ncvsurv  R Documentation 
Fit coefficients paths for MCP or SCADpenalized Cox regression models over a grid of values for the regularization parameter lambda, with option for an additional L2 penalty.
ncvsurv(
X,
y,
penalty = c("MCP", "SCAD", "lasso"),
gamma = switch(penalty, SCAD = 3.7, 3),
alpha = 1,
lambda.min = ifelse(n > p, 0.001, 0.05),
nlambda = 100,
lambda,
eps = 1e04,
max.iter = 10000,
convex = TRUE,
dfmax = p,
penalty.factor = rep(1, ncol(X)),
warn = TRUE,
returnX,
...
)
X 
The design matrix of predictor values. 
y 
The timetoevent outcome, as a twocolumn matrix or

penalty 
The penalty to be applied to the model. Either "MCP" (the default), "SCAD", or "lasso". 
gamma 
The tuning parameter of the MCP/SCAD penalty (see details). Default is 3 for MCP and 3.7 for SCAD. 
alpha 
Tuning parameter for the Mnet estimator which controls the
relative contributions from the MCP/SCAD penalty and the ridge, or L2
penalty. 
lambda.min 
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. 
nlambda 
The number of lambda values. Default is 100. 
lambda 
A userspecified sequence of lambda values. By default, a
sequence of values of length 
eps 
Convergence threshhold. The algorithm iterates until the RMSD for
the change in linear predictors for any coefficient is less than

max.iter 
Maximum number of iterations (total across entire path). Default is 1000. 
convex 
Calculate index for which objective function ceases to be locally convex? Default is TRUE. 
dfmax 
Upper bound for the number of nonzero coefficients. Default is no upper bound. However, for large data sets, computational burden may be heavy for models with a large number of nonzero coefficients. 
penalty.factor 
A multiplicative factor for the penalty applied to each
coefficient. If supplied, 
warn 
Return warning messages for failures to converge and model saturation? Default is TRUE. 
returnX 
Return the standardized design matrix along with the fit? By
default, this option is turned on if X is under 100 MB, but turned off for
larger matrices to preserve memory. Note that certain methods, such as

... 
Not used. 
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 loglikelihood is
diagonalized (see references for details). The objective function is
defined to be
Q(\betaX, y) = \frac{1}{n} L(\betaX, y) + P_\lambda(\beta),
where the loss function L is the deviance (2 times the partial loglikelihood) from the Cox regression mode. See here for more details.
Presently, ties are not handled by ncvsurv
in a particularly
sophisticated manner. This will be improved upon in a future release of
ncvreg.
An object with S3 class ncvsurv
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
.
A vector of length nlambda
containing the number of iterations until convergence at each value of lambda
.
The sequence of regularization parameter values in the path.
Same as above.
The last index for which the objective function is locally convex. The smallest value of lambda for which the objective function is convex is therefore lambda[convex.min]
, with corresponding coefficients beta[,convex.min]
.
The deviance of the fitted model at each value of lambda
.
The number of instances.
For Cox models, the following objects are also returned (and are necessary to
estimate baseline survival conditonal 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.
Additionally, if returnX=TRUE
, the object will also contain
The standardized design matrix.
Breheny P and Huang J. (2011) Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Annals of Applied Statistics, 5: 232253. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/10AOAS388")}
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: 113. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v039.i05")}
plot.ncvreg()
, cv.ncvsurv()
data(Lung)
X < Lung$X
y < Lung$y
op < par(mfrow=c(2,2))
fit < ncvsurv(X, y)
plot(fit, main=expression(paste(gamma,"=",3)))
fit < ncvsurv(X, y, gamma=10)
plot(fit, main=expression(paste(gamma,"=",10)))
fit < ncvsurv(X, y, gamma=1.5)
plot(fit, main=expression(paste(gamma,"=",1.5)))
fit < ncvsurv(X, y, penalty="SCAD")
plot(fit, main=expression(paste("SCAD, ",gamma,"=",3)))
par(op)
fit < ncvsurv(X,y)
ll < log(fit$lambda)
op < par(mfrow=c(2,1))
plot(ll, BIC(fit), type="l", xlim=rev(range(ll)))
lam < fit$lambda[which.min(BIC(fit))]
b < coef(fit, lambda=lam)
b[b!=0]
plot(fit)
abline(v=lam)
par(op)
S < predict(fit, X, type='survival', lambda=lam)
plot(S, xlim=c(0,200))
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