AIM (version 1.01)

cox.main: Main effect Cox adaptive index model

Description

Estimate adpative index model for survival outcomes in the context of Cox regression. The resulting index characterizes the main covariate effect on the hazard.

Usage

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

Arguments

x
n by p matrix. The covariate matrix
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 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

Value

cox.main returns maxsc, which is the partial likelihood score test statistics 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
maxsc
observed partial likelihood score test statistics for the main effect

Details

cox.main sequentially estimates a sequence of adaptive index models with up to "nsteps" terms for survival outcomes. The appropriate number of binary rules can be selected via K-fold cross-validation (cv.cox.main).

References

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.

Examples

Run this code
## 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)


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


## compute the index based on the 2nd model of 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)

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