I always like throw in a vote for penalized regression perspectives: using R's glmnet function you can fit a cox model with all your variables, and it will automatically shrink the non-important variables down to 0.

From the glmnet examples:

set.seed(1010)
n=1000;p=100
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)


beta=rnorm(nzc)
fx=x[,seq(nzc)]%*%beta/3
hx=exp(fx)
ty=rexp(n,hx)
tcens=rbinom(n=n,prob=.3,size=1)# censoring indicator
y=cbind(time=ty,status=1-tcens) # y=Surv(ty,1-tcens) with library(survival)
foldid=sample(rep(seq(10),length=n))
fit1_cv=cv.glmnet(x,y,family="cox",foldid=foldid)
plot(fit1_cv)
title("Cox Family",line=2.5)

I always like throw in a vote for penalized regression perspectives: using R's glmnet function you can fit a Cox model with all your variables, and it will automatically shrink the coefficient for non-important variables down to 0.

From the glmnet examples:

set.seed(1010)
n=1000;p=100
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)


beta=rnorm(nzc)
fx=x[,seq(nzc)]%*%beta/3
hx=exp(fx)
ty=rexp(n,hx)
tcens=rbinom(n=n,prob=.3,size=1)# censoring indicator
y=cbind(time=ty,status=1-tcens) # y=Surv(ty,1-tcens) with library(survival)
foldid=sample(rep(seq(10),length=n))
fit1_cv=cv.glmnet(x,y,family="cox",foldid=foldid)
plot(fit1_cv)
title("Cox Family",line=2.5)