AIM (version 1.01)

logistic.interaction: Interaction logistic adaptive index model

Description

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

Usage

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

Arguments

x

n by p matrix. The covariate matrix

trt

n vector. The treatment indicator

y

n 0/1 vector. The binary response variable

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

weight

a positive value. The weight given to responses. "weight=0" means that all observations are equally weighted.

Value

logistic.interaction returns maxsc, which is the observed 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

maxsc

observed score test statistics for the interaction

Details

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

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

## 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)

## fit the interaction logistic AIM
a=logistic.interaction(x, trt, y, 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)