Fit regularization paths for Cox models with grouped penalties over a grid of values for the regularization parameter lambda.
grpsurv(
X,
y,
group = 1:ncol(X),
penalty = c("grLasso", "grMCP", "grSCAD", "gel", "cMCP"),
gamma = ifelse(penalty == "grSCAD", 4, 3),
alpha = 1,
nlambda = 100,
lambda,
lambda.min = {
if (nrow(X) > ncol(X))
0.001
else 0.05
},
eps = 0.001,
max.iter = 10000,
dfmax = p,
gmax = length(unique(group)),
tau = 1/3,
group.multiplier,
warn = TRUE,
returnX = FALSE,
...
)An object with S3 class "grpsurv" containing:
The fitted matrix of coefficients. The number of rows is equal to
the number of coefficients, and the number of columns is equal to nlambda.
Same as above.
The sequence of lambda values in the path.
Same as above.
Same as above.
Same as above.
The deviance of the fitted model at each value of lambda.
The number of observations.
A vector of length nlambda containing estimates of effective
number of model parameters all the points along the regularization path. For
details on how this is calculated, see Breheny and Huang (2009).
A vector of length nlambda containing the number of iterations
until convergence at each value of lambda.
A named vector containing the multiplicative constant applied to each group's penalty.
For Cox models, the following objects are also returned (and are necessary
to estimate baseline survival conditional on the estimated regression
coefficients), all of which are ordered by time on study (i.e., the ith row
of W does not correspond to the ith row of X):
Matrix of exp(beta) values for each subject over all lambda
values.
Times on study.
Failure event indicator.
The design matrix.
The time-to-event outcome, as a two-column matrix or
Surv object. The first column should be time on
study (follow up time); the second column should be a binary variable with 1
indicating that the event has occurred and 0 indicating (right) censoring.
A vector describing the grouping of the coefficients. For
greatest efficiency and least ambiguity (see details), it is best if
group is a factor or vector of consecutive integers, although
unordered groups and character vectors are also allowed. If there are
coefficients to be included in the model without being penalized, assign
them to group 0 (or "0").
The penalty to be applied to the model. For group selection,
one of grLasso, grMCP, or grSCAD. For bi-level
selection, one of gel or cMCP. See below for details.
Tuning parameter of the group or composite MCP/SCAD penalty (see details). Default is 3 for MCP and 4 for SCAD.
grpsurv allows for both a group penalty and an L2
(ridge) penalty; alpha controls the proportional weight of the
regularization parameters of these two penalties. The group penalties'
regularization parameter is lambda*alpha, while the regularization
parameter of the ridge penalty is lambda*(1-alpha). Default is 1: no
ridge penalty.
The number of lambda values. Default is 100.
A user-specified sequence of lambda values. By default, a
sequence of values of length nlambda is computed automatically,
equally spaced on the log scale.
The smallest value for lambda, as a fraction of lambda.max. Default is .001 if the number of observations is larger than the number of covariates and .05 otherwise.
Convergence threshhold. The algorithm iterates until the RMSD
for the change in linear predictors for each coefficient is less than
eps. Default is 0.001.
Maximum number of iterations (total across entire path). Default is 10000.
Limit on the number of parameters allowed to be nonzero. If this limit is exceeded, the algorithm will exit early from the regularization path.
Limit on the number of groups allowed to have nonzero elements. If this limit is exceeded, the algorithm will exit early from the regularization path.
Tuning parameter for the group exponential lasso; defaults to 1/3.
A vector of values representing multiplicative factors by which each group's penalty is to be multiplied. Often, this is a function (such as the square root) of the number of predictors in each group. The default is to use the square root of group size for the group selection methods, and a vector of 1's (i.e., no adjustment for group size) for bi-level selection.
Return warning messages for failures to converge and model saturation? Default is TRUE.
Return the standardized design matrix? Default is FALSE.
Not used.
Patrick Breheny
The sequence of models indexed by the regularization parameter lambda
is fit using a coordinate descent algorithm. In order to accomplish this,
the second derivative (Hessian) of the Cox partial log-likelihood is
diagonalized (see references for details). The objective function is
defined to be $$Q(\beta|X, y) = \frac{1}{n} L(\beta|X, y) + $$$$
P_\lambda(\beta)$$
where the loss function L is the negative partial log-likelihood (half the
deviance) from the Cox regression model.
See here for more details.
Presently, ties are not handled by grpsurv in a particularly
sophisticated manner. This will be improved upon in a future release of
grpreg.
Breheny P and Huang J. (2009) Penalized methods for bi-level variable selection. Statistics and its interface, 2: 369-380. tools:::Rd_expr_doi("10.4310/sii.2009.v2.n3.a10")
Huang J, Breheny P, and Ma S. (2012). A selective review of group selection in high dimensional models. Statistical Science, 27: 481-499. tools:::Rd_expr_doi("10.1214/12-sts392")
Breheny P and Huang J. (2015) Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors. Statistics and Computing, 25: 173-187. tools:::Rd_expr_doi("10.1007/s11222-013-9424-2")
Breheny P. (2015) The group exponential lasso for bi-level variable selection. Biometrics, 71: 731-740. tools:::Rd_expr_doi("10.1111/biom.12300")
Simon N, Friedman JH, Hastie T, and Tibshirani R. (2011) Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent. Journal of Statistical Software, 39: 1-13. tools:::Rd_expr_doi("10.18637/jss.v039.i05")
plot.grpreg(), predict.grpsurv(), cv.grpsurv()
data(Lung)
X <- Lung$X
y <- Lung$y
group <- Lung$group
fit <- grpsurv(X, y, group)
plot(fit)
S <- predict(fit, X, type='survival', lambda=0.05)
plot(S, xlim=c(0,200))
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