cv.cox.main: Cross-validation in main effect Cox AIM
In AIM: AIM: adaptive index model

Description Usage Arguments Details Value References Author(s) Examples

Cross-validation for selecting the number of binary rules in the main effect AIM with survival outcomes.

1	cv.cox.main(x, y, status, K.cv=5, num.replicate=1, nsteps, mincut=0.1, backfit=F, maxnumcut=1, dirp=0)

`x`	n by p matrix. The covariate matrix
`y`	n vector. The observed follow-up time
`status`	n 0/1 vector. The status indicator. 1=failure and 0=alive.
`K.cv`	K.cv-fold cross validation
`num.replicate`	number of independent replications of K-fold cross validations.
`nsteps`	the maximum number of binary rules to be included in the index
`backfit`	T/F. Whether the existing split points are adjusted after including new binary rules
`mincut`	the minimum cutting proportion for the binary rule at either end. It typically is between 0 and 0.2.
`maxnumcut`	the maximum number of binary splits per predictor
`dirp`	p vector. The given direction of the binary split for each of the p predictors. 0 represents "no pre-given direction"; 1 represents "(x>cut)"; -1 represents "(x<cut)". Alternatively, "dirp=0" represents that there is no pre-given direction for any of the predictor.

cv.cox.main implements the K-fold cross-validation for the main effect Cox AIM. It estimates the partial likelihood score test statistics in the test set for testing the association between the survival time and index constructed using training data. It also provides pre-validated fits for each observation and pre-validated partial likelihood score test statistics. The output can be used to select the optimal number of binary rules.

cv.cox.main returns

`kmax`	the optimal number of binary rules based the cross-validation
`meanscore`	nsteps-vector. The cross-validated partial likelihood score test statistics (significant at 0.05, if greater than 1.96) for the association between survival time and index.
`pvfit.score`	nsteps-vector. The pre-validated partial likelihood score test statistics (significant at 0.05, if greater than 1.96) for the association between survival time and index.
`preval`	nsteps by n matrix. Pre-validated fits for individual observation

L Tian and R Tibshirani Adaptive index models for marker-based risk stratification, Tech Report, available at http://www-stat.stanford.edu/~tibs/AIM.

R Tibshirani and B Efron, Pre-validation and inference in microarrays, Statist. Appl. Genet. Mol. Biol., 1:1-18, 2002.

Lu Tian and Robert Tibshirani

## generate data

set.seed(1)

n=200
p=10
x=matrix(rnorm(n*p), n, p)
z=(x[,1]<0.2)+(x[,5]>0.2)
beta=1
fail.time=rexp(n)*exp(-beta*z)
cen.time=rexp(n)*1.25
y=pmin(fail.time, cen.time)
y=round(y*10)/10
delta=1*(fail.time<cen.time)


## cross-validate the main effect Cox AIM 
a=cv.cox.main(x, y, delta, nsteps=10, K.cv=3, num.replicate=3)
 

## examine the test statistics in the test set 
par(mfrow=c(1,2))
plot(a$meanscore, type="l")
plot(a$pvfit.score, type="l")


## construct the index with the optimal number of binary rules 
k.opt=a$kmax
a=cox.main(x, y, delta, nsteps=k.opt)
print(a)