pcoxtime: Fit penalized Cox model

In pcoxtime: Penalized Cox Proportional Hazard Model for Time-Dependent Covariates

Fit penalized Cox model

Description

Fits a Cox model with either lasso, ridge or elasticnet penalty for both time-independent and time-dependent (varying) covariates survival data.

Usage

pcoxtime(
  formula,
  data,
  alpha = 1,
  lambda = 1,
  maxiter = 1e+05,
  tol = 1e-08,
  quietly = FALSE,
  lambmax = FALSE,
  origin_scale = TRUE,
  contrasts.arg = NULL,
  xlevs = NULL,
  na.action = na.omit,
  ...
)

Arguments

formula	object of class formula describing the model. The response is specified similar to Surv function from package survival. The terms (predictors) are specified on the right of "~" in the formula.
data	optional data frame containing variables specified in the formula.
alpha	elasticnet mixing parameter, with 0 ≤α≤ 1. See details
lambda	tuning parameter for the lasso penalization, with λ ≥ 0. λ = 0 fits unpenalized Cox model. See details
maxiter	maximum number of iterations to convergence. Default is 1e4. Consider increasing it if the model does not converge.
tol	convergence threshold for proximal gradient gradient descent. Each proximal update continues until the relative change in all the coefficients (i.e. √{∑(β_{k+1} - β_k)^2}/stepsize) is less than tol. The default value is 1e-8.
quietly	logical. If TRUE, iteration progress printed.
lambmax	logical. Sufficiently large, λ_{\max}, that sets β = 0 for regularization path. If TRUE, λ_{\max} is returned.
origin_scale	logical. If TRUE (default), the estimated coefficients are returned on the original covariate scale. Otherwise, FALSE, coefficients are standardized.
contrasts.arg	an optional list. See the contrasts.arg of model.matrix.default.
xlevs	a named list of character vectors giving the full set of levels to be assumed for each factor. See model.frame.
na.action	a function which indicates what should happen when the data contain NAs. See model.frame.
...	additional arguments not implemented.

Details

The algorithm estimates the coefficients based on observed survival data, with either time-independent or time-dependent covariates, through penalized partial log-likelihood

\mathrm{pen} ~ \mathit{\ell(β)_{α, λ}} = -\mathit{\ell(β)} + P_{α, λ}(β)

using elasticnet (which combines both lasso and ridge) penalty

λ≤ft(α∑_{i=1}^p|β_i| + 0.5(1 - α)∑_{i=1}^pβ_i^2 \right)

.

alpha = 1 (α) is the lasso penalty, and alpha = 0 is the ridge penalty. lambda = 0 fits the standard Cox proportional hazard model.

User can provide a particular lambda. Typical usage is to use the pcoxtimecv to select the optimal lambda first.

The routine to handle time-dependent covariates is similar to that implemented in coxph: if there are tied event times, Breslow approximation is used.

Value

An S3 object of class pcoxtime:

coef	a named vector of coefficients. If any of the coefficients violates KKT conditions, the model will print a warning but still return coefficient estimates.
min.nloglik	estimated log-likelihood at convergence.
min.dev	the deviation satisfying the tol stopping creteria.
iter.dev	deviations between previous and current coefficient estimate at each iteration.
convergence	convergence message containing the number of iterations
n	the number of observations used in the fit.
n.risk	the number of individuals at risk at time t.
n.event	the number of events that occur at time t.
n.censor	the number of subjects who exit the risk set, without an event, at time t.
time	time points defined by the risk set.
Y	Surv object defining the event times and event status.
data	data frame used.
timevarlabel, eventvarlabel	time and event variables, respectively.
predictors	a vector of predictors/covariates in the model.
lambda, alpha	lambda and alpha used, respectively.
formula	model formula used in the fit.
means	vector of column means of the X matrix. Subsequent survival curves are adjusted to this value.
assign, xlevels, terms	See model.frame for assign, xlevels, contrasts and terms.

See Also

coxph, pcoxtimecv

Examples

# Time-independent covariates
if (packageVersion("survival")>="3.2.9") {
	data(cancer, package="survival")
} else {
	data(veteran, package="survival")
}
## Fit unpenalized Cox using pcoxtime
lam <- 0 # Should fit unpenalized Cox model
pfit1 <- pcoxtime(Surv(time, status) ~ factor(trt) + karno + diagtime + age + prior
	, data = veteran
	, lambda = lam 
	, alpha = 1
)
print(pfit1)

## fit survival::coxph
cfit1 <- coxph(Surv(time, status) ~ factor(trt) + karno + diagtime + age + prior
	, data = veteran
	, method = 'breslow'
	, ties = "breslow"
)
print(cfit1)

## Penalized Cox model (pcoxtime) 
lam <- 0.1
alp <- 0.5
pfit2 <- pcoxtime(Surv(time, status) ~ factor(trt) + karno + diagtime + age + prior
	, data = veteran
	, lambda = lam 
	, alpha = alp
)
print(pfit2)

# Time-varying covariates
data(heart, package="survival")
lam <- 0.1
alp <- 0.8
pfit2 <- pcoxtime(Surv(start, stop, event) ~ age + year + surgery + transplant
	, data = heart
	, lambda = lam
	, alpha = alp
)
print(pfit2)

pcoxtime documentation built on May 13, 2022, 1:05 a.m.