AIM (version 1.01)

cv.lm.main: Cross-validation in main effect linear AIM

Description

Cross-validation for selecting the number of binary rules in the main effect linear AIM

Usage

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

Arguments

x

n by p matrix. The covariate matrix

y

n vector. The continuous response variable

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

mincut

the minimum cutting proportion for the binary rule at either end. It typically is between 0 and 0.2.

backfit

T/F. Whether the existing split points are adjusted after including new a binary rule

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

Value

cv.lm.main returns

kmax

the optimal number of binary rules based the cross-validation

meanscore

nsteps-vector. The cross-validated 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 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

References

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.

Details

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

Examples

## generate data
set.seed(1)

n=400
p=10
x=matrix(rnorm(n*p), n, p)
z=(x[,1]<0.2)+(x[,5]>0.2)
beta=1
y=beta*z+rnorm(n)


## cross-validate the linear main effects AIM
a=cv.lm.main(x, y,  nsteps=10, K.cv=5, num.replicate=3)
 
## examine score 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=lm.main(x, y, nsteps=k.opt)
print(a)