scadcox: SCAD regularized loglikelihood for Cox proportional hazards regression models

Description

These functions solve SCAD regularized loglikelihood for Cox proportional hazards regression models; scadcox does the one-step SCAD while fullscadcox solves the SCAD in a fully iterative method.

Usage

scadcox(x, time, status,  method="efron", wt.initsoln=NULL, lambda, 
    initsoln=NULL, weight = NULL, function.precision=1e-10,
    nopenalty.subset=NULL)
    
fullscadcox(x, time, status,  method="efron", lambda, 
    initsoln=NULL, weight = NULL, function.precision=1e-10,
    nopenalty.subset=NULL, eps0=1e-5, maxloop=10)

Arguments

an (n * p) matrix of features.

time

an (n) vector of the follow up time for right censored data.

status

an (n) vector of the status indicator, normally 0=alive, 1=dead.

method

indicates how to handle observations that have tied (i.e., identical) survival times. The default "efron" method is generally preferred to the once-popular "breslow" method.

wt.initsoln

a (p) vector of initial solution for one-step SCAD.

lambda

the regularization parameter.

initsoln

a (p) vector of initial solution.

weight

an optional (n) vector of weights to be used in the fitting process.

function.precision

function.precision parameter used in the internal solver. Default is 1e-10.

nopenalty.subset

a set of indices for the predictors that are not subject to the L1 penalty.

eps0

an effecitve zero.

maxloop

the maximum number of loops for the SCAD iteration.

Value

They return a (p) vector of estimated coefficients.

References

Jianqing Fan and Runze Li (2002) Variable Selection for Cox's Proportional Hazards Model and Frailty Model. The Annals of Statistics, 30, 74-99. Hui Zou and Runze Li (2008) One-step Sparse Estimates in Nonconcave Penalized Likelihood Models (with discussion). The Annals of Statistics, 36, 1509-1533

Examples

Run this code

set.seed(0)
n=400
p=1000
truerho=0.5
beta <- c(4,4,4,-6*sqrt(2),4/3, rep(0,p-5))

corrmat=diag(rep(1-truerho, p))+matrix(truerho, p, p)
corrmat[,4]=sqrt(truerho)
corrmat[4, ]=sqrt(truerho)
corrmat[4,4]=1
corrmat[,5]=0
corrmat[5,]=0
corrmat[5,5]=1
cholmat=chol(corrmat)

x=matrix(rnorm(p*n, mean=0, sd=1), n, p)
x=x%*%cholmat

myrates <- exp(x%*%beta)

ytrue <- rexp(n, rate = myrates) 
cen <- rexp(n, rate = 0.1 )
time <- pmin(ytrue, cen)
status <- as.numeric(ytrue <= cen)

w1 <- scadcox(x[,1:100],time,status,lambda=0.003)
w2 <- coxph(Surv(time,status)~x[,1:100])$coef