chooseMDoubleBootstrap: Choose the bootstrap sample size for stage 1 inference

Description

Choose the resample size for stage 1 bootstrap using double bootstrap. The form of m is: $ m = n^[1+Xi(1-pHat)/(1+Xi)]$, where the tuning parameter Xi is chosen via double bootstrap and pHat is the estimated non-regularity level computed by getModel. Example could be found under qLearn.

Usage

chooseMDoubleBootstrap(s2Formula,s1Formula,
completeData,s2Treat,interact,s2Indicator,alpha=0.05,
boot1Num=500,boot2Num=500,...)

Arguments

s2Formula

stage 2 regression formula

s1Formula

Stage 1 regression formula

completeData

data frame containing all the variables

s2Treat

character string: name of the stage 2 treatment variable

interact

character vector: names of variables that interact with s2Treat

s2Indicator

character string: names of the stage 2 treatment indicator variable

alpha

level of significance

boot1Num

numbers of bootstrap sampling for first order bootstrap

boot2Num

numbers of bootstrap sampling for second order bootstrap

...

other arguments of the lm function

Value

m: resample size for stage 1 bootstrap

References

Chakraborty, B., and Laber, E.B. (2012). Inference for Optimal Dynamic Treatment Regimes using an Adaptive m-out-of-n Bootstrap Scheme. Submitted.

Examples

Run this code

set.seed(100)
# Simple Simulation on 1000 subjects
sim<-matrix(0,nrow=1000,ncol=7)
colnames(sim)<-c("H1","A1","Y1","H2","A2","Y2","IS2")
sim<-as.data.frame(sim)

# Randomly generate stage 1 covariates and stage 1 and 2 treatments
sim[,c("H1","A1","A2")]<-2*rbinom(1000*3,1,0.5)-1

# Generate stage 2 covariates based on H1 and T1
expit<-exp(0.5*sim$H1+0.5*sim$A1)/(1+exp(0.5*sim$H1+0.5*sim$A1))
sim$H2<-2*rbinom(1000,1,expit)-1

# Assume stage 1 outcome Y1 is 0
# Generate stage 2 outcome Y2 
sim$Y2<-0.5*sim$A2+0.5*sim$A2*sim$A1-0.5*sim$A1+rnorm(1000)

# Randomly assign 500 subjects to S2
sim[sample(1000,500),"IS2"]<-1 
sim[sim$IS2==0,c("A2","Y2")]<-NA

# Define models for both stages
s2Formula<-Y2~H1*A1+A1*A2+A2:H2
s1Formula<-Y1~H1*A1

# Use boot1Num=boot2Num=20 in the example to save computational time
# In real case should use greater number 
m<-chooseMDoubleBootstrap(s2Formula,s1Formula,sim,s2Treat="A2",
interact=c("A1","H2"),s2Indicator="IS2",boot1Num=20,boot2Num=20)