chooseMDoubleBootstrap: Choose the bootstrap sample size for stage 1 inference

In qLearn: Estimation and inference for Q-learning

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

Author(s)

Jingyi Xin [e-mail], Bibhas Chakraborty [e-mail], and Eric B.Laber [e-mail]

References

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

See Also

qLearn

Examples

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) 

Example output

[1] 1
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coverage =  0.35 
[1] "here2"
[1] 0.05
[1] 851
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coverage =  0.7 
[1] "here2"
[1] 0.075
[1] 789
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coverage =  0.45 
[1] "here2"
[1] 0.1
[1] 735
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coverage =  0.85 
[1] "here2"
[1] 0.125
[1] 686
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coverage =  0.8 
[1] "here2"
[1] 0.15
[1] 642
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coverage =  0.85 
[1] "here2"
[1] 0.175
[1] 603

qLearn documentation built on May 2, 2019, 9:18 a.m.