cox.ridge: Fit a Cox model with a ridge penalty on all covariates

Description

Fits a simple Cox model with a ridge penalty on all coefficients. The penalty weight can be optimized using a REML-type likelihood method or be chosen by the user.

Usage

cox.ridge(formula, lambda = 1, lambdaFixed = FALSE, eps = 10e-6, data = sys.parent(),
iter.max = 200, mon = FALSE)

Arguments

formula

a formula object, with the response on the left of a '~' operator, and the terms on the right. The response must be a survival object as returned by the 'Surv' function.

lambdaFixed

when TRUE the function does not seek to optimize the penalty weight.

lambda

When lambdaFixed is FALSE lambda is a scalar giving the starting value for the weight of the penalty. When lambdaFixed is true lambda is the chosen weight of the penalty.

eps

a small value. The criterion of convergance.

data

an optional data frame containing the variables named in the formula.

iter.max

maximum number of iterations, default is 200.

mon

when true the function prints out the computed lambda weigh in each iteration.

Value

call: function call.
coef: the vector of coefficients.
loglik: the penalized log-likelihood of the model.
time: a vector with failure/censoring times.
death: a vector of status indicator.
X: a matrix of covariates.
iter: number of iterations used to maximise likelihood at a fixed lambda.
inter.it: number of iterations used to find optimal lambda.'
lambda: optimal weight of the penalty.
Hat: the hat matrix at convergance.
hess: the Hessian matrix of second derivatives.

References

Perperoglou A.(2013)Cox models with dynamic ridge penalties on time varying effects of the covariates. Statistics in Medicine, to appear

Examples

Run this code

data(ova)
attach(ova)
X <- cbind(karn,diam,figo)
X <- apply(X,2,function(x){(x-mean(x))/sqrt(var(x))})#standardize covariates
fit <- cox.ridge(Surv(time,death)~X,lambda=1)
fit ##regression coefficients correspond to the standardized covariates