cv.logistic.interaction: Cross-validation in interaction logistic 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 interaction AIM with binary outcomes.

1	cv.logistic.interaction(x, trt, y, K.cv=5, num.replicate=1, nsteps, mincut=0.1, backfit=F, maxnumcut=1, dirp=0, weight=1)

`x`	n by p matrix. The covariate matrix
`trt`	n vector. The treatment indicator
`y`	n 0/1 vector. The binary 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 a new 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<cut)". Alternatively, "dirp=0" represents that there is no pre-given direction for any of the predictor.
`weight`	a positive value. The weight given to responses: "weight=0" means that all observations are equally weighted.

cv.logistic.interaction implements the K-fold cross-validation for the interaction logistic AIM. It estimates the score test statistics in the test set for testing the treatment*index interaction. It also provides pre-validated fits for each observation and pre-validated score test statistic. The output can be used to select the optimal number of binary rules.

cv.logistic.interaction 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 treatment*index interaction.
`pvfit.score`	nsteps-vector, the pre-validated score test statistics (significant at 0.05, if greater than 1.96) for the treatment*index interaction.
`preval`	nsteps by n matrix. Prevalidated 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=400
p=10
x=matrix(rnorm(n*p), n, p)
z=(x[,1]<0.2)+(x[,5]>0.2)
trt=rbinom(n,1, 0.5)
beta=1
prb=1/(1+exp(trt-beta*trt*z-0.5))
y=rbinom(n,1,prb)


## cross-validate the logistic interaction AIM 
a=cv.logistic.interaction(x, trt, y, nsteps=10, K.cv=4, num.replicate=5)
 
## 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=logistic.interaction(x, trt, y, nsteps=k.opt)
print(a)

Loading required package: survival
$res
$res[[1]]
     jmax      cutp maxdir    maxsc
[1,]    1 0.3065579     -1 3.308045

$res[[2]]
     jmax      cutp maxdir    maxsc
[1,]    1 0.3065579     -1 3.308045
[2,]    5 0.2854559      1 4.734028

$res[[3]]
     jmax      cutp maxdir    maxsc
[1,]    1 0.3065579     -1 3.308045
[2,]    5 0.2854559      1 4.734028
[3,]    9 0.9669120      1 5.224655


$maxsc
[1] 3.308045 4.734028 5.224655