Fit a Cox regression model with elastic net regularization for a path of lambda values

Fit a Cox regression model via penalized maximum likelihood for a path of lambda values. Can deal with (start, stop] data and strata, as well as sparse design matrices.

cox.path(
  x,
  y,
  weights = NULL,
  offset = NULL,
  alpha = 1,
  nlambda = 100,
  lambda.min.ratio = ifelse(nobs < nvars, 0.01, 1e-04),
  lambda = NULL,
  standardize = TRUE,
  thresh = 1e-10,
  exclude = NULL,
  penalty.factor = rep(1, nvars),
  lower.limits = -Inf,
  upper.limits = Inf,
  maxit = 1e+05,
  trace.it = 0,
  ...
)

Arguments

x: See glmnet help file
y: Survival response variable, must be a Surv or stratifySurv object.
weights: See glmnet help file
offset: See glmnet help file
alpha: See glmnet help file
nlambda: See glmnet help file
lambda.min.ratio: See glmnet help file
lambda: See glmnet help file
standardize: See glmnet help file
thresh: Convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the maximum change in the objective after any coefficient update is less than thresh times the null deviance. Default value is 1e-10.
exclude: See glmnet help file
penalty.factor: See glmnet help file
lower.limits: See glmnet help file
upper.limits: See glmnet help file
maxit: See glmnet help file
trace.it: Controls how much information is printed to screen. Default is trace.it=0 (no information printed). If trace.it=1, a progress bar is displayed. If trace.it=2, some information about the fitting procedure is printed to the console as the model is being fitted.
...: Other arguments passed from glmnet (not used right now).

Value

An object of class "coxnet" and "glmnet".

a0: Intercept value, NULL for "cox" family.
beta: A nvars x length(lambda) matrix of coefficients, stored in sparse matrix format.
df: The number of nonzero coefficients for each value of lambda.
dim: Dimension of coefficient matrix.
lambda: The actual sequence of lambda values used. When alpha=0, the largest lambda reported does not quite give the zero coefficients reported (lambda=inf would in principle). Instead, the largest lambda for alpha=0.001 is used, and the sequence of lambda values is derived from this.
dev.ratio: The fraction of (null) deviance explained. The deviance calculations incorporate weights if present in the model. The deviance is defined to be 2*(loglike_sat - loglike), where loglike_sat is the log-likelihood for the saturated model (a model with a free parameter per observation). Hence dev.ratio=1-dev/nulldev.
nulldev: Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the 0 model.
npasses: Total passes over the data summed over all lambda values.
jerr: Error flag, for warnings and errors (largely for internal debugging).
offset: A logical variable indicating whether an offset was included in the model.
call: The call that produced this object.
nobs: Number of observations.

Details

Sometimes the sequence is truncated before nlambda values of lambda have been used. This happens when cox.path detects that the decrease in deviance is marginal (i.e. we are near a saturated fit).

Examples

set.seed(2)
nobs <- 100; nvars <- 15
xvec <- rnorm(nobs * nvars)
xvec[sample.int(nobs * nvars, size = 0.4 * nobs * nvars)] <- 0
x <- matrix(xvec, nrow = nobs)
beta <- rnorm(nvars / 3)
fx <- x[, seq(nvars / 3)] %*% beta / 3
ty <- rexp(nobs, exp(fx))
tcens <- rbinom(n = nobs, prob = 0.3, size = 1)
jsurv <- survival::Surv(ty, tcens)
fit1 <- glmnet:::cox.path(x, jsurv)

# works with sparse x matrix
x_sparse <- Matrix::Matrix(x, sparse = TRUE)
fit2 <- glmnet:::cox.path(x_sparse, jsurv)

# example with (start, stop] data
set.seed(2)
start_time <- runif(100, min = 0, max = 5)
stop_time <- start_time + runif(100, min = 0.1, max = 3)
status <- rbinom(n = nobs, prob = 0.3, size = 1)
jsurv_ss <- survival::Surv(start_time, stop_time, status)
fit3 <- glmnet:::cox.path(x, jsurv_ss)

# example with strata
jsurv_ss2 <- stratifySurv(jsurv_ss, rep(1:2, each = 50))
fit4 <- glmnet:::cox.path(x, jsurv_ss2)