cox.interaction: Interaction Cox adaptive index model
In AIM: AIM: adaptive index model

Description Usage Arguments Details Value Author(s) References Examples

Estimate adpative index model for survival outcomes in the context of Cox regression. The resulting index characterizes the interaction between covariates and treatment.

1	cox.interaction(x, trt, y, delta, nsteps=8, mincut=.1, backfit=F, maxnumcut=1, dirp=0)

`x`	n by p matrix. The covariate matrix
`trt`	n vector. The treatment indicator
`y`	n vector. The observed follow-up time
`delta`	n 0/1 vector. The status indicator. 1=failure and 0=alive.
`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 re-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)" and -1 represents "(x<cut)". Alternatively, "dirp=0" represents that there is no pre-given direction for any of the predictor.

cox.interaction sequentially estimates a sequence of adaptive index models with up to "nsteps" terms for survival outcomes. The aglorithm seeks the index having the strong interaction with the treatment in the Cox regression. The appropriate number of binary rules can be selected via K-fold cross-validation (cv.cox.interaction).

cox.interaction returns maxsc, which is the observed partial likelihood score test statistics for the index*treatment interaction in the fitted model and res, which is a list with components

`jmaa`	number of predictors
`cutp`	split points for the binary rules
`maxdir`	direction of split: 1 represents "(x>cut)" and -1 represents "(x<cut)"
`maxsc`	observed partial likelihood score test statistics for the interaction

Lu Tian and Robert Tibshirani

Lu Tian and Robert Tibshirani (2010) "Adaptive index models for marker-based risk stratification", Tech Report, available at http://www-stat.stanford.edu/~tibs/AIM.

## 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
trt=rbinom(n,1,0.5)
fail.time=rexp(n)*exp(-beta*z*trt)
cen.time=rexp(n)*1.25
y=pmin(fail.time, cen.time)
y=round(y*10)/10
delta=1*(fail.time<cen.time)


## fit the interaction Cox AIM model 
a=cox.interaction(x, trt, y, delta, nsteps=10)
 
## examine the model sequence 
print(a)

## compute the index based on the 2nd model in the sequence using data x 
z.prd=index.prediction(a$res[[2]],x)

## compute the index based on the 2nd model of the sequence using new data xx, and compare the result with the true index
nn=10
xx=matrix(rnorm(nn*p), nn, p)
zz=(xx[,1]<0.2)+(xx[,5]>0.2)
zz.prd=index.prediction(a$res[[2]],xx) 
cbind(zz, zz.prd)