COXvanISISscad: (Iterative) Sure Independence Screening ((I)SIS) in the Cox proportional hazards regression model

Description

These functions implement the iterative sure independence screening with COXvanISISscad for vanilla ISIS and COXvarISISscad for variant ISIS in Cox proportional hazards regression model.

Usage

COXvanISISscad(x, time, status,  method = "efron", nsis=NULL, folds=NULL, 
rank.method="obj", eps0=1e-5, inittype='NoPen', tune.method="AIC",
ISIStypeCumulative=FALSE, DOISIS=TRUE, maxloop=5)

COXvarISISscad(x, time, status,  method = "efron", nsis=NULL, folds=NULL, 
rank.method="obj", eps0=1e-5, inittype='NoPen', tune.method="AIC",
vartype="First",  ISIStypeCumulative=FALSE, DOISIS=TRUE, maxloop=5)

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.

nsis

number of pedictors recuited by (I)SIS.

folds

fold information for cross validation.

rank.method

the criterion for ranking predictor variables in (I)SIS. It can be either obj or coeff.

tune.method

method for tuning regularization parameter.

inittype

inittype specifies the type of initial solution for the one-step SCAD. It can be either NoPen or L1.

vartype

vartype specifies variant (I)SIS of first type or second type.

ISIStypeCumulative

ISIStypeCumulative specifies whether to penalize variables selected by the previous step of the ISIS iteration in the following SCAD step. (ISIStypeCumulative= FALSE put penalties on all variables. In this case, the procedure is

DOISIS

DOISIS specifies whether to do iterative SIS.

maxloop

maximum number of loops in iterative SIS.

eps0

an effective zero relative to the scale of the maximum absolute marginal regression coefficients.

Value

Returns an object with
initRANKorderinitial predictor ranking order for vanilla SIS.
detail.pickind, detail.ISISinddetails of each loop of ISIS.
SISindthe vector of indices selected by SIS.
ISISindthe vector of indices selected by ISIS.
normal.exitindicator of normal exit.
nsisnumber of pedictors recuited by (I)SIS.
initRANKorder1, initRANKorder2initial predictor ranking order for variant SIS.

References

Jianqing Fan and Jinchi Lv (2008) Sure independence screening for ultra-high dimensional feature space (with discussion) Journal of Royal Statistical Society B, 36, 849-911. Jianqing Fan, Richard Samworth, and Yichao Wu (2009) Ultrahigh dimensional variable selection: beyond the linear model Journal of Machine Learning Research, to appear. Jianqing Fan and Rui Song (2009) Sure Independence Screening in Generalized Linear Models with NP-Dimensionality, technical report.

Examples

Run this code

set.seed(0)
n=150
p=200
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)

cox.van.sis <- COXvanISISscad(x, time, status)

cox.var.sis <- COXvarISISscad(x, time, status, vartype='Second')

#####compare the result
cox.van.sis$SIS

cox.van.sis$ISIS

cox.var.sis$SIS

cox.var.sis$ISIS