambda=NULL, gamma=switch(penalty, SCAD = 3.7, 3),
standardize=TRUE, thresh=1e-3, maxit=1e+4, nfolds=10, foldid=NULL)
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 |
lambda |
A user supplied sequence of |
nlambda |
The number of |
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. |
nfolds |
The number of cross-validation folds. Default is 10. |
foldid |
An optional vector of values between 1 and nfolds identifying what fold each observation is in. |
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. |
mBetaSTD |
The coefficient in standardized form gives maximum log-likelihood value using the first cross-validation method. |
mBetaO |
The coefficient in original form gives maximum log-likelihood value using the first cross-validation method. |
pBetaSTD |
The coefficient in standardized form gives maximum log-likelihood value using the penalized cross-validation method. |
pBetaO |
The coefficient in original formgives maximum log-likelihood value using the penalized cross-validation method. |
fit |
A matrix includes lambda value, the mean cross-validation error. |
lambda |
The lambda values used. |
g |
A vector indicating the group structure of the covariates. |
cvmax |
The maximum value of log likelihood. |
lambda.max |
The value of lambda corresponds to the maximum value of log likelihood using the first cross-validation method. |
lambda.pcvl |
The value of lambda corresponds to the maximum value of log likelihood using the penalized cross-validation method. |
Author(s)
Xuan Dang <xuandang11289@gmail.com>
References
Verweij PJ, Houwelingen HC. Cross-validation in survival analysis. Statistics in Medicine 1993; 12(24): 385-395.
Ternes N, Rotolo F, Michiels S. Empirical extensions of the lasso penalty to reduce the false discovery rate in highdimensional Cox regression models. Statistics in Medicine 2016; 35(15): 2561-73.
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))
cvfit <- cv.grpCox(x,y,g,m,penalty="glasso")
plot.llCV(cvfit)
plot.gCoef(cvfit$aBetaO, cvfit$g, cvfit$lambda)
Cross-validation for grpCoxOverlap
Description
Does k-fold cross-validation for grpCoxOverlap
Usage
cv.grpCoxOverlap(X0, y, group, penalty=c("glasso", "gSCAD", "gMCP"),
lambda=NULL, nlambda=100, rlambda=NULL,gamma=switch(penalty, SCAD = 3.7, 3),
standardize=TRUE, thresh=1e-3, maxit=1e+4, nfolds=10, foldid=NULL,
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 |
lambda |
A user supplied sequence of |
nlambda |
The number of |
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. |
nfolds |
The number of cross-validation folds. Default is 10. |
foldid |
An optional vector of values between 1 and nfolds identifying what fold each observation is in. |
returnLatent |
Return the coefficient matrix in latent space. Default is TRUE. |
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. |
mBetaLatent |
The coefficient in latent space gives maximum log-likelihood value using the first cross-validation method. |
mBetaOri |
The coefficient in original space gives maximum log-likelihood value using the first cross-validation method. |
pBetaLatent |
The coefficient in latent space gives maximum log-likelihood value using the penalized cross-validation method. |
pBetaOri |
The coefficient in original space gives maximum log-likelihood value using the penalized cross-validation method. |
fit |
A matrix includes lambda value, the mean cross-validation error. |
lambda |
The lambda values used. |
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. |
cvmax |
The maximum value of log likelihood. |
lambda.max |
The value of lambda corresponds to the maximum value of log likelihood using the first cross-validation method. |
lambda.pcvl |
The value of lambda corresponds to the maximum value of log likelihood using the penalized cross-validation method. |
Author(s)
Xuan Dang <xuandang11289@gmail.com>
References
Verweij PJ, Houwelingen HC. Cross-validation in survival analysis. Statistics in Medicine 1993; 12(24): 385-395.
Ternes N, Rotolo F, Michiels S. Empirical extensions of the lasso penalty to reduce the false discovery rate in highdimensional Cox regression models. Statistics in Medicine 2016; 35(15): 2561-73.
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))
cvfit <- cv.grpCoxOverlap(x, y, group, penalty="glasso", nlambda=50)
plot.llCV(cvfit)
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 |
lambda |
A user supplied sequence of |
nlambda |
The number of |
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 <xuandang11289@gmail.com>
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)
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 |
lambda |
A user supplied sequence of |
nlambda |
The number of |
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 <xuandang11289@gmail.com>
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$lambda)
Plots the coefficient paths
Description
Plots the coefficient values as a function of the lambda values used.
Usage
## S3 method for class 'Coef'
plot(x, lambda, label=TRUE,xlab="log(Lambda)",
ylab="Coefficients",title=NULL,...)
Arguments
x |
A matrix of coefficients. |
lambda |
The lambda values used. |
label |
The indices of covariates. Default is TRUE. |
xlab |
The name of the x-axis. |
ylab |
The name of the y-axis. |
title |
The title of the plot. |
... |
further arguments to plot |
Details
A plot is produced, and nothing is returned.
Value
No return value.
Author(s)
Xuan Dang <xuandang11289@gmail.com>
Examples
set.seed(100001)
N <- 50
p <- 6
times <- 1:p
rho <- 0.5
H <- abs(outer(times, times, "-"))
C <- 1 * rho^H
C[cbind(1:p, 1:p)] <- C[cbind(1:p, 1:p)]
sigma <- matrix(C,p,p)
mu <- rep(0,p)
x <- mvrnorm(n=N, mu, sigma)
beta <- c(0, .8, 1, 2, 1, 0)
hx <- exp(x %*% beta)
ty <- rexp(N,hx)
tcens <- 1 - rbinom(n=N, prob = 0.2, size = 1)
y <- data.frame(illt=ty, ills=tcens)
names(y) <- c("time", "status")
group <- list(g1 = c(1,2,3,4), g2 = c(1,2,6), g3 = c(2,3), g4 = c(4,5), g5 = c(5))
fit <- grpCoxOverlap(x, y, group, penalty="glasso", nlambda=50)
# plot the coefficient values in latent space
plot.gCoef(fit$aBetaLatent, fit$glatent, fit$lambda)
# plot the coefficient values in original space
plot.Coef(fit$aBetaOri, fit$lambda)
Plots the coefficient paths with the same color for the covariates in the same group.
Description
Plots the coefficient values as a function of the lambda values used. The covariates in the same group have the same color.
Usage
## S3 method for class 'gCoef'
plot(x,g,lambda,label=TRUE,xlab="log(Lambda)",
ylab="Coefficients", title=NULL,...)
Arguments
x |
A matrix of coefficients. |
g |
A vector indicating the group structure of the covariates. |
lambda |
The lambda values used. |
label |
The indices of covariates. Default is TRUE. |
xlab |
The name of the x-axis. |
ylab |
The name of the y-axis. |
title |
The title of the plot. |
... |
further arguments to plot |
Details
A plot is produced, and nothing is returned.
Value
No return value.
Author(s)
Xuan Dang <xuandang11289@gmail.com>
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)
Plot the cross-validation curve produced by cv.grpCox or cv.grpCoxOverlap
Description
Plots the cross-validation curve, and upper and lower standard deviation curves, as a function of the lambda values used.
Usage
## S3 method for class 'llCV'
plot(x,...)
Arguments
x |
fitted cv.grpCox or cv.grpCoxOverlap object |
... |
further arguments to plot |
Details
A plot is produced, and nothing is returned.
Value
No return value.
Author(s)
Xuan Dang <xuandang11289@gmail.com>
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))
cvfit <- cv.grpCox(x,y,g,m,penalty="glasso")
plot.llCV(cvfit)